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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Earth Sci.</journal-id>
<journal-title>Frontiers in Earth Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Earth Sci.</abbrev-journal-title>
<issn pub-type="epub">2296-6463</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1074729</article-id>
<article-id pub-id-type="doi">10.3389/feart.2022.1074729</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Earth Science</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Variations of the seismic <italic>b-value</italic> along the Dead Sea transform</article-title>
<alt-title alt-title-type="left-running-head">Sharon et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/feart.2022.1074729">10.3389/feart.2022.1074729</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Sharon</surname>
<given-names>Matty</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2062074/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Kurzon</surname>
<given-names>Ittai</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1997995/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Wetzler</surname>
<given-names>Nadav</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2136168/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Sagy</surname>
<given-names>Amir</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1158120/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Marco</surname>
<given-names>Shmuel</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/586128/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Ben-Avraham</surname>
<given-names>Zvi</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2096249/overview"/>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>Geological Survey of Israel</institution>, <addr-line>Jerusalem</addr-line>, <country>Israel</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Department of Geophysics</institution>, <institution>Tel Aviv University</institution>, <addr-line>Tel Aviv</addr-line>, <country>Israel</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>Institute of Earth Sciences</institution>, <institution>Hebrew University of Jerusalem</institution>, <addr-line>Jerusalem</addr-line>, <country>Israel</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/898414/overview">Guido Maria Adinolfi</ext-link>, University of Sannio, Italy</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1074425/overview">Matteo Taroni</ext-link>, Istituto Nazionale di Geofisica e Vulcanologia (INGV), Italy</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1170330/overview">Alessandro Vuan</ext-link>, Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (Italy), Italy</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Ittai Kurzon, <email>ittaik@gsi.gov.il</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Structural Geology and Tectonics, a section of the journal Frontiers in Earth Science</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>21</day>
<month>12</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="collection">
<year>2022</year>
</pub-date>
<volume>10</volume>
<elocation-id>1074729</elocation-id>
<history>
<date date-type="received">
<day>19</day>
<month>10</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>30</day>
<month>11</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2022 Sharon, Kurzon, Wetzler, Sagy, Marco and Ben-Avraham.</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Sharon, Kurzon, Wetzler, Sagy, Marco and Ben-Avraham</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>The frequency-magnitude distribution follows the Gutenberg-Richter empirical law, in which the scaling between small and large earthquakes is represented by the <italic>b-value</italic>. Laboratory experiments have shown that the <italic>b-value</italic> is related to fault mechanics with an inverse dependency to the differential stress, as was also inferred from observational datasets through relations with earthquake depth and style of faulting. In this study, we aim to obtain a better understanding of the geological structure and tectonics along the Dead Sea transform (DST), by examining relations of the <italic>b-value</italic> to three source parameters: the earthquake depth, the seismic moment release, and the predominant style of faulting. We analyse a regional earthquake catalogue of &#x223c;20,300 earthquakes that were recorded between 1983 and 2020 in a regional rectangle between latitudes 27.5&#xb0;N&#x2212;35.5&#xb0;N and longitudes 32&#xb0;E&#x2212;38&#xb0;E. We convert the duration magnitudes, Md, to moment magnitudes, Mw, applying a new regional empirical relation, by that achieving a consistent magnitude type for the entire catalogue. Exploring the variations in the <italic>b-value</italic> for several regions along and near the DST, we find that the <italic>b-value</italic> increases from 0.93 to 1.19 as the dominant style of faulting changes from almost pure strike-slip, along the DST, to normal faulting at the Galilee, northern Israel. Focusing on the DST, our temporal analysis shows an inverse correlation between the <italic>b-value</italic> and the seismic moment release, whereas the spatial variations are more complex, showing combined dependencies on seismogenic depth and seismic moment release. We also identify seismic gaps that might be related to locking or creeping of sections along the DST and should be considered for hazard assessment. Furthermore, we observe a northward decreasing trend of the <italic>b-value</italic> along the DST, which we associate to an increase of the differential stress due to structural variations, from more extensional deformation in the south to more compressional deformation in the north.</p>
</abstract>
<kwd-group>
<kwd>seismic moment release</kwd>
<kwd>seismogenic zones</kwd>
<kwd>seismic gap</kwd>
<kwd>spatial variation analysis</kwd>
<kwd>temporal variation</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="s1">
<title>1 Introduction</title>
<p>One of the most fundamental observations in earthquake seismology is that the frequency-magnitude relation follows the Gutenberg-Richter empirical law (<xref ref-type="bibr" rid="B60">Gutenberg and Richter, 1944</xref>):<disp-formula id="e1">
<mml:math id="m1">
<mml:mrow>
<mml:mi mathvariant="italic">log</mml:mi>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>a</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>b</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>where N is the cumulative number of earthquakes of at least a magnitude <italic>M</italic>; and <italic>a</italic> and <italic>b</italic> are seismicity parameters.</p>
<p>Whilst the <italic>a-value</italic> reflects the seismic activity level and unless normalised, varies in different time windows, the <italic>b-value</italic> reflects the proportion between small and large earthquakes, and thus has a significant impact for hazard evaluations (<xref ref-type="bibr" rid="B36">Frankel, 1995</xref>; <xref ref-type="bibr" rid="B106">Petersen et al., 2011</xref>; <xref ref-type="bibr" rid="B91">Marzocchi and Taroni, 2014</xref>; <xref ref-type="bibr" rid="B85">Magrin et al., 2017</xref>; <xref ref-type="bibr" rid="B146">Sokolov et al., 2017</xref>). Yet, some observations suggest that the frequency-magnitude relation (Eq. <xref ref-type="disp-formula" rid="e1">1</xref>) might deviate at the upper bound of the magnitude distribution, since some fault zones are characterised with repeated large earthquakes of approximately the same size (i.e., &#x201c;characteristic&#x201d; behaviour; <xref ref-type="bibr" rid="B158">Wesnousky et al., 1983</xref>; <xref ref-type="bibr" rid="B130">Schwartz and Coppersmith, 1984</xref>).</p>
<p>Although a <italic>b-value</italic> of a unity has been previously suggested on a global scale based on real-data analyses (<xref ref-type="bibr" rid="B38">Frohlich and Davis, 1993</xref>; <xref ref-type="bibr" rid="B35">Felzer et al., 2004</xref>; <xref ref-type="bibr" rid="B34">El-Isa and Eaton, 2014</xref>) and theoretical considerations (<xref ref-type="bibr" rid="B78">King, 1983</xref>), other studies have been aimed to understand its variations with regards to earthquake mechanics (e.g. <xref ref-type="bibr" rid="B126">Scholz, 1968</xref>, <xref ref-type="bibr" rid="B125">2015</xref>; <xref ref-type="bibr" rid="B86">Main et al., 1989</xref>; <xref ref-type="bibr" rid="B66">Henderson and Main, 1992</xref>; <xref ref-type="bibr" rid="B82">Lei et al., 2000</xref>; <xref ref-type="bibr" rid="B150">Tan et al., 2019</xref>). It has been previously demonstrated that the <italic>b-value</italic> varies with the style of faulting, with typical values of 0.7&#x2013;0.8, 0.9&#x2013;1.0, and 1.1&#x2013;1.2 for thrust, strike-slip and normal faulting, respectively, with values in-between for oblique faulting (<xref ref-type="bibr" rid="B129">Schorlemmer et al., 2005</xref>; <xref ref-type="bibr" rid="B108">Petruccelli et al., 2019a</xref>). This dependency has been shown by other studies as well (<xref ref-type="bibr" rid="B59">Gulia and Wiemer, 2010</xref>; <xref ref-type="bibr" rid="B125">Scholz, 2015</xref>; <xref ref-type="bibr" rid="B22">Bora et al., 2018</xref>; <xref ref-type="bibr" rid="B17">Beall et al., 2022</xref>), suggesting an inverse correlation of the <italic>b-value</italic> with the differential stress, considering the Anderson theory of faulting (<xref ref-type="bibr" rid="B9">Anderson, 1905</xref>). The inverse dependency of the <italic>b-value</italic> with the differential stress has been also shown through rock fracture experiments (<xref ref-type="bibr" rid="B126">Scholz, 1968</xref>; <xref ref-type="bibr" rid="B8">Amitrano, 2003</xref>; <xref ref-type="bibr" rid="B118">Rivi&#xe8;re et al., 2018</xref>), and dependency with the earthquake depth considering rheological models (<xref ref-type="bibr" rid="B94">Mori and Abercrombie, 1997</xref>; <xref ref-type="bibr" rid="B46">Gerstenberger et al., 2001</xref>; <xref ref-type="bibr" rid="B147">Spada et al., 2013</xref>; <xref ref-type="bibr" rid="B125">Scholz, 2015</xref>; <xref ref-type="bibr" rid="B116">Rigo et al., 2018</xref>). In such cases, the <italic>b-value</italic> has been observed to decrease with depth, within the brittle part of the earth&#x2019;s crust.</p>
<p>Previous estimations of the frequency-magnitude relation in the region of Israel (<xref ref-type="bibr" rid="B20">Ben-Menahem, 1981</xref>, <xref ref-type="bibr" rid="B19">1991</xref>; <xref ref-type="bibr" rid="B124">Salamon et al., 1996</xref>; <xref ref-type="bibr" rid="B138">Shapira and Hofstetter, 2002</xref>; <xref ref-type="bibr" rid="B61">Hamiel et al., 2009</xref>) were mainly focused on hazard perspective, and had limited data for investigating variations of the <italic>b-value</italic>. In this study we systematically calculate the <italic>b-value</italic>, focusing on &#x223c;500-km of the southern part of the Dead Sea transform (DST), a &#x223c;1,000-km long continental transform plate boundary that links between the Red Sea spreading centre and the convergence zone in southern Turkey (e.g., <xref ref-type="bibr" rid="B40">Garfunkel, 2014</xref>). Our purpose is to investigate variations of the <italic>b-value</italic> and their relation to the earthquake depth, the style of faulting, and the seismic moment release; hence examining whether and to what extent does the <italic>b-value</italic> relate to mechanical properties of the fault zone. We examine spatial variations of the <italic>b-value</italic> with the seismogenic depth, which we estimate according to the 75th and 95th percentiles of the seismicity depth distribution, because they reflect the alteration in the seismogenic depth along the DST (e.g., <xref ref-type="bibr" rid="B133">Shalev et al., 2013</xref>; <xref ref-type="bibr" rid="B159">Wetzler and Kurzon, 2016</xref>). Possible correlations with the seismic moment release are examined in both space (e.g., <xref ref-type="bibr" rid="B22">Bora et al., 2018</xref>) and time (e.g. <xref ref-type="bibr" rid="B28">Cao and Gao, 2002</xref>) analyses, for receiving insights about the seismicity of the region and for further understanding variations of the <italic>b-value</italic>.</p>
<p>Determination of the <italic>b-value</italic> is often limited within spatial zones, based on seismological or tectonic considerations, which in many cases reflect the dominant style of faulting (e.g. <xref ref-type="bibr" rid="B112">Radulian et al., 2000</xref>, <xref ref-type="bibr" rid="B111">2018</xref>; <xref ref-type="bibr" rid="B14">Bala et al., 2003</xref>; <xref ref-type="bibr" rid="B24">Bus et al., 2009</xref>) and may also be implemented for hazard evaluation purposes (<xref ref-type="bibr" rid="B36">Frankel, 1995</xref>; <xref ref-type="bibr" rid="B65">Helmstetter et al., 2006</xref>; <xref ref-type="bibr" rid="B170">Yadav et al., 2012</xref>; <xref ref-type="bibr" rid="B10">Ashish et al., 2016</xref>; <xref ref-type="bibr" rid="B87">Maiti and Kamai, 2020</xref>; <xref ref-type="bibr" rid="B88">Mandal et al., 2021</xref>; <xref ref-type="bibr" rid="B172">Yagoda-Biran et al., 2021</xref>). A preliminary seismogneic zonation in the region (<xref ref-type="bibr" rid="B135">Shamir et al., 2001</xref>) and its following analysis of the frequency-magnitude relation (<xref ref-type="bibr" rid="B138">Shapira and Hofstetter, 2002</xref>) were based on a rather sparse seismological dataset. A more recent seismogenic zonation (<xref ref-type="bibr" rid="B139">Sharon, 2020</xref>) was based on the density distribution of epicentres and seismic moment release, and their spatial relation to the main seismic sources (<xref ref-type="bibr" rid="B141">Sharon et al., 2020</xref>). However, this zonation is not adequate to show systematic relation between the <italic>b-value</italic> and the faulting style because many of these previous zones are too small to achieve well-determined <italic>b-value</italic> with our current data. For this purpose, we introduce here a rather simplified and broad new tectonic zonation in the DST and its periphery, according to the seismic network capability and the local tectonics.</p>
<p>In this study we first relocate the earthquakes recorded between January 1983 and September 2020 (<xref ref-type="bibr" rid="B159">Wetzler and Kurzon, 2016</xref>). Then, due to inconsistent magnitude type within the original catalogue, we generated a catalogue, choosing M<sub>w</sub> as the preferred homogenous magnitude type, since it is physical-based and is not saturated at high magnitudes (<xref ref-type="bibr" rid="B76">Kanamori, 1977</xref>; <xref ref-type="bibr" rid="B64">Hanks and Kanamori, 1979</xref>). Subsequently, we estimate the completeness magnitude, <inline-formula id="inf1">
<mml:math id="m2">
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and calculate the frequency-magnitude parameters with respect to the seismogenic depth, the seismic moment release and the tectonic regime associated with the prevailing style of faulting. Specifically, we perform a systematic and thorough spatio-temporal investigation of the <italic>b-value</italic> at the DST and its periphery.</p>
</sec>
<sec id="s2">
<title>2 Tectonic settings</title>
<p>The DST was formed during the Miocene, as the African-Arabian plate broke, generating the Suez rift and the DST. While the Suez rift has shown minor signs of post-Miocene deformation, the DST is considered to be the main source of post-Miocene deformation in the region (<xref ref-type="bibr" rid="B42">Garfunkel and Bartov, 1977</xref>; <xref ref-type="bibr" rid="B73">Joffe and Garfunkel, 1987</xref>; <xref ref-type="bibr" rid="B148">Steckler et al., 1988</xref>). It consists of a &#x223c;1000-km long &#x223c;N-S orientated fault system, which is the largest in the Levant (<xref ref-type="fig" rid="F1">Figure 1</xref>). Evaluation from geologic and geodetic sources indicate Quaternary slip rates of 4&#x2013;5&#xa0;mm/yr (<xref ref-type="bibr" rid="B41">Garfunkel, 2010</xref>; <xref ref-type="bibr" rid="B123">Sadeh et al., 2012</xref>; <xref ref-type="bibr" rid="B90">Marco and Klinger, 2014</xref>; <xref ref-type="bibr" rid="B62">Hamiel et al., 2018</xref>). Our study focuses on the southern section of the DST (<xref ref-type="fig" rid="F1">Figure 1</xref>), dominated by a left-lateral strike-slip overall displacement of &#x223c;105-km accumulated over the past &#x223c;16&#x2013;20 million years (<xref ref-type="bibr" rid="B110">Quennell, 1959</xref>; <xref ref-type="bibr" rid="B39">Garfunkel, 1981</xref>, <xref ref-type="bibr" rid="B40">2014</xref>; <xref ref-type="bibr" rid="B101">Nuriel et al., 2017</xref>).</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Seismic map of the study area showing the main fault segments of the Dead Sea transform (DST) and of the northwest orientated Carmel-Tirza fault system (CTF) system (<xref ref-type="bibr" rid="B141">Sharon et al., 2020</xref>); recorded seismicity of 1983&#x2013;2020 (expansion of <xref ref-type="bibr" rid="B159">Wetzler and Kurzon 2016</xref> catalogue), highlighting the most significant events in the past century: the 1927 M six at the northern Dead Sea, and the M<sub>W</sub> 7.2 at the Gulf of Elat (Aqaba). Black arrows denote the relative plate motion along the DST.</p>
</caption>
<graphic xlink:href="feart-10-1074729-g001.tif"/>
</fig>
<p>The lateral motion on the DST occurs on left-stepping strike-slip and oblique-slip fault segments that delimit a string of en-echelon arranged pull-apart basins (<xref ref-type="bibr" rid="B39">Garfunkel, 1981</xref>; <xref ref-type="bibr" rid="B173">Zak and Freund, 1981</xref>; <xref ref-type="bibr" rid="B43">Garfunkel and Ben-Avraham, 2001</xref>). The DST is topographically expressed by a pronounced 5&#x2013;25&#xa0;km wide valley, bordered by normal faults that extend along the valley margins. The north-eastern edge of the study area comprises the Lebanon restraining bend (LRB; <xref ref-type="fig" rid="F1">Figure 1</xref>), where the DST is branched into several segments, transferring the strike-slip motion into the Lebanon area (<xref ref-type="bibr" rid="B56">Gomez et al., 2003</xref>, <xref ref-type="bibr" rid="B55">2007</xref>). The northern section of the DST crosses northwest Syria in a N-S orientation, most of it outside our study area.</p>
<p>South of Lebanon, the Sinai sub-plate has several fault systems, associated with Quaternary internal-deformation: the Carmel-Tirza fault zone (CTF; <xref ref-type="fig" rid="F1">Figure 1</xref>) divides the Israel-Sinai sub-plate into two tectonic domains (<xref ref-type="bibr" rid="B97">Neev et al., 1976</xref>; <xref ref-type="bibr" rid="B18">Ben-Avraham and Ginzburg, 1990</xref>; <xref ref-type="bibr" rid="B123">Sadeh et al., 2012</xref>) where the southern part is more rigid, while the northern consists of a set of graben-and-horst structures with E-W-striking normal faults associated with S-N extension (<xref ref-type="bibr" rid="B119">Ron and Eyal, 1985</xref>). The CTF consists of SE-NW orientated fault segments, with normal and oblique motions (<xref ref-type="bibr" rid="B37">Freund, 1970</xref>). It is associated with coeval motion of &#x223c;0.7&#xa0;mm/yr left-lateral slip and &#x223c;0.6&#xa0;mm/yr extension rates (<xref ref-type="bibr" rid="B123">Sadeh et al., 2012</xref>), with recent seismicity in its eastern side that sprawl over several parallel fault segments (<xref ref-type="bibr" rid="B68">Hofstetter et al., 1996</xref>; <xref ref-type="bibr" rid="B141">Sharon et al., 2020</xref>).</p>
<p>To the south of the CTF, several &#x223c;E-W striking faults are associated with mainly dextral slip and some normal faulting (<xref ref-type="bibr" rid="B21">Bentor and Vroman, 1954</xref>; <xref ref-type="bibr" rid="B15">Bartov, 1974</xref>; <xref ref-type="bibr" rid="B175">Zilberman et al., 1996</xref>), which occurred mainly during the Neogene or in earlier periods (<xref ref-type="bibr" rid="B157">Weinberger et al., 2020</xref>). An additional fault system of &#x223c;NNE striking faults in southern Israel is associated with normal faulting and minor extension component along the transform system, and was more active during Quaternary times (<xref ref-type="bibr" rid="B16">Bartov et al., 1998</xref>; <xref ref-type="bibr" rid="B12">Avni et al., 2000</xref>, <xref ref-type="bibr" rid="B13">2001</xref>; <xref ref-type="bibr" rid="B27">Calvo and Bartov, 2001</xref>; <xref ref-type="bibr" rid="B89">Marco, 2007</xref>).</p>
<p>The potential for strong earthquakes along the DST is demonstrated by the earthquakes of the 1927&#xa0;M<sub>L</sub> 6.2 near Jericho, north of the Dead Sea (<xref ref-type="bibr" rid="B137">Shapira et al., 1993</xref>), and the 1995 M<sub>W</sub> 7.2 Nuweiba (<xref ref-type="bibr" rid="B67">Hofstetter et al., 2003</xref>) in the Gulf of Elat (Aqaba), along with pre-instrumental records, leading to estimations of up to M<sub>W</sub> &#x223c;7.5 (<xref ref-type="bibr" rid="B7">Ambraseys, 2009</xref>; <xref ref-type="bibr" rid="B2">Agnon, 2014</xref>; <xref ref-type="bibr" rid="B90">Marco and Klinger, 2014</xref>; <xref ref-type="bibr" rid="B177">Zohar et al., 2016</xref>, <xref ref-type="bibr" rid="B176">2017</xref>; <xref ref-type="bibr" rid="B84">Lu et al., 2020</xref>). Deep-crust seismicity, correlated with low heat flow areas, particularly in the Dead Sea basin, probably indicates a cold crust, with deep brittle to ductile transition zone (<xref ref-type="bibr" rid="B5">Aldersons et al., 2003</xref>; <xref ref-type="bibr" rid="B134">Shalev et al., 2007</xref>, <xref ref-type="bibr" rid="B133">2013</xref>; <xref ref-type="bibr" rid="B6">Aldersons and Ben-Avraham, 2014</xref>; <xref ref-type="bibr" rid="B159">Wetzler and Kurzon, 2016</xref>).</p>
</sec>
<sec id="s3">
<title>3 Seismological dataset</title>
<p>We analyse an earthquake catalogue from 1 January 1983 until 28 September 2020, recorded by &#x223c;210 stations. The majority of the data originates in the stations of the Israel Seismic Network (ISN), including many new stations deployed under the framework of the TRUAA network, established for the purpose of Earthquake Early Warning System for the state of Israel (<xref ref-type="bibr" rid="B80">Kurzon et al., 2020</xref>). In addition, some of the data comes from local CTBT and CNF stations (Comprehensive Nuclear Test-Ban Treaty, and Cooperating National Facility, respectively), and a minority originates in stations of other networks: the GEOFON global network of GFZ, the JSO seismic observatory of Jordan and the CQ seismic network of Cyprus.</p>
<p>In the original catalogue, documented by the ISN, there are 23,316 earthquakes between the latitudes <inline-formula id="inf2">
<mml:math id="m3">
<mml:mrow>
<mml:mrow>
<mml:mn>27.5</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mrow>
<mml:mn>35.5</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and longitudes <inline-formula id="inf3">
<mml:math id="m4">
<mml:mrow>
<mml:mrow>
<mml:mn>32</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mrow>
<mml:mn>38</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
<mml:mi>E</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, referred here as the Rectangular Area (RA; <xref ref-type="fig" rid="F1">Figure 1</xref>). Following <xref ref-type="bibr" rid="B159">Wetzler and Kurzon (2016)</xref>, we applied similar procedure and methods for earthquake relocation: applying the regional velocity model of <xref ref-type="bibr" rid="B50">Gitterman et al. (2005)</xref>, earthquakes are located by the genloc library (<xref ref-type="bibr" rid="B105">Pavlis et al., 2004</xref>) of the Antelope seismic software package (&#x3c;<ext-link ext-link-type="uri" xlink:href="http://www.brtt.com/">www.brtt.com</ext-link>&#x3e;). Horizontal median errors are 420&#xa0;m in longitude, 510&#xa0;m in latitude, and the vertical median error is 750&#xa0;m, calculated according to <xref ref-type="bibr" rid="B104">Pavlis (1986)</xref>. The relocated catalogue has &#x223c;23,200 events (<xref ref-type="fig" rid="F1">Figure 1</xref>), with improved locations, and loosing less than 0.5% of the events due to large location errors. The magnitude range of the catalogue is <inline-formula id="inf4">
<mml:math id="m5">
<mml:mrow>
<mml:mn>0.1</mml:mn>
<mml:mo>&#x2264;</mml:mo>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>7.2</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, from which &#x223c;2,900 are with unknown magnitudes (<xref ref-type="table" rid="T1">Table 1</xref>).</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>The number of <inline-formula id="inf5">
<mml:math id="m6">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf6">
<mml:math id="m7">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi>w</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> magnitudes, determined for the investigated catalogue. The right-most field is for events that contain no magnitude.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left"/>
<th align="left">
<inline-formula id="inf7">
<mml:math id="m8">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold">M</mml:mi>
<mml:mi mathvariant="bold-italic">d</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="left">
<inline-formula id="inf8">
<mml:math id="m9">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold">M</mml:mi>
<mml:mi mathvariant="bold">w</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="left">
<inline-formula id="inf9">
<mml:math id="m10">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold">M</mml:mi>
<mml:mi mathvariant="bold-italic">d</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mtext>&#xa0;</mml:mtext>
<mml:msub>
<mml:mi mathvariant="bold">M</mml:mi>
<mml:mi mathvariant="bold-italic">w</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="left">
<bold>None</bold>
</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">RA</td>
<td align="left">16,546</td>
<td align="left">5,537</td>
<td align="left">1,756</td>
<td align="left">2,895</td>
</tr>
<tr>
<td align="left">NCA</td>
<td align="left">3,965</td>
<td align="left">2,895</td>
<td align="left">810</td>
<td align="left">938</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The catalogue includes two magnitude types: duration magnitude (M<sub>d</sub>) and the moment magnitude (M<sub>w</sub>). <xref ref-type="table" rid="T1">Table 1</xref> summarises the two types of magnitude that were determined for the relocated catalogue. The magnitudes of the M<sub>w</sub> 7.2 1995 Nuweiba earthquake and the M<sub>w</sub> 5.1 2004 Dead Sea earthquake were fixed according to <xref ref-type="bibr" rid="B67">Hofstetter et al. (2003)</xref> and <xref ref-type="bibr" rid="B69">Hofstetter et al. (2008)</xref>, respectively.</p>
<p>The detection sensitivity of the seismic network is primarily dependent on the background noise and the distribution of seismic stations. The seismic network coverage area (NCA; <xref ref-type="fig" rid="F2">Figure 2</xref>) was recently determined by <xref ref-type="bibr" rid="B141">Sharon et al. (2020)</xref> according to the total threshold number of wave arrivals at seismic stations, accounting for their spatial distribution, hence, including hypocentres that are relatively well-constrained, with relatively low magnitude of completeness (<inline-formula id="inf10">
<mml:math id="m11">
<mml:mrow>
<mml:mfenced open="" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
</inline-formula>. Therefore, determination of the frequency-magnitude parameters within the NCA can be based on more data, consisting of a larger range of magnitudes.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Seismic stations utilised for recording the earthquakes of the examined catalogue, and the ensuing seismic network coverage area (NCA) delimited by the green polygon.</p>
</caption>
<graphic xlink:href="feart-10-1074729-g002.tif"/>
</fig>
</sec>
<sec id="s4">
<title>4 The frequency-magnitude relation</title>
<sec id="s4-1">
<title>4.1 Magnitude conversion</title>
<p>Earthquake magnitude can be estimated by a wide range of methods and parameters, depending on the spectral properties of the source, the seismic phases, the instrumentation capabilities, and the consideration of path and site effects. Therefore, magnitude estimation does not behave uniformly for all magnitude ranges, and also saturates at different levels (<xref ref-type="bibr" rid="B76">Kanamori, 1977</xref>, <xref ref-type="bibr" rid="B75">1983</xref>; <xref ref-type="bibr" rid="B154">Utsu, 2002</xref>). Thus, magnitude conversion to a single type of magnitude is vital for seismological analyses that require homogenous earthquake catalogue with consistent magnitude type, such as analysis of the frequency-magnitude relation.</p>
<p>The moment magnitude (M<sub>w</sub>) is based on the physical dimensions of the seismic source, does not saturate at extreme rupture size, and hence is more adequate to represent a wide range of magnitudes (<xref ref-type="bibr" rid="B76">Kanamori, 1977</xref>; <xref ref-type="bibr" rid="B64">Hanks and Kanamori, 1979</xref>; <xref ref-type="bibr" rid="B31">Choy and Boatwright, 1995</xref>). Therefore, a common practice is converting other magnitude types to M<sub>w</sub> (<xref ref-type="bibr" rid="B132">Scordilis, 2006</xref>; <xref ref-type="bibr" rid="B171">Yadav et al., 2009</xref>, <xref ref-type="bibr" rid="B170">2012</xref>; <xref ref-type="bibr" rid="B121">Ross et al., 2016</xref>; <xref ref-type="bibr" rid="B79">Kumar et al., 2020</xref>), which is widely used as a unified magnitude for seismological and hazard-related applications (e.g. <xref ref-type="bibr" rid="B23">Bormann and Di Giacomo, 2011</xref>). In the original Israel catalogue, about 70% of the events are assigned only with M<sub>d</sub>, without M<sub>w</sub>, and less than 10% are estimated by both magnitude types. Therefore, by converting M<sub>d</sub> to M<sub>w</sub>, we intent to achieve a catalogue of a uniform magnitude type, M<sub>w</sub>, that can be the basis for the current seismological analysis, as well as for future investigations.</p>
<p>Considering that many of the magnitude types are determined by a set of parameters, varying according to geological, seismological and instrumentational settings, there is no global formula that converts between <inline-formula id="inf11">
<mml:math id="m12">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf12">
<mml:math id="m13">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi>w</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>; hence, unique formulas are deduced for different regions. A few regression techniques have been suggested and employed for converting magnitudes, and the justification for applying a single method or the other, are based either on theory or empirical observations (e.g. <xref ref-type="bibr" rid="B170">Yadav et al., 2012</xref>; <xref ref-type="bibr" rid="B74">Kadirio&#x11f;lu and Kartal, 2016</xref>; <xref ref-type="bibr" rid="B33">Das et al., 2018</xref>). In this study we examine M<sub>d</sub> to M<sub>w</sub> conversion, applying both, ordinary least squares (OLS) regressions, (e.g. <xref ref-type="bibr" rid="B132">Scordilis, 2006</xref>; <xref ref-type="bibr" rid="B30">Castello et al., 2007</xref>; <xref ref-type="bibr" rid="B11">Ataeva et al., 2015</xref>; <xref ref-type="bibr" rid="B121">Ross et al., 2016</xref>), and orthogonal regression (OR; e.g., <xref ref-type="bibr" rid="B51">Glaister, 2005</xref>; <xref ref-type="bibr" rid="B29">Castellaro et al., 2006</xref>; <xref ref-type="bibr" rid="B77">Kane and Mroch, 2020</xref>).</p>
<p>Although it is more common to convert magnitudes through linear regressions, <xref ref-type="bibr" rid="B11">Ataeva et al. (2015)</xref> added a quadratic regression and obtained better fit to observations in the same region. We examine their approach for M<sub>d</sub> to M<sub>w</sub> conversion, fitting both linear and quadratic regressions. For comparison, we also examine part of their obtained regressions on the much larger data utilised here.</p>
<p>The regression coefficients published by <xref ref-type="bibr" rid="B11">Ataeva et al. (2015)</xref> were deduced in the forms of:<disp-formula id="e2">
<mml:math id="m14">
<mml:mrow>
<mml:mi>log</mml:mi>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>a</mml:mi>
<mml:mo>&#x2217;</mml:mo>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>b</mml:mi>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>and<disp-formula id="e3">
<mml:math id="m15">
<mml:mrow>
<mml:mi>log</mml:mi>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>a</mml:mi>
<mml:mo>&#x2217;</mml:mo>
<mml:msubsup>
<mml:mi>M</mml:mi>
<mml:mi>d</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>b</mml:mi>
<mml:mo>&#x2217;</mml:mo>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>c</mml:mi>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>for the linear and quadratic regressions, respectively. We convert <italic>M</italic>
<sub>0</sub> to <italic>M</italic>
<sub>
<italic>w</italic>
</sub> following the relationship (<xref ref-type="bibr" rid="B64">Hanks and Kanamori, 1979</xref>; <xref ref-type="bibr" rid="B4">Aki and Richards, 2002</xref>):<disp-formula id="e4">
<mml:math id="m16">
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>w</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mi>log</mml:mi>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>9.1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>referring to <inline-formula id="inf13">
<mml:math id="m17">
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> units of N-m (e.g. <xref ref-type="bibr" rid="B142">Shearer, 2009</xref>).</p>
<p>In this manner we achieve the standard coefficient correlations summarised in <xref ref-type="table" rid="T2">Table 2</xref> along with our current results. Examining the performance of the linear and quadratic fits using <xref ref-type="bibr" rid="B11">Ataeva et al. (2015)</xref> regression parameters, in comparison to the fits obtained in the current study, we note a clear improvement in the goodness of fit, observed by the lower values of the Root Mean Square error (RMSE) of the current study (<xref ref-type="table" rid="T2">Table 2</xref>). This result is not surprising, as <xref ref-type="bibr" rid="B11">Ataeva et al. (2015)</xref> results are based only on &#x223c;100 earthquakes, compared with &#x223c;1,800 earthquakes for the current results (<xref ref-type="table" rid="T1">Table 1</xref>).</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Coefficient correlation parameters (a, b, c) that correspond to linear and quadratic regressions of the forms <inline-formula id="inf14">
<mml:math id="m18">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi mathvariant="normal">w</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mo>&#x2a;</mml:mo>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">d</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi mathvariant="normal">b</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf15">
<mml:math id="m19">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi mathvariant="normal">w</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msubsup>
<mml:mrow>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mo>&#x2a;</mml:mo>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">d</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="normal">b</mml:mi>
<mml:mo>&#x2a;</mml:mo>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">d</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi mathvariant="normal">c</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, respectively; RMSE and AICc of these regressions are in respect to earthquakes located within RA; a) The regression coefficients of <xref ref-type="bibr" rid="B11">Ataeva et al. (2015)</xref> are from S-wave analysis and the magnitude range of <inline-formula id="inf16">
<mml:math id="m20">
<mml:mrow>
<mml:mn>2.7</mml:mn>
<mml:mo>&#x2264;</mml:mo>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>5.6</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, and were achieved through Eqs <xref ref-type="disp-formula" rid="e1">1</xref>&#x2013;<xref ref-type="disp-formula" rid="e3">3</xref> (see Methods section); b) Comparison between orthogonal regression and quadratic OLS regresion.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th colspan="6" align="left">a</th>
</tr>
<tr>
<th align="center">Regression type and data source</th>
<th align="center">a</th>
<th align="center">b</th>
<th align="center">c</th>
<th align="center">RMSE</th>
<th align="center">AICc</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Linear (<xref ref-type="bibr" rid="B11">Ataeva et al., 2015</xref>)</td>
<td align="center">0.90</td>
<td align="center">0.11</td>
<td align="center">-</td>
<td align="center">0.287</td>
<td align="center">-</td>
</tr>
<tr>
<td align="center">Quadratic (<xref ref-type="bibr" rid="B11">Ataeva et al., 2015</xref>)</td>
<td align="center">0.13</td>
<td align="center">&#x2212;0.13</td>
<td align="center">2.11</td>
<td align="center">0.400</td>
<td align="center">-</td>
</tr>
<tr>
<td align="center">Linear (RA)</td>
<td align="center">0.81</td>
<td align="center">0.52</td>
<td align="center">-</td>
<td align="center">0.170</td>
<td align="center">&#x2212;4.46e &#x2b; 03</td>
</tr>
<tr>
<td align="center">Quadratic (RA)</td>
<td align="center">0.03</td>
<td align="center">0.65</td>
<td align="center">0.69</td>
<td align="center">0.167</td>
<td align="center">&#x2212;4.52e &#x2b; 03</td>
</tr>
</tbody>
</table>
<table>
<thead valign="top">
<tr>
<th colspan="6" align="left">b</th>
</tr>
<tr>
<th align="center">Regression type</th>
<th align="center">a</th>
<th align="center">b</th>
<th align="center">c</th>
<th align="center">RMSE</th>
<th align="center">AICc</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Linear Orthogonal (RA)</td>
<td align="center">0.77</td>
<td align="center">0.64</td>
<td align="center">-</td>
<td align="center">0.139</td>
<td align="center">&#x2212;6.71e &#x2b; 03</td>
</tr>
<tr>
<td align="center">Quadratic (RA)</td>
<td align="center">0.03</td>
<td align="center">0.65</td>
<td align="center">0.69</td>
<td align="center">0.132</td>
<td align="center">&#x2212;6.90e &#x2b; 03</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>In <xref ref-type="fig" rid="F3">Figure 3</xref>, we compare between two OLS regressions, linear and quadratic, finding a relatively lower RMSE values obtained by the OLS quadratic fit (<xref ref-type="fig" rid="F3">Figure 3C</xref>) compared with the linear OLS fit (<xref ref-type="fig" rid="F3">Figure 3A</xref>). The parameters retain stable residuals around zero throughout the entire magnitude range for both regression types (<xref ref-type="fig" rid="F3">Figure 3B, D</xref>). However, both the lowest and highest magnitude ranges suggest that the quadratic fit (<xref ref-type="fig" rid="F3">Figure 3D</xref>) shows more constrained convergence around the line y&#x3d;0 in comparison to some bias in the linear fit (<xref ref-type="fig" rid="F3">Figure 3B</xref>). In addition, the total RMSE of the quadratic fit is slightly smaller (<xref ref-type="table" rid="T2">Table 2</xref>), and also the AICc method (<xref ref-type="bibr" rid="B71">Hurvich and Tsai, 1989</xref>), based on the Akaike Information Criteria (<xref ref-type="bibr" rid="B179">Akaike, 1974</xref>), shows lower values for the quadratic fit (<xref ref-type="table" rid="T2">Table 2</xref>). We also examined a linear orthogonal regression (OR), comparing it to the quadratic OLS fit. The quadratic OLS has better fit, reflected in its lower RMSE and AICc values (<xref ref-type="table" rid="T2">Table 2</xref>).</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Linear and Quadratic fits of the current study, within the RA. Black lines in <bold>(A,C)</bold> are linear and quadratic fits, respectively, within RA, superimposed on the associated earthquake data. Dashed yellow lines represent 1:1 ratio. Residuals from these fits are scattered for the linear <bold>(B)</bold> and quadratic <bold>(D)</bold> fits; where the black line is the linear fit of these residuals, dashed yellow line represents 1:1 ratio; Green and Red lines show the detailed RMSE in intervals of 25 events in an ascending order of magnitudes, and in intervals of a single magnitude, respectively, calculated separately for the negative and positive residuals.</p>
</caption>
<graphic xlink:href="feart-10-1074729-g003.tif"/>
</fig>
<p>The stability of the regressions and corresponding residuals with detailed RMSE were also tested for earthquakes within NCA (<xref ref-type="sec" rid="s13">Supplementary Figure S1</xref>), showing similar results (<xref ref-type="table" rid="T2">Table 2</xref>; <xref ref-type="sec" rid="s13">Supplementary Table S1</xref>). For a more robust conversion that is based on a larger number of earthquakes, we choose to use the parameters obtained by the entire research area (RA); hence, our M<sub>d</sub> to M<sub>w</sub> conversion formula (<xref ref-type="table" rid="T2">Table 2</xref>) is:<disp-formula id="e5">
<mml:math id="m21">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi mathvariant="normal">w</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.03</mml:mn>
<mml:msubsup>
<mml:mrow>
<mml:mo>&#x2217;</mml:mo>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">d</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>0.65</mml:mn>
<mml:msub>
<mml:mrow>
<mml:mo>&#x2217;</mml:mo>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">d</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>0.69</mml:mn>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>
</p>
</sec>
<sec id="s4-2">
<title>4.2 The magnitude of completeness and the <italic>b-value</italic>
</title>
<p>The magnitude of completeness (M<sub>c</sub>) is the minimum magnitude of which the seismic network detects all the events. Therefore, it marks the point from which the frequency-magnitude distribution is linear. We apply a few algorithms, by <xref ref-type="bibr" rid="B53">Goebel et al. (2017)</xref>, following <xref ref-type="bibr" rid="B3">Aki (1965)</xref> and <xref ref-type="bibr" rid="B32">Clauset et al. (2009)</xref>, based on Kolmogorov-Smirnov test, and by <xref ref-type="bibr" rid="B93">Mizrahi et al. (2021)</xref>, is also based on <xref ref-type="bibr" rid="B32">Clauset et al. (2009)</xref>, deducing M<sub>c</sub> with high statistical robustness. Both algorithms suggest a completeness magnitude of 2.1 for the NCA. Similarly, in a previous work (<xref ref-type="bibr" rid="B139">Sharon, 2020</xref>), M<sub>c</sub> was estimated as 2.0 for the NCA, for the years 1983&#x2013;2017. This is in consent with prior estimations of <xref ref-type="bibr" rid="B136">Shapira (1992)</xref>, obtaining M<sub>c</sub> &#x3d; 2.0 for a region, approximately overlapping the NCA, between the years 1984&#x2013;1991. The predominant (or even the only) magnitude type in the analyses of <xref ref-type="bibr" rid="B139">Sharon (2020)</xref> and <xref ref-type="bibr" rid="B136">Shapira (1992)</xref> was M<sub>d</sub>. Our conversion formulation (Eq. <xref ref-type="disp-formula" rid="e5">5</xref>) indicates that M<sub>d</sub>&#x3d;2.0 is approximately equivalent to M<sub>w</sub> of 2.1. Thus, we conclude that the magnitude of completeness for our homogenised catalogue is 2.1. As the NCA dataset is the one used later for more detailed analysis, by plotting the moment magnitude as a function of the sequential number of events (e.g., <xref ref-type="bibr" rid="B174">Zhuang et al., 2017</xref>; <xref ref-type="bibr" rid="B25">Bustos et al., 2022</xref>), we demonstrate that there are no clear short-term periods of magnitude incompleteness, within the NCA dataset (<xref ref-type="fig" rid="F4">Figure 4</xref>).</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Moment magnitudes arranged by the sequential number of events. Mw is set to the obtained magnitude of completeness, Mc&#x3d;2.1, demonstrating that there is no clear short-term magnitude incompleteness in the data used for the following analysis, within the network coverage area (NCA).</p>
</caption>
<graphic xlink:href="feart-10-1074729-g004.tif"/>
</fig>
<p>In general, higher M<sub>c</sub> is expected for remote seismicity for which the seismic sensitivity decreases. This is demonstrated for earthquakes recorded in the entire research area (RA), where both algorithms of <xref ref-type="bibr" rid="B53">Goebel et al. (2017)</xref> and <xref ref-type="bibr" rid="B93">Mizrahi et al. (2021)</xref> suggest that M<sub>c</sub> &#x3d; 3.8.</p>
<p>We calculate the <italic>b-value</italic> through the Maximum Likelihood Estimation by the following equation (<xref ref-type="bibr" rid="B182">Marzocchi and Sandri, 2003</xref>; following <xref ref-type="bibr" rid="B181">Fisher, 1950</xref>; <xref ref-type="bibr" rid="B185">Utsu, 1966</xref>; and <xref ref-type="bibr" rid="B180">Bender, 1983</xref>):<disp-formula id="e6">
<mml:math id="m22">
<mml:mrow>
<mml:mi>b</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mi>ln</mml:mi>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mover accent="true">
<mml:mi>M</mml:mi>
<mml:mo>&#xaf;</mml:mo>
</mml:mover>
<mml:mo>&#x2212;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>M</mml:mi>
<mml:mo>/</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(6)</label>
</disp-formula>where <inline-formula id="inf17">
<mml:math id="m23">
<mml:mrow>
<mml:mover accent="true">
<mml:mi>M</mml:mi>
<mml:mo>&#xaf;</mml:mo>
</mml:mover>
</mml:mrow>
</mml:math>
</inline-formula> is the sampling average of the magnitudes, M<sub>c</sub> is the completeness magnitude, and <inline-formula id="inf18">
<mml:math id="m24">
<mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:mi>M</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the magnitude bin interval in which the data is examined. The standard error of the <italic>b-value</italic> is obtained from the following formula (<xref ref-type="bibr" rid="B143">Shi and Bolt, 1982</xref>):<disp-formula id="e7">
<mml:math id="m25">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>b</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>2.30</mml:mn>
<mml:msup>
<mml:mi>b</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:munderover>
<mml:mstyle displaystyle="true">
<mml:mo>&#x2211;</mml:mo>
</mml:mstyle>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:munderover>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mover accent="true">
<mml:mi>M</mml:mi>
<mml:mo>&#xaf;</mml:mo>
</mml:mover>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>/</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>0.5</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>where <italic>n</italic> is the number of earthquakes.</p>
<p>We calculate the frequency-magnitude parameters for several zones (<xref ref-type="fig" rid="F5">Figures 5</xref>, <xref ref-type="fig" rid="F6">6</xref>): first, for regional zones: RA and NCA, and then for zones that differ in their local tectonics (<xref ref-type="fig" rid="F5">Figure 5</xref>; <xref ref-type="table" rid="T3">Table 3</xref>). The zone of the DST is defined here by a &#x223c;25-km width polygon representing the deformation zone of the southern section of the DST (excluding the Gulf of Elat due to the lack of seismic coverage). The width of the polygon increases up to 28-km in pull-apart basins, and decreases to 20-km at more localised sections that consist of long straight fault segments. For the rest of the NCA, the polygon of the CTF seismogenic zone (<xref ref-type="bibr" rid="B139">Sharon, 2020</xref>) is adopted to divide the off-fault seismicity into southern and northern Off-Fault Zones, OFZ(S) and OFZ(N), respectively (<xref ref-type="fig" rid="F5">Figure 5</xref>). These two zones are also bounded by the DST polygon from the east and hence reflect two local tectonic provinces (<xref ref-type="bibr" rid="B97">Neev et al., 1976</xref>; <xref ref-type="bibr" rid="B18">Ben-Avraham and Ginzburg, 1990</xref>; <xref ref-type="bibr" rid="B123">Sadeh et al., 2012</xref>) that are separated from the main active fault zones. The frequency-magnitude parameters are presented in <xref ref-type="table" rid="T3">Table 3</xref> for each of these tectonic zones (<xref ref-type="fig" rid="F5">Figure 5</xref>), and their detailed plots are provided in <xref ref-type="fig" rid="F6">Figure 6</xref>. In addition, the frequency-magnitude parameters of the seismogenic zones (<xref ref-type="bibr" rid="B139">Sharon, 2020</xref>) are provided in <xref ref-type="sec" rid="s13">Supplementary Table S2</xref>.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Tectonic zones and their <italic>b-values</italic>, within the NCA. DST is in yellow, CTF is in purple; Off Fault Zones (OFZ) have two sections: south [OFZ (S), in orange], and north [OFZ (N), in green] of the CTF, differing in their prevailing style of faulting. Note the partial overlap between DST and both CTF and OFZ (N). Bold and thin black lines are the main seismic sources and Quaternary faults, respectively (<xref ref-type="bibr" rid="B141">Sharon et al., 2020</xref>). Also shown are focal mechanism diagrams, demonstrating the dominant style of faulting in each tectonic zone, inferred from geological, seismological and geodetic observations (see text for further details).</p>
</caption>
<graphic xlink:href="feart-10-1074729-g005.tif"/>
</fig>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>The frequency-magnitude relation for all earthquakes recorded between 1983 and 2020, within <bold>(A)</bold> RA; <bold>(B)</bold> NCA; <bold>(C)</bold> DST; <bold>(D)</bold> CTF; <bold>(E)</bold> OFZ (S); <bold>(F)</bold> OFZ (N). Dashed parts are extrapolations. Note that the <italic>y</italic>-axis marks the annual rate of seismicity, and not the total number of events. The tectonic zones of sub-plots <italic>c&#x2013;f</italic> are presented in <xref ref-type="fig" rid="F5">Figure 5</xref>.</p>
</caption>
<graphic xlink:href="feart-10-1074729-g006.tif"/>
</fig>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Seismic characteristics of tectonic zones (<xref ref-type="fig" rid="F4">Figures 4</xref>, <xref ref-type="fig" rid="F5">5</xref>).</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Zone</th>
<th align="left">
<italic>a-value</italic>
</th>
<th align="left">
<italic>b-value</italic>
</th>
<th align="left">Events</th>
<th align="center">Magnitude range (Mc in bold)</th>
<th align="center">M<sub>0</sub> release(N&#x2a;m)</th>
<th align="center">75th depth percentile (km)</th>
<th align="center">95th depth percentile (km)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">RA</td>
<td align="left">
<inline-formula id="inf19">
<mml:math id="m26">
<mml:mrow>
<mml:mn>5.62</mml:mn>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>0.16</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">
<inline-formula id="inf20">
<mml:math id="m27">
<mml:mrow>
<mml:mn>1.15</mml:mn>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>0.04</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">660</td>
<td align="left">
<inline-formula id="inf21">
<mml:math id="m28">
<mml:mrow>
<mml:mi mathvariant="bold">3.8</mml:mi>
<mml:mo>&#x2264;</mml:mo>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>w</mml:mi>
</mml:msub>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>7.2</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">9.90e &#x2b; 18</td>
<td align="left">34.0</td>
<td align="left">45.3</td>
</tr>
<tr>
<td align="left">NCA</td>
<td align="left">
<inline-formula id="inf22">
<mml:math id="m29">
<mml:mrow>
<mml:mn>3.63</mml:mn>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>0.05</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">
<inline-formula id="inf23">
<mml:math id="m30">
<mml:mrow>
<mml:mn>0.96</mml:mn>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>0.02</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">1561</td>
<td align="left">
<inline-formula id="inf24">
<mml:math id="m31">
<mml:mrow>
<mml:mi mathvariant="bold">2.1</mml:mi>
<mml:mo>&#x2264;</mml:mo>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>w</mml:mi>
</mml:msub>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>5.1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">3.16e &#x2b; 17</td>
<td align="left">16.8</td>
<td align="left">25.3</td>
</tr>
<tr>
<td align="left">DST</td>
<td align="left">
<inline-formula id="inf25">
<mml:math id="m32">
<mml:mrow>
<mml:mn>3.50</mml:mn>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>0.05</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">
<inline-formula id="inf26">
<mml:math id="m33">
<mml:mrow>
<mml:mn>0.93</mml:mn>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>0.02</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">1301</td>
<td align="left">
<inline-formula id="inf27">
<mml:math id="m34">
<mml:mrow>
<mml:mi mathvariant="bold">2.1</mml:mi>
<mml:mo>&#x2264;</mml:mo>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>w</mml:mi>
</mml:msub>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>5.1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">3.00e &#x2b; 17</td>
<td align="left">17.1</td>
<td align="left">25.2</td>
</tr>
<tr>
<td align="left">CTF</td>
<td align="left">
<inline-formula id="inf28">
<mml:math id="m35">
<mml:mrow>
<mml:mn>3.07</mml:mn>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>0.11</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">
<inline-formula id="inf29">
<mml:math id="m36">
<mml:mrow>
<mml:mn>0.99</mml:mn>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>0.05</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">368</td>
<td align="left">
<inline-formula id="inf30">
<mml:math id="m37">
<mml:mrow>
<mml:mi mathvariant="bold">2.1</mml:mi>
<mml:mo>&#x2264;</mml:mo>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>w</mml:mi>
</mml:msub>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>5.0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">1.27e &#x2b; 17</td>
<td align="left">14.7</td>
<td align="left">21.9</td>
</tr>
<tr>
<td align="left">OFZ(S)</td>
<td align="left">
<inline-formula id="inf31">
<mml:math id="m38">
<mml:mrow>
<mml:mn>2.62</mml:mn>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>0.15</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">
<inline-formula id="inf32">
<mml:math id="m39">
<mml:mrow>
<mml:mn>0.96</mml:mn>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>0.07</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">154</td>
<td align="left">
<inline-formula id="inf33">
<mml:math id="m40">
<mml:mrow>
<mml:mi mathvariant="bold">2.1</mml:mi>
<mml:mo>&#x2264;</mml:mo>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>w</mml:mi>
</mml:msub>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>4.4</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">2.05e &#x2b; 16</td>
<td align="left">19.2</td>
<td align="left">28.4</td>
</tr>
<tr>
<td align="left">OFZ(N)</td>
<td align="left">
<inline-formula id="inf34">
<mml:math id="m41">
<mml:mrow>
<mml:mn>2.82</mml:mn>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>0.26</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">
<inline-formula id="inf35">
<mml:math id="m42">
<mml:mrow>
<mml:mn>1.19</mml:mn>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>0.12</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">80</td>
<td align="left">
<inline-formula id="inf36">
<mml:math id="m43">
<mml:mrow>
<mml:mi mathvariant="bold">2.1</mml:mi>
<mml:mo>&#x2264;</mml:mo>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>w</mml:mi>
</mml:msub>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>3.4</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">2.74e &#x2b; 15</td>
<td align="left">7.9</td>
<td align="left">18.1</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec id="s5">
<title>5 Variations of the <italic>b-value</italic>
</title>
<sec id="s5-1">
<title>5.1 Spatial variations of the <italic>b-value</italic>
</title>
<p>We first examine whether the differences in the <italic>b-values</italic> between the tectonic zones (<xref ref-type="table" rid="T3">Table 3</xref>; <xref ref-type="fig" rid="F5">Figure 5</xref>) reflect different style of faulting. We examine only the tectonic zones, within the NCA, all affected by a similar network coverage, reflected also by similar magnitude of completeness values of Mc&#x3d;2.1 (<xref ref-type="fig" rid="F5">Figure 5</xref>). The strike-slip dominated DST (<xref ref-type="bibr" rid="B39">Garfunkel, 1981</xref>, <xref ref-type="bibr" rid="B40">2014</xref>; <xref ref-type="bibr" rid="B70">Hofstetter et al., 2007</xref>; <xref ref-type="bibr" rid="B90">Marco and Klinger, 2014</xref>) shows a <italic>b-value</italic> of 0.93. The CTF zone, which accommodates an extensional and strike-slip associated deformation (<xref ref-type="bibr" rid="B37">Freund, 1970</xref>; <xref ref-type="bibr" rid="B1">Achmon, 1986</xref>; <xref ref-type="bibr" rid="B122">Rotstein et al., 1993</xref>; <xref ref-type="bibr" rid="B68">Hofstetter et al., 1996</xref>; <xref ref-type="bibr" rid="B123">Sadeh et al., 2012</xref>), has a <italic>b-value</italic> of 0.99. The Galilee area, marked by OFZ(N), is mostly extension-dominated normal faulting (<xref ref-type="bibr" rid="B37">Freund, 1970</xref>; <xref ref-type="bibr" rid="B120">Ron et al., 1984</xref>; <xref ref-type="bibr" rid="B70">Hofstetter et al., 2007</xref>), and shows a <italic>b-value</italic> of 1.19. The OFZ(S), an area of sparse seismicity associated with strike-slip and extensional structures (<xref ref-type="bibr" rid="B21">Bentor and Vroman, 1954</xref>; <xref ref-type="bibr" rid="B15">Bartov, 1974</xref>; <xref ref-type="bibr" rid="B175">Zilberman et al., 1996</xref>; <xref ref-type="bibr" rid="B12">Avni et al., 2000</xref>; <xref ref-type="bibr" rid="B49">Ginat et al., 2000</xref>, <xref ref-type="bibr" rid="B48">2002</xref>), shows a <italic>b-value</italic> of 0.96. These <italic>b-values</italic>, including their errors (<xref ref-type="bibr" rid="B143">Shi and Bolt, 1982</xref>), show a subtle preference of higher <italic>b-values</italic> for extensional faulting. This trend is most prominent for the OFZ(N) (<xref ref-type="fig" rid="F5">Figure 5</xref>) with a <italic>b-value</italic> of 1.19. We further explore the significance of this trend through two statistical methods: the Utsu&#x2019;s method (<xref ref-type="bibr" rid="B155">Utsu, 1999</xref>; e.g., <xref ref-type="bibr" rid="B169">Xie et al., 2019</xref>) and the Student&#x2019;s t-test (<xref ref-type="bibr" rid="B57">Gosset, 1908</xref>; e.g., <xref ref-type="bibr" rid="B109">Petruccelli et al., 2018</xref>). In both methods, we test the statistical significance for ten pairs, comprising the relations between the five tectonic zones (including the &#x201c;parent&#x201d; NCA zone), and present the results by significance level matrices (<xref ref-type="table" rid="T4">Table 4</xref>), in which the significance level (<inline-formula id="inf37">
<mml:math id="m44">
<mml:mrow>
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</mml:math>
</inline-formula>) is between 0 and 1; <inline-formula id="inf38">
<mml:math id="m45">
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mo>.</mml:mo>
<mml:mi>l</mml:mi>
<mml:mo>.</mml:mo>
<mml:mo>&#x3c;</mml:mo>
<mml:mn>0.01</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> is highly significant and <inline-formula id="inf39">
<mml:math id="m46">
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mo>.</mml:mo>
<mml:mi>l</mml:mi>
<mml:mo>.</mml:mo>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> indicates identical datasets (e.g., <xref ref-type="bibr" rid="B155">Utsu, 1999</xref>).</p>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Analysis of statistical significance for the Tectonic Zones, showing the significance level (<inline-formula id="inf40">
<mml:math id="m47">
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mo>.</mml:mo>
<mml:mi>l</mml:mi>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>) matrices according to a) Utsu&#x2019;s test; and b) the Student&#x2019;s t-test. The statistical significance follows a color scheme (<xref ref-type="table" rid="T4">Table 4c</xref>) defined by the range of <inline-formula id="inf41">
<mml:math id="m48">
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mo>.</mml:mo>
<mml:mi>l</mml:mi>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>, in which the green shades show <inline-formula id="inf42">
<mml:math id="m49">
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mo>.</mml:mo>
<mml:mi>l</mml:mi>
<mml:mo>.</mml:mo>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>0.05</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> threshold required for obtaining statistical significance. While the Utsu&#x2019;s test show high similarity between the datasets, and therefore except for one pair (DST &#x2190;&#x2192;OFZ(N)) does not indicate statistical significance, the Student&#x2019;s t-test shows that seven out of 10 pairs are significantly different from each other, with <inline-formula id="inf43">
<mml:math id="m50">
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mo>.</mml:mo>
<mml:mi>l</mml:mi>
<mml:mo>.</mml:mo>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>0.05</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>. The stages of calculation for the t-test are provided in the Tables A3 and A4 of the Supplementary material.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">&#xa0;</th>
<th align="left">NCA</th>
<th align="left">DST</th>
<th align="left">CTF</th>
<th align="left">OFZ(S)</th>
<th align="left">OFZ(N)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td colspan="6" align="left">A. Utsu&#x2019;s test significance level matrix</td>
</tr>
<tr>
<td align="left">
<bold>NCA</bold>
</td>
<td align="right">1</td>
<td align="right">0.257</td>
<td align="right">0.319</td>
<td align="right">0.367</td>
<td align="right">0.070</td>
</tr>
<tr>
<td align="left">
<bold>DST</bold>
</td>
<td align="right">0.257</td>
<td align="right">1</td>
<td align="right">0.211</td>
<td align="right">0.343</td>
<td align="right">0.043</td>
</tr>
<tr>
<td align="left">
<bold>CTF</bold>
</td>
<td align="right">0.319</td>
<td align="right">0.211</td>
<td align="right">1</td>
<td align="right">0.349</td>
<td align="right">0.126</td>
</tr>
<tr>
<td align="left">
<bold>OFZ(S)</bold>
</td>
<td align="right">0.367</td>
<td align="right">0.343</td>
<td align="right">0.349</td>
<td align="right">1</td>
<td align="right">0.112</td>
</tr>
<tr>
<td align="left">
<bold>OFZ(N)</bold>
</td>
<td align="right">0.070</td>
<td align="right">0.043</td>
<td align="right">0.126</td>
<td align="right">0.112</td>
<td align="right">1</td>
</tr>
<tr>
<td colspan="6" align="left">B. Student&#x2019;s t-test significance level matrix</td>
</tr>
<tr>
<td align="left">
<bold>NCA</bold>
</td>
<td align="right">1</td>
<td align="right">&#x3c;0.01</td>
<td align="right">0.014</td>
<td align="right">0.328</td>
<td align="right">&#x3c;0.01</td>
</tr>
<tr>
<td align="left">
<bold>DST</bold>
</td>
<td align="right">&#x3c;0.01</td>
<td align="right">1</td>
<td align="right">&#x3c;0.01</td>
<td align="right">0.085</td>
<td align="right">&#x3c;0.01</td>
</tr>
<tr>
<td align="left">
<bold>CTF</bold>
</td>
<td align="right">0.014</td>
<td align="right">&#x3c;0.01</td>
<td align="right">1</td>
<td align="right">0.120</td>
<td align="right">&#x3c;0.01</td>
</tr>
<tr>
<td align="left">
<bold>OFZ(S)</bold>
</td>
<td align="right">0.328</td>
<td align="right">0.085</td>
<td align="right">0.120</td>
<td align="right">1</td>
<td align="right">&#x3c;0.01</td>
</tr>
<tr>
<td align="left">
<bold>OFZ(N)</bold>
</td>
<td align="right">&#x3c;0.01</td>
<td align="right">&#x3c;0.01</td>
<td align="right">&#x3c;0.01</td>
<td align="right">&#x3c;0.01</td>
<td align="right">1</td>
</tr>
<tr>
<td colspan="6" align="left">C. Color scheme</td>
</tr>
<tr>
<td align="left">
</td>
<td colspan="5" align="left">s.l&#x3c;0.01</td>
</tr>
<tr>
<td align="left">&#xa0;</td>
<td colspan="5" align="left">0.01&#x3c;s.l&#x3c;0.05</td>
</tr>
<tr>
<td align="left">&#xa0;</td>
<td colspan="5" align="left">0.05&#x3c;s.l&#x3c;0.2</td>
</tr>
<tr>
<td align="left">&#xa0;</td>
<td colspan="5" align="left">0.2&#x3c;s.l&#x3c;1</td>
</tr>
<tr>
<td align="left">&#xa0;</td>
<td colspan="5" align="left">s.l&#x3d;1</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>In <xref ref-type="table" rid="T4">Table 4</xref> we present the results obtained by Utsu&#x2019;s method. In this method, we first compute the AIC (Akaike Information Criteria; <xref ref-type="bibr" rid="B179">Akaike, 1974</xref>) for each examined dataset. Then the difference between each dataset-pair (<inline-formula id="inf44">
<mml:math id="m51">
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<mml:mi>I</mml:mi>
<mml:mi>C</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>) is calculated for each dataset, and the significance level is given by the probability <inline-formula id="inf45">
<mml:math id="m52">
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:mi>A</mml:mi>
<mml:mi>I</mml:mi>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="bibr" rid="B155">Utsu, 1999</xref>); when <italic>p</italic> <inline-formula id="inf46">
<mml:math id="m53">
<mml:mrow>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>0.05</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> the two examined datasets are significantly different. According to Utsu&#x2019;s method only one pair shows clear statistical significance (DST&#x2190;&#x2192;OFZ(N); <xref ref-type="table" rid="T4">Table 4</xref>). In <xref ref-type="table" rid="T4">Table 4</xref> we present the results obtained by the <italic>Student&#x2019;s t-test</italic> method. The type of <italic>t-test</italic> is chosen according to the ratio between each pair&#x2019;s <italic>b-value</italic> standard deviations, <inline-formula id="inf47">
<mml:math id="m54">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="bibr" rid="B115">Rice, 2006</xref>) defining whether the variances of the <italic>b-values</italic> are similar or not between two tectonic zones (<xref ref-type="sec" rid="s13">Supplementary Table S3</xref>). By setting the statistical significance requirement to <inline-formula id="inf48">
<mml:math id="m55">
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mo>.</mml:mo>
<mml:mi>l</mml:mi>
<mml:mo>.</mml:mo>
<mml:mo>&#x3c;</mml:mo>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.05</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> (e.g., <xref ref-type="bibr" rid="B155">Utsu, 1999</xref>) and by using the <italic>Student&#x2019;s t-distribution table</italic> (<xref ref-type="sec" rid="s13">Supplementary Table S4</xref>), we determine whether the observed differences between the <italic>b-values</italic> of two tectonic zones are statistically significant or a matter of chance, hence insignificant (<xref ref-type="table" rid="T4">Table 4</xref>). In addition to <italic>Utsu&#x2019;s</italic> method, the Student&#x2019;s <italic>t-test</italic> method suggests that except for the OFZ(S) related pairs, all the other pairs are significantly different from each other, meaning that the differences between the <italic>b-values</italic> are not randomly distributed. Hence, they may be attributed to physical causes, such as the predominant faulting style (<xref ref-type="bibr" rid="B129">Schorlemmer et al., 2005</xref>). Such differences between the two methods have been observed, for example, by <xref ref-type="bibr" rid="B109">Petruccelli et al. (2018)</xref>, as the Student&#x2019;s <italic>t-test</italic> method has shown more dataset-pairs with statistical significance than the Utsu&#x2019;s method, for all the intermediate cases (those that do not reflect a pure faulting style; see <xref ref-type="table" rid="T3">Tables 3</xref>, <xref ref-type="table" rid="T4">4</xref> in <xref ref-type="bibr" rid="B109">Petruccelli et al., 2018</xref>).</p>
</sec>
<sec id="s5-2">
<title>5.2 Spatial variations of the <italic>b-value</italic> along the DST</title>
<p>We further explore in detail the spatial variations of the <italic>b-value</italic> along the main tectonic feature, within the DST polygon (<xref ref-type="fig" rid="F5">Figure 5</xref>), by systematically scanning it in a 60-km long latitudinal bands, at 1-km increments, using the DST&#x2019;s polygon completeness level of <italic>M</italic>
<sub>
<italic>c</italic>
</sub>
<italic>&#x3d;2.1</italic> (<xref ref-type="table" rid="T3">Table 3</xref>; <xref ref-type="sec" rid="s13">Supplementary Figure S2</xref>). These spatial bands represent the approximate minimum length to capture at least 100 events at each sample, with only one gap in between the bands (<xref ref-type="fig" rid="F7">Figure 7</xref>). The <italic>b-value</italic> and its error (<xref ref-type="bibr" rid="B143">Shi and Bolt 1982</xref>) are calculated at each sample, where the mean number of events in these spatial bands is 185. An additional sparse-seismicity profile (50&#x2013;99 events per sample; <xref ref-type="fig" rid="F7">Figure 7</xref>) aligns with the main profile, showing a consistent behaviour of the <italic>b-value</italic> profile along the DST. In addition, the error bar band around the profile shows that the changes in the <italic>b-value</italic> are significant, substantially larger than the errors. The same spatial profiling is generated for the 75th and 95th hypocentre depth percentiles, and for the accumulated seismic moment converted from the magnitudes (<xref ref-type="fig" rid="F7">Figure 7</xref>). The depth percentiles mark the depth profiles for which 75% and 95% of the events within the spatial bands are shallower, respectively. The accumulated seismic moment, which is the sum of seismic moments of all events within the spatial bands, is calculated at each sample.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Top part: Map showing the DST polygon (yellow), defining the data for the analysis. The black lines show the main sources (see <xref ref-type="bibr" rid="B141">Sharon et al., 2020</xref>). Bottom part: Spatial variations of the <italic>b-value</italic> (in blue), of the 75th and 95th hypocentre depth percentiles (dashed yellow and red lines, respectively) and of the cumulative seismic moment release (in Green). Note the left axes are directed downwards. Solid and dashed lines of the <italic>b-value</italic> indicate at least 100 events, and 50&#x2013;99 events per sample, respectively, and are shown with their light blue error bar band surrounding them; the blue linear dashed curve marks the spatial trend of the <italic>b-value</italic>. Within the Top part, the brown polygon marks zones with high values of seismic density and seismic moment density (see <xref ref-type="bibr" rid="B141">Sharon et al., 2020</xref>), overlapping the DST polygon. These zones emphasize two seismic gaps: 1) HSG&#x2014;Hazeva Seismic Gap (latitudes &#x223c;30.7&#xb0;&#x2013;30.8&#xb0;N), and 2) BSG&#x2014;Beit She&#x2019;an Seismic Gap (latitudes &#x223c;32.4&#xb0;&#x2013;32.6&#xb0;N); the latter is prominent enough to also leave a gap within the <italic>b-value</italic> profile (Bottom Part).</p>
</caption>
<graphic xlink:href="feart-10-1074729-g007.tif"/>
</fig>
<p>The profiles presented in <xref ref-type="fig" rid="F7">Figure 7</xref> show rather complex correlations between the <italic>b-value</italic> and both the seismogenic depth and seismic moment release. We observe an inverse correlation of the <italic>b-value</italic> with the seismogenic depth along the DST, with lower <italic>b-values</italic> for deep seismogenic zones (i.e., latitudes 30.3&#xb0;&#x2013;30.7&#xb0;, 30.9&#xb0;&#x2013;31.3&#xb0;). A similar trend is presented in <xref ref-type="sec" rid="s13">Supplementary Figure S3</xref>) for the tectonic (<xref ref-type="fig" rid="F5">Figure 5</xref>) and seismogenic zones (<xref ref-type="bibr" rid="B139">Sharon, 2020</xref>; provided also in the <xref ref-type="sec" rid="s13">Supplementary Figure S4</xref>). In addition, the seismic moment release shows at the southern section an inverse correlation with the <italic>b-value</italic> (latitudes 29.3&#xb0;&#x2013;31.0&#xb0;; <xref ref-type="fig" rid="F7">Figure 7</xref>); for example, this is emphasized at the &#x201c;quasi-spike&#x201d; of the <italic>b-value</italic> in latitude &#x223c;30.8<inline-formula id="inf49">
<mml:math id="m56">
<mml:mrow>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>. In contrast, the <italic>b-value</italic> increase at &#x223c;31.7<inline-formula id="inf50">
<mml:math id="m57">
<mml:mrow>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>, cannot be clearly correlated either to the seismogenic depth or to the seismic moment release, and seems to correspond to the M<sub>w</sub> 5.1 mainshock (<xref ref-type="bibr" rid="B69">Hofstetter et al., 2008</xref>) with its aftershock sequence (see <xref ref-type="fig" rid="F7">Figure 7A</xref>). This increase may reflect delocalization at the northern Dead Sea basin associated with its structural complexity (e.g., <xref ref-type="bibr" rid="B44">Garfunkel and Ben-Avraham, 1996</xref>). Yet, with all the complexity of the <italic>b-value</italic> profile, the overall trend shows that the <italic>b-value</italic> decreases northward along the DST (dashed blue linear trend line in <xref ref-type="fig" rid="F7">Figure 7</xref>).</p>
</sec>
<sec id="s5-3">
<title>5.3 Temporal variations of the <italic>b-value</italic> along the DST</title>
<p>Since the relationship between the <italic>b-value</italic> and the seismic moment release has not been comprehensively studied, it is not clear whether the inverse spatial correlation (southern section, <xref ref-type="fig" rid="F7">Figure 7</xref>) is a typical relationship, or whether it is biased by specific significant seismic activity (e.g., mainshocks, aftershocks, swarms). Therefore, some insights may be obtained by examining the temporal relations between the <italic>b-value</italic> and the seismic moment release. Statistical methods have been developed for examining high-resolution temporal variations of the <italic>b-value</italic> (e.g. <xref ref-type="bibr" rid="B161">Wiemer et al., 1998</xref>; <xref ref-type="bibr" rid="B95">Mousavi et al., 2017</xref>). However, applying them requires focusing on specific sub-zones, reducing to too small datasets in the case of the DST, due to the relatively low-intensity seismicity. Therefore, we investigate the temporal correlation of the <italic>b-value</italic> with the seismic moment release (<xref ref-type="fig" rid="F8">Figure 8</xref>), by applying a rather simple technique, calculating the <italic>b-value</italic> in a moving time window, with a fixed number of 100 events per window, and a time interval of five events; also here, the DST&#x2019;s polygon completeness level of <italic>M</italic>
<sub>
<italic>c</italic>
</sub> <italic>2.1</italic> is applied (<xref ref-type="table" rid="T3">Table 3</xref>; <xref ref-type="sec" rid="s13">Supplementary Figure S5</xref>). Similar temporal analysis of the <italic>b-value</italic>, using a fixed number of events, has been shown and discussed in other studies (e.g., <xref ref-type="bibr" rid="B100">Nuannin et al., 2004</xref>; <xref ref-type="bibr" rid="B152">Tormann et al., 2013</xref>). In addition, as the catalogue consists of earthquakes recorded continuously by the ISN, we assume the data is inherently homogenous, with no temporal bias that can be caused by data comprising a combination of different catalogues (e.g. <xref ref-type="bibr" rid="B178">Z&#xfa;&#xf1;iga and Wiemer, 1999</xref>; <xref ref-type="bibr" rid="B151">Tormann et al., 2010</xref>).</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>
<bold>(A)</bold> Temporal variations of the <italic>b-value</italic> (in blue) with their light blue error bar band around them, and of the cumulative seismic moment release (in green; note the axis on the left is directed downwards) in the DST (<xref ref-type="fig" rid="F5">Figures 5</xref>, <xref ref-type="fig" rid="F7">7</xref>), based on 100-event time windows in 5-event intervals. Also marked are the <italic>b-values</italic> calculated for specific time-windows [<bold>(B&#x2013;E)</bold>; dashed grey lines], verifying the fluctuations seen in the <italic>b-value</italic> profile; their frequency magnitude curves are presented in panel 8 <bold>(B&#x2013;E)</bold>. Two reductions of the <italic>b-value</italic> can be related to swarm activities at the Sea of Galilee, during 2013 and 2018 (dashed orange rectangles; <xref ref-type="bibr" rid="B185">Wetzler et al., 2019</xref>).</p>
</caption>
<graphic xlink:href="feart-10-1074729-g008.tif"/>
</fig>
<p>The temporal analysis (<xref ref-type="fig" rid="F8">Figure 8</xref>) mainly shows an inverse correlation between the <italic>b-value</italic> and the seismic moment release (<xref ref-type="fig" rid="F8">Figure 8A</xref>). We also examine the <italic>b-value</italic> in specific time windows, with a minimum of 450 events per time window, achieving higher statistical confidence. Their frequency-magnitude plots are presented in <xref ref-type="fig" rid="F8">Figures 8B&#x2013;E</xref>. These time-windows deduce <italic>b-values</italic> that fit the fluctuating <italic>b-value</italic> profile obtained by the fixed-amount-of-events method.</p>
</sec>
</sec>
<sec sec-type="discussion" id="s6">
<title>6 Discussion</title>
<sec id="s6-1">
<title>6.1 Relation to the differential stress and faulting mechanism</title>
<p>The seismogenic depth along the DST fluctuates correlatively with the thermal profile (<xref ref-type="bibr" rid="B133">Shalev et al., 2013</xref>; <xref ref-type="bibr" rid="B159">Wetzler and Kurzon, 2016</xref>). The &#x3e;25-km deep seismicity in some parts (<xref ref-type="fig" rid="F7">Figure 7</xref>), particularly in the Dead Sea basin, indicates a cold crust with a deep brittle-to-ductile transition zone (<xref ref-type="bibr" rid="B5">Aldersons et al., 2003</xref>; <xref ref-type="bibr" rid="B133">Shalev et al., 2013</xref>; <xref ref-type="bibr" rid="B6">Aldersons and Ben-Avraham, 2014</xref>; <xref ref-type="bibr" rid="B159">Wetzler and Kurzon, 2016</xref>), whereas shallow brittle-to-ductile transition occurs in zones of shallower seismogenic depth. The differential stress within the brittle crust increases with depth (e.g. <xref ref-type="bibr" rid="B144">Sibson, 1974</xref>, <xref ref-type="bibr" rid="B145">1984</xref>; <xref ref-type="bibr" rid="B83">Llana-F&#xfa;nez and L&#xf5;pez-Fern&#xe1;ndez, 2015</xref>) as the confining pressure grows (<xref ref-type="bibr" rid="B26">Byerlee, 1968</xref>). Hence, deeper seismogenic zones are associated with higher differential stress because they include deeper portion of earth&#x2019;s (brittle-) crust. We therefore interpret the inverse correlation between the <italic>b-value</italic> and the seismogenic depth (<xref ref-type="fig" rid="F7">Figure 7</xref>) as related to the differential stress within the brittle crust. This interpretation is consistent with previous laboratory (<xref ref-type="bibr" rid="B8">Amitrano, 2003</xref>) and seismic observations (<xref ref-type="bibr" rid="B46">Gerstenberger et al., 2001</xref>; <xref ref-type="bibr" rid="B147">Spada et al., 2013</xref>; <xref ref-type="bibr" rid="B125">Scholz, 2015</xref>; <xref ref-type="bibr" rid="B107">Petruccelli et al., 2019b</xref>), which showed inverse correlation between the <italic>b-value</italic> and the depth of earthquakes, and hence with their corresponding differential stress.</p>
<p>The increase of the <italic>b-value</italic> in tectonic zones, as the predominant faulting style changes from strike-slip dominated DST to normal faulting dominated OFZ(N) (<xref ref-type="fig" rid="F5">Figure 5</xref>), is interpreted here as another expression of the inverse dependency of <italic>b-value</italic> with differential stress environments (<xref ref-type="bibr" rid="B129">Schorlemmer et al., 2005</xref>; <xref ref-type="bibr" rid="B83">Llana-F&#xfa;nez and L&#xf5;pez-Fern&#xe1;ndez, 2015</xref>; <xref ref-type="bibr" rid="B107">Petruccelli et al., 2019b</xref>). This relation is shown by normal faults that are associated with relatively lower differential stresses and higher <italic>b-values</italic>, while strike-slip faults that are associated with higher differential stresses, and lower <italic>b-values</italic>.</p>
<p>We also observe an overall trend of the <italic>b-value</italic> decreasing northwards, within the DST polygon (<xref ref-type="fig" rid="F7">Figure 7</xref>). This trend may be caused by variations of mechanical parameters such as the internal friction angle and faulting geometry (<xref ref-type="bibr" rid="B8">Amitrano, 2003</xref>; <xref ref-type="bibr" rid="B108">Petruccelli et al., 2019a</xref>). Such variations can be linked to geometrical changes of the plate boundary (<xref ref-type="bibr" rid="B39">Garfunkel, 1981</xref>; <xref ref-type="bibr" rid="B73">Joffe and Garfunkel, 1987</xref>) and perhaps a transition from the extensional pull-apart basins of the Gulf of Elat (<xref ref-type="bibr" rid="B114">Reilinger et al., 2006</xref>) in the southern end of the DST polygon, closer to the Red Sea rift, to the transpressional LRB in the north (<xref ref-type="bibr" rid="B55">Gomez et al., 2007</xref>; <xref ref-type="bibr" rid="B156">Weinberger et al., 2009</xref>). Differences in the differential stress associated with these structural variations may also be related to post-Neogene widening of the fault zone along the southern section of the DST in the study area (latitudes&#x3c;31&#xb0;; <xref ref-type="fig" rid="F7">Figure 7</xref>), while its northern section (latitudes&#x3e;33&#xb0;; <xref ref-type="fig" rid="F7">Figure 7</xref>) underwent convergence and shortening (<xref ref-type="bibr" rid="B12">Avni et al., 2000</xref>; <xref ref-type="bibr" rid="B89">Marco, 2007</xref>; <xref ref-type="bibr" rid="B156">Weinberger et al., 2009</xref>; <xref ref-type="bibr" rid="B41">Garfunkel, 2010</xref>).</p>
</sec>
<sec id="s6-2">
<title>6.2 The <italic>b-value</italic> and the seismic moment release</title>
<p>The <italic>b-value</italic> shows an inverse correlation with the seismic moment release, at least in the southern section of the DST (latitudes&#x3c;31&#xb0;; <xref ref-type="fig" rid="F7">Figure 7</xref>), and a clearer inverse correlation is seen in the temporal analysis (<xref ref-type="fig" rid="F8">Figure 8</xref>). The inverse correlation aligns with the theoretical study of <xref ref-type="bibr" rid="B167">Wyss (1973)</xref> and with observations from other tectonic domains (e.g., <xref ref-type="bibr" rid="B28">Cao and Gao, 2002</xref>; <xref ref-type="bibr" rid="B22">Bora et al., 2018</xref>).</p>
<p>Seismic moment release is affected by two main factors: the accumulation of seismic moment of small events, and the addition of seismic moment from more significant events. The latter, when exists, tends to dominate over the former. In many aftershock sequences it has been observed that the <italic>b-value</italic> increases (<xref ref-type="bibr" rid="B149">Suyehiro, 1966</xref>; <xref ref-type="bibr" rid="B47">Gibowicz, 1974</xref>; <xref ref-type="bibr" rid="B78">King, 1983</xref>; <xref ref-type="bibr" rid="B160">Wiemer and Katsumata, 1999</xref>; <xref ref-type="bibr" rid="B58">Gulia et al., 2018</xref>), due to the stress relaxation after the mainshock and activation of fault branches at the periphery of the rupture, while some have shown a decrease in the <italic>b-value</italic> around the mainshock (e.g., <xref ref-type="bibr" rid="B96">Mukhopadhyay et al., 2013</xref>). A decrease in <italic>b-value</italic> prior to the main shock has been observed in other studies, and was associated to an increase of the differential stress (e.g. <xref ref-type="bibr" rid="B127">Schorlemmer and Wiemer, 2005</xref>; <xref ref-type="bibr" rid="B118">Rivi&#xe8;re et al., 2018</xref>).</p>
<p>In the case of the DST, the seismicity observed here is within magnitudes of up to M<sub>w</sub> 5.1, consisting of: one significant mainshock of M<sub>w</sub> 5.1 in 2004 at the Dead Sea basin, two swarms at the Sea of Galilee of M<sub>w</sub> &#x223c;3.5 and &#x223c;4.5, in 2013 and 2018, respectively, and sporadic seismicity of up to M<sub>w</sub> 4.4, throughout the DST. Except for the swarms, which show a clear decrease of the <italic>b-values</italic> (<xref ref-type="fig" rid="F8">Figure 8</xref>), all the main shocks, including the M<sub>w</sub> 5.1, are characterised by a relatively short aftershock activity (<xref ref-type="bibr" rid="B69">Hofstetter et al., 2008</xref>); for the M<sub>w</sub> 5.1 event, the complete aftershock sequence includes 23 events above the M<sub>c</sub> of 2.1. The <italic>b-value</italic> spatial peak, corresponding to this sequence in the spatial <italic>b-value</italic> profile (Lat &#x223c;31.7; <xref ref-type="fig" rid="F7">Figure 7</xref>), is not aligned with the spatial seismogenic depth profile and the spatial seismic moment release profiles. Therefore, it seems that the temporal variation of the <italic>b-value</italic> within the DST mainly reflects the effect of moderate seismicity (M<sub>w</sub> 3&#x2013;5) on the whole size distribution, a phenomena that has been observed particularly in small datasets (<xref ref-type="bibr" rid="B183">Marzocchi et al., 2020</xref>), and in this case - with low aftershock activity. For the swarms (<xref ref-type="fig" rid="F8">Figure 8</xref>), the reduction in the <italic>b-value</italic> reflects the repetition of similar size mainshocks, typical for swarms (e.g., <xref ref-type="bibr" rid="B52">Goebel et al., 2016</xref>, <xref ref-type="bibr" rid="B186">Wetzler et al., 2019</xref>).</p>
</sec>
<sec id="s6-3">
<title>6.3 Seismic gaps along the DST</title>
<p>Some of the sections along the DST, which show extremely low seismic activity, were documented by <xref ref-type="bibr" rid="B141">Sharon et al. (2020)</xref>. The most prominent ones (<xref ref-type="fig" rid="F7">Figure 7</xref>) are the Hazeva Seismic Gap (HSG) and the Beit She&#x2019;an Seismic Gap (BSG). The HSG contains a &#x201c;quasi-spike&#x201d; <italic>b-value</italic> rise, which correlates to a rather similar &#x201c;quasi-spike&#x201d; of low seismic moment release (<xref ref-type="fig" rid="F7">Figure 7</xref>). Since high <italic>b-values</italic> also relate to weak zones that may be associated with creeping (<xref ref-type="bibr" rid="B128">Schorlemmer et al., 2004</xref>; <xref ref-type="bibr" rid="B168">Wyss et al., 2004</xref>; <xref ref-type="bibr" rid="B152">Tormann et al., 2013</xref>, <xref ref-type="bibr" rid="B153">2014</xref>), the combination of a high <italic>b-value</italic> with low seismic activity implies that local creeping occurs in this zone. Geodetic data from the BSG has been interpreted to show shallow crustal creep (1.5 &#xb1; 1.0&#xa0;km) in its northernmost part (<xref ref-type="bibr" rid="B63">Hamiel et al., 2016</xref>). <xref ref-type="bibr" rid="B141">Sharon et al. (2020)</xref> suggested that the relative absence of seismicity in this gap is caused by slip partitioning of the DST activity to the CTF (<xref ref-type="bibr" rid="B123">Sadeh et al., 2012</xref>; <xref ref-type="bibr" rid="B62">Hamiel et al., 2018</xref>), and to some extent, shallow creeping. Assuming the low <italic>b-value</italic> in the southern part of the BSG is not an artefact of the small amount of data, it may indicate a particularly locked section (e.g., asperity; <xref ref-type="bibr" rid="B163">Wiemer and Wyss, 1997</xref>, <xref ref-type="bibr" rid="B162">2002</xref>; <xref ref-type="bibr" rid="B165">Wyss, 2001</xref>; <xref ref-type="bibr" rid="B147">Spada et al., 2013</xref>; <xref ref-type="bibr" rid="B153">Tormann et al., 2014</xref>). The sparse seismicity observed here and the relative quiescence along the segment in the past centuries, as well as the associated large displacement deficit (<xref ref-type="bibr" rid="B90">Marco and Klinger, 2014</xref>; <xref ref-type="bibr" rid="B81">Lefevre et al., 2018</xref>), should be accounted for in seismic hazard assessment.</p>
</sec>
<sec id="s6-4">
<title>6.4 Comparison to other continental transform plate boundaries</title>
<p>Comparison of <italic>b-values</italic> between different tectonic domains may be problematic, since some factors can dramatically affect the <italic>b-value</italic>: the magnitude type (<xref ref-type="bibr" rid="B166">Wyss, 2020</xref>) and its calibration (<xref ref-type="bibr" rid="B151">Tormann et al., 2010</xref>), changes in the network operating procedures (<xref ref-type="bibr" rid="B178">Z&#xfa;&#xf1;iga and Wiemer, 1999</xref>), the spatial frame (e. g., <xref ref-type="bibr" rid="B103">Page and Felzer, 2015</xref>), and the time window in respect of the seismic cycle (e.g., <xref ref-type="bibr" rid="B113">Raub et al., 2017</xref>); that is, assuming a correct choice of the completeness magnitude and well-calculated <italic>b-value</italic> (i.e., the method used). Thus, although the <italic>b-value</italic> is expected to vary between regions according to the faulting style (<xref ref-type="bibr" rid="B129">Schorlemmer et al., 2005</xref>), such interpretations between different faults of different regions should be made carefully. Here, we compare our results, regarding the DST, with three other major continental transform fault systems (e.g., <xref ref-type="bibr" rid="B45">Gauriau and Dolan, 2021</xref>).</p>
<p>A <italic>b-value</italic> of 1.03 was deduced for a 20-km width spatial zone surrounding the southern San Andreas fault (<xref ref-type="bibr" rid="B103">Page and Felzer, 2015</xref>). Rather similar <italic>b-values</italic> were achieved in a wider zone (0.99&#x2013;1.01; <xref ref-type="bibr" rid="B72">Hutton et al., 2010</xref>). Two zones, comprised of widths of 10 and 20&#xa0;km off the northern part of the San Andreas fault, California, yielded <italic>b-values</italic> of 0.99 and 0.93, respectively (<xref ref-type="bibr" rid="B166">Wyss, 2020</xref>). In New Zealand, a <italic>b-value</italic> of 0.98 was obtained for a 20-km wide zone along the central Alpine fault (<xref ref-type="bibr" rid="B166">Wyss, 2020</xref>), which accommodates reverse slip rates of approximately 20&#x2013;40% of its horizontal motion (<xref ref-type="bibr" rid="B99">Norris and Cooper, 2001</xref>). A larger zone surrounding the central Alpine fault deduced a <italic>b-value</italic> of <italic>0.85</italic> (<xref ref-type="bibr" rid="B92">Michailos et al., 2019</xref>). Seismicity from the area of the North Anatolian fault, Turkey, divided into three parts, yielded <italic>b-values</italic> of 1.01&#x2013;1.02 in its eastern and central parts, and 1.13 in the western part (<xref ref-type="bibr" rid="B102">&#xd6;zt&#xfc;rk, 2011</xref>).</p>
<p>Our results indicate a <italic>b-value</italic> of 0.93 for the DST with a gentle spatial trend associated with tensional and compressional components in the edges of the study area. Considering that the northern part of the San Andreas fault is somewhat affected by a compression regime (e.g., <xref ref-type="bibr" rid="B131">Schwartz et al., 1990</xref>; <xref ref-type="bibr" rid="B164">Williams et al., 2006</xref>), and that the western part of the North Anatolian fault accommodates normal faulting components (<xref ref-type="bibr" rid="B184">Reilinger et al., 1997</xref>), their corresponding <italic>b-values</italic> imply also a gentle faulting-style dependency of the <italic>b-value</italic>, similar to our DST observations. In addition, the <italic>b-value</italic> of the DST is somewhat lower compared with these other major strike-slip faults, despite reverse component in parts of the San Andreas fault and particularly in the Alpine fault. This might be due to relatively deeper seismicity of the DST (up to 21&#x2013;27&#xa0;km), in comparison to the other examined faults, possibly associated with increased differential stress along significant parts of the DST.</p>
</sec>
</sec>
<sec sec-type="conclusion" id="s7">
<title>7 Conclusions</title>
<p>We analyse &#x223c;20,300 earthquakes along the DST and its periphery and provide a new conversion formula from <inline-formula id="inf51">
<mml:math id="m58">
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> to <inline-formula id="inf52">
<mml:math id="m59">
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>w</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. After converting magnitudes, we determine the frequency-magnitude parameters for the complete catalogue, and to five significant subsets. Our <italic>b-value</italic> results align with previous studies in the region (<xref ref-type="bibr" rid="B124">Salamon et al., 1996</xref>; <xref ref-type="bibr" rid="B138">Shapira and Hofstetter, 2002</xref>; <xref ref-type="bibr" rid="B61">Hamiel et al., 2009</xref>; <xref ref-type="bibr" rid="B84">Lu et al., 2020</xref>), providing a high resolution characterisation of the frequency-magnitude statistical parameters, including within well-defined tectonic zones, consisting the network coverage area.</p>
<p>Variations of the <italic>b-value</italic> within the tectonic zones correspond to changes in the tectonic regime and presumably to the associated style of faulting, with values that vary from 0.93 in the strike-slip dominated DST to 1.19 in the normal faulting dominated OFZ(N)). In addition, high-resolution spatial profile along the DST reveals a decreasing trend of the <italic>b-value</italic> towards the north. This trend corresponds to a possible increased differential stress associated with a gradual change in the faulting regime, from an extension component at the south, where the DST shifts from the extensional pull-apart basins of the Gulf of Elat, closer to the Red Sea rift, to a compression component at the north, approaching the LRB. Hence, we propose that these variations reflect the inverse dependency of the <italic>b-value</italic> with the differential stress as revealed from the <xref ref-type="bibr" rid="B9">Anderson (1905)</xref> theory of faulting.</p>
<p>The DST spatial profile reveals an inverse dependency between the <italic>b-value</italic> and the seismogenic depth as the <italic>b-value</italic> decreases with the deepening of the seismogenic depth. Considering that deeper seismogenic zones are distributed over depths of higher differential stress, we suggest that this inverse correlation results from variations in the differential stress, which increases with depth within the brittle part of the crust, showing rheological dependency of the <italic>b-value.</italic>
</p>
<p>Our analyses show that within the DST zone, the <italic>b-value</italic> inversely correlates with seismic moment release, reflecting a weak role of aftershocks within the DST. While the temporal fluctuations of the <italic>b-value</italic> better reflect this correlation, its spatial variations are linked to both the seismic moment release and the seismogenic depth.</p>
<p>The observations from this study are in line with previously-suggested dependency between the <italic>b-value</italic> and the differential stress (<xref ref-type="bibr" rid="B126">Scholz, 1968</xref>, <xref ref-type="bibr" rid="B125">2015</xref>; <xref ref-type="bibr" rid="B8">Amitrano, 2003</xref>; <xref ref-type="bibr" rid="B54">Goebel et al., 2013</xref>). Considering this dependency and associated previous observations, we also suggest that anomalous <italic>b-values</italic> may indicate creeping and locked sections of the fault in two seismic gaps defined here&#x2014;the Hazeva and Beit She&#x2019;an seismic gaps, respectively. Our results contribute to the seismo-tectonic understanding of the DST, and should also be considered for seismic hazard evaluation in the region. In addition, as the observed spatio-temporal relations between the <italic>b-value</italic> and the seismic moment release are not well understood, this relation should be further investigated in higher resolution, and when more detailed data will be available for the region.</p>
<sec id="s7-1">
<title>7.1 Data and resources</title>
<p>The seismic catalogue used in this study is an updated relocated catalogue, based on what was presented in <xref ref-type="bibr" rid="B159">Wetzler and Kurzon, 2016</xref>, and can be downloaded at: &#x3c;<ext-link ext-link-type="uri" xlink:href="https://www.gov.il/en/Departments/General/seismic-catalogs-files">https://www.gov.il/en/Departments/General/seismic-catalogs-files</ext-link>&#x3e;. Maps were generated using QGIS open source mapping software [(&#x3c;<ext-link ext-link-type="uri" xlink:href="https://www.qgis.org/">https://www.qgis.org/</ext-link>&#x3e;), last accessed November 2022], and the global high resolution population GIS layers were downloaded from &#x3c;<ext-link ext-link-type="uri" xlink:href="https://www.worldpop.org/">https://www.worldpop.org/</ext-link>&#x3e;. Many of the figures were generated by Matlab (&#x3c;<ext-link ext-link-type="uri" xlink:href="https://www.mathworks.com/products/matlab.html">https://www.mathworks.com/products/matlab.html</ext-link>&#x3e;), last accessed November 2022, and all figures were finalized using Microsoft PowerPoint. Naturally, we cannot cover all aspects in the main manuscript, and accordingly, we have added a Supplemental Material section, providing more details and additional supporting analyses.</p>
</sec>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s8">
<title>Data availability statement</title>
<p>Publicly available datasets were analyzed in this study. This data can be found here: <ext-link ext-link-type="uri" xlink:href="https://www.gov.il/en/Departments/General/seismic-catalogs-files">https://www.gov.il/en/Departments/General/seismic-catalogs-files</ext-link>.</p>
</sec>
<sec id="s9">
<title>Author contributions</title>
<p>MS and IK contributed to the conception and the design of the study. MS and IK performed the majority of the data analysis. MS and NW performed additional data analysis. MS wrote the first draft of the manuscript. IK and NW wrote sections of the manuscript. AS and SM provided essential geological and geophysical insights. All authors contributed to manuscript revision, read, and approved the submitted version.</p>
</sec>
<sec id="s10">
<title>Funding</title>
<p>This study was supported by the Ministry of Energy grants: 214-11-10, 219-11-054 and 222-11-001.</p>
</sec>
<ack>
<p>We thank Andrey Polozov, Ran Nof, Marina Gorstein, Yuval Tal, Yariv Hamiel and Marcelo Rosensaft for their assistance and their useful comments. We thank the guest associate editor, Guido Adinolfi, and two reviewers for their helpful comments, assisting us in improving the manuscript.</p>
</ack>
<sec sec-type="COI-statement" id="s11">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s12">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<sec id="s13">
<title>Supplementary material</title>
<p>The Supplementary Material for this article can be found online at: <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/feart.2022.1074729/full#supplementary-material">https://www.frontiersin.org/articles/10.3389/feart.2022.1074729/full&#x23;supplementary-material</ext-link>
</p>
<supplementary-material xlink:href="DataSheet1.PDF" id="SM1" mimetype="application/PDF" xmlns:xlink="http://www.w3.org/1999/xlink"/>
</sec>
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