Abstract
The crustal low-velocity zone (LVZ), an important anomaly found in some regional structures of Iceland, is still absent in the Icelandic average velocity structure due to limitations of tomography methods. Using stations from the HOTSPOT experiment and other supplemental stations throughout Iceland, we apply the frequency-Bessel transform method (F-J method) to extract the first two mode dispersion curves from ambient noise data. We obtain an average S-wave velocity (Vs) model of Iceland down to 120 km depth, where two LVZs at depths of 12–22 km and below 55 km are found. The shallow LVZ, whose rationalities are justified using theoretical dispersion curves of certain models to recover themselves, may improve the understanding of the Icelandic average crust. Furthermore, our model shows better representativeness by comparing travel time residuals of the primary wave between observed and synthetic data predicted using different average velocity models. Based on the variations of the Vs gradient, the Icelandic crust with an average thickness of 32 km is divided into the upper crust (0–10 km), middle crust (10–22 km), and lower crust (22–32 km). The asthenosphere starts from the deeper LVZ at 55 km depth, potentially indicating the relatively concentrated melt in this depth range. In this study, crustal LVZs are revealed both in a volcanic active zone and a non-volcanic zone, which may also suggest the LVZ in the average model has more complex origins than the high-temperature zone beneath the central volcanoes. The prevalent thick-cold crustal model of Iceland, considered to rule out the existence of a broad region of partial melt in the crust, also strengthens the possibility of diverse origins. The variations in petrology may also contribute to the crustal LVZ in the average model.
1 Introduction
The interaction between the spreading Mid-Atlantic rift and Iceland hotspot promotes frequent magmatic events such as eruptions in central volcanoes (blue points in Figure 1) and distinct fissure swarms (blue lines in Figure 1, ) in Iceland. Previous studies based on seismic tomography have revealed a cylindrical low-velocity anomaly in the mantle of Iceland (e.g., Wolfe et al., 1997; ; ; Rickers et al., 2013), which may be a result of the upwelling plume. In addition, some evidence from geochemical anomalies around the ridge also supports the plume hypothesis (e.g., Schilling, 1973; White et al., 1992; Shorttle and Maclennan, 2011).
FIGURE 1
After the first seismic field observation during the 1960s, a great deal of work has been undertaken to study the crust of Iceland which has obtained similar seismic velocities, but the thickness of the Icelandic crust has been a subject of controversial debate for a long time due to different interpretations of such velocities. There are two dominant but different models of the Icelandic crust. The early thin-hot crust model underlain by an unusual low-velocity uppermost mantle has a thickness of approximately 10–20 km (e.g., Tryggvason, 1962; Pálmason, 1971). The downward extrapolation of near-surface temperature gradients obtained from shallow boreholes in Iceland predicts supra-solidus temperatures and partially molten basaltic material at 10–20 km depths (e.g.,
Due to the existence of the plume, the thickness of the Icelandic crust increases in some areas, and the thickest crust is found near the center of the hotspot (
In contrast to traditional seismic methods, ambient noise tomography conquers the defects in the non-homogeneous distribution of seismic events, significantly improving the spatial resolution of seismic images with numerous ray paths. After pioneering works for theoretical foundations (e.g.,
In this study, we apply the recently developed frequency-Bessel transform method (F-J method) (Wang et al., 2019; Xi et al., 2021; Zhou and Chen, 2021) to extract the first two modes of dispersion curves from the ambient noise data of Iceland. We invert the multimodal dispersion curves to obtain a high-resolution average S-wave velocity () structure of Iceland, which reveals a crustal LVZ. To analyze the possible origins of the low-velocity anomaly, we also circle two subregions, volcanic and non-volcanic zones, and obtain their Vs structures. By recovering different models with their theoretical dispersion curves and comparing the predicted travel time with the observed travel time of the primary wave from earthquake events, we investigate the reliability of this LVZ and the rationality of the average structure.
2 Methods
2.1 The F-J method
Wang et al. (2019) developed the F-J method to extract multimodal dispersion curves from ambient noise cross-correlation functions (NCFs). The method was successfully applied to establish the structures in various areas through the inversion of multimodal dispersion curves (e.g., Wu et al., 2020; Zhan et al., 2020; Li et al., 2022; Ma et al., 2022). We briefly describe the F-J method below.
Wang et al. (2019) defined the F-J spectrum aswhere denotes the angular frequency, indicates the wave number, is the zeroth order Bessel function, and is the vertical component of the stacked NCF in the frequency domain of two stations separated at . They further demonstrated that the highlighted parts of the F-J spectrum corresponded to dispersion curves. Based on this property of , they developed the F-J method to extract dispersion curves from the image. In this study, to extract dispersion curves from NCFs, we apply the F-J method and a relevant python package CC-FJpy as described by Li et al. (2021).
2.2 Inversion
It has been reported that is more sensitive to the dispersion curve than and density (e.g., Xia et al., 1999; Xia et al., 2003; Pan et al., 2019). To reduce uncertainty, we use empirical relations proposed by
We adopt the inversion algorithm proposed by Pan et al. (2019) to invert the structure parameterized as a 1D multilayered model, which is divided into dozens of homogeneous elemental layers with fixed thickness, and the only unknown parameters to be inverted are the values in each elemental layer. Therefore, the dimension of is the total number of elemental layers. The misfit function of our inversion is formulated as follows:where and are the indices for modes of dispersion curves and the sampled frequency points, respectively; is the synthetic phase velocity; is the observed phase velocity; is the weight of the dispersion curve for th mode; is the number of modes of the dispersion curve; and are the currently inverted and the initial , respectively; is a regularization item to smooth the inversion process avoiding overfitting. In this study, the damping factor is 0.02 near the maximum curvature of the L-curve (e.g.,
The reference model (Supplementary Figure S1) is derived from the average model of Li and Detrick (2006) and the crustal model of
FIGURE 2

F-J spectra and inversion results. (A) Icelandic average F-J spectrum obtained by the F-J method in the frequency domain. The cyan solid line denotes the phase velocity bandwidth (0.008–0.050 Hz) obtained by Li and Detrick (2006), the red solid line (0.040–0.250 Hz) is the group velocity bandwidth (
3 Data processing and results
3.1 Data and the F-J spectra
We apply the vertical component of continuous seismic data recorded by 44 broadband stations across Iceland to analyze the average structure of Iceland. Thirty stations of the XD array (HOTSPOT experiment, red triangles in Figure 1) were operated from July 1996 to July 1998 (e.g.,
Cross-correlation processing steps similar to those proposed by
We apply CC-FJpy (Li et al., 2021) to acquire the F-J spectra (Figures 2A,B) from NCFs, and the fundamental mode dispersion curve could then be extracted from the peak values of the spectra. Figure 2A shows comparisons of the frequency bandwidth of dispersion curve with those of previous studies in this area. Our dispersion range, represented by the blue solid line (0.020–0.285 Hz), has a good balance between high and low frequency ranges. We also extract the dispersion curve of the first higher-mode ranges from 0.343 to 0.403 Hz. Some dispersion points with a period of 20–50 s obtained by Li and Detrick (2006) are projected onto the periodic domain F-J spectrum (Figure 2B), which shows some consistency in the dispersion information obtained from both studies.
3.2 The average S-wave structure
The fundamental dispersion curve is used to invert the average S-wave structure of Iceland (Figures 2C,D), and points with frequencies lower than 0.06 Hz are reserved more densely to provide deeper constraints. We calculate the theoretical dispersion curves of multimodes (blue dots in Figure 2A) of the final model in Figure 2C based on the theory of generalized reflection and transmission coefficients (
To analyze the sensitivity of for dispersion curves of the first two modes at the determined frequency range, we calculate the depth and frequency distribution sensitivity kernel function of the dispersion curves (
FIGURE 3

Sensitivity analysis: the variations of the partial derivatives of Rayleigh wave first two mode phase velocity relative to Vs with depths and frequencies. The sensitivity of the fundamental mode at the point of 0.02 Hz and 120 km, ∼0.015, is identified by a black line in the color bar. Here, C is the phase velocity. (A) Sensitivity for the fundamental mode dispersion curve (black line). (B) Sensitivity for the first higher-mode dispersion curve (black line). (C) Sensitivity curves for the fundamental mode dispersion curve at 25, 30, 40, and 50 s.
There are some corrections both on the amplitude of the crustal LVZ and the velocity structure above ∼20 km from the constrained model without the first higher-mode (green line in Figure 4A) to the model with the first higher-mode constraint (red line in Figure 4A), which coincide with the sensitivity distribution (Figure 3B). The theoretical dispersion curves computed from the estimated model in Figure 2C correlate well with the fundamental mode energy peak of the F-J spectrum, while there are some differences between the theoretical and observed results for the first higher-mode (blue dots in Figure 2A). This inconsistency may be due to insufficient fundamental mode constraints. Theoretical dispersion curves computed from the estimated model in Figure 2E show a good agreement with the first two modes’ energy peaks of the F-J spectrum (green dots in Figure 2A).
FIGURE 4

(A) Comparisons among average structures constrained by the fundamental mode (green line), first two modes (red line), Icelandic average model (black dashed line) from Li and Detrick (2006), and ak135 model (gray dotted line,
Our model has good agreement with the result of Li and Detrick (2006) on the LVZ below ∼55 km (Figure 4A), and this LVZ may suggest partial melt in the Icelandic plume head (
3.3 The S-wave structures of two subregions
To provide more evidence on the distribution and origins of the crustal LVZ found in our average model, we capture the velocity structures of two subregions. One located outside the volcanic zone is covered by eight stations from the XD array and the station BORG (Figure 5A), while another one located in the volcanic zone has nine stations from the XD array and 13 stations from the Z7 array (Figure 5B). Similar to the analysis of the average structure, we use the F-J method to obtain the dispersion spectra from the ambient noise data here. Multimodal dispersion curves are obtained to invert the structures of subregions, and the theoretical dispersion curves of final models are also projected into the spectra.
FIGURE 5

Stations coverage of subregions. (A) Subregion outside the volcanic zone is covered by the XD array (red angles) and station BORG (blue angle). (B) Subregion in the volcanic zone is covered by the XD array (red angles) and Z7 array (purple angles).
We have extracted the fundamental mode dispersion curves both from the F-J spectrum outside the volcanic zone (0.045–0.339 Hz, Figure 6A) and in the volcanic zone (0.041–0.255 Hz, Figure 7A), and the first higher-mode dispersion curve (0.372–0.434 Hz, Figure 7A) from the latter. It should be noted that the suddenly decreased phase velocity of the fundamental mode dispersion peak energy above ∼0.27 Hz in the volcanic zone (Figure 7A) may be caused by severe variations in the shallow structure, which cannot be represented by a 1-D model integrating with the deep structure. Taking into account that the sudden change part only occupies a small portion of the total dispersion energy, we eliminate it and integrate the shallow and the deep structures with a 1-D model. The inversion results show that there are crustal LVZs in both subregions. The amplitude of the LVZ with ∼4.6% in the volcanic zone (Figure 7B) is greater than that with ∼1.5% outside the volcanic zones (Figure 6B) (e.g.,
FIGURE 6

F-J spectrum and inversion results from the subregion outside the volcanic zone. (A) F-J spectrum and theoretical dispersion curves (blue dotted lines) calculated from the fundamental mode constraint. (B) Inversion results and standard deviation () of each layer. (C) Fitting between the observed dispersion curves (red dots) and theoretical dispersion curves (dark lines).
FIGURE 7

F-J spectrum and inversion results from the subregion of the volcanic zone. (A) F-J spectrum and theoretical dispersion curves, including the blue and cyan dotted lines calculated from the fundamental and the first two mode constraints, respectively. (B) Inversion results and standard deviation () of each layer. (C) Fitting between the observed dispersion curves (red dots) and theoretical dispersion curves (dark lines).
3.4 Travel time comparison
To test the rationality of the Icelandic average model, we select four earthquakes on or offshore Iceland in 1997 (yellow stars in Figure 8A, event parameters are shown in Table 1). Primary waves of these four earthquakes have high SNRs, which ensure the determination of primary wave real onset is reliable. Meanwhile, twenty ray paths of primary waves recorded by selected stations of the XD array show a good coverage for the whole of Iceland (Figure 8A).
FIGURE 8

Comparison of various travel time calculated from different models and ray paths. (A) Distribution of different ray paths and natural earthquakes in Iceland are indicated as black solid lines and yellow stars, respectively. The increasing number represents the gradual increase of path distances, and the letters marked on the stars are event codes. The path combinations of earthquakes and stations can be seen in the Supplementary Table S1. (B) Travel time residuals compared to the observed primary wave travel time are calculated from the ak135 model (
TABLE 1
| Code | Date | Time (UTC) | Latitude () | Longitude () | Depth (km) | Magnitude (mb) |
|---|---|---|---|---|---|---|
| A | 1997-04-12 | 23:04:44 | 64.0231 | 21.3652 | 10.0 | 4.1 |
| B | 1997-07-22 | 16:21:41 | 66.3101 | 18.3981 | 10.0 | 4.7 |
| C | 1997-08-24 | 03:04:22 | 63.9422 | 21.2948 | 10.0 | 4.8 |
| D | 1997-09-20 | 15:51:49 | 66.2503 | 18.3403 | 10.0 | 4.6 |
Event parameters for the four local earthquakes used in this study.
We use the TauP tool (
4 Discussion
4.1 Tests for the crustal LVZ
The minimal velocity of the crustal LVZ between 12 and 22 km (red line in Figure 4A) is 3.89 km/s, which is approximately 3% lower than the velocity of 4.01 km/s above the LVZ. We also conduct a series of tests to estimate the reliability of the LVZ. For instance, the anomaly is substituted with an incremental structure to create a model (green line in Figure 9A), whose theoretical dispersion curves are shown in Figure 9B (green dots) and deviate from the energy peak at 0.04–0.14 Hz. However, the theoretical dispersion curves of the original model fit well with the energy peak (blue dots in Figure 9B); thus, the existence of the LVZ in this average model is robust. To detect anomaly resolution, the LVZ is reduced to 2% creating a new model (blue line in Figure 9A), and the inversion results of the first 60 km using theoretical dispersion curves of this model are shown in Figure 9C. The same frequency points of theoretical dispersion curves as those of the dispersion curves in Figure 2 are used to invert, and all other inversion parameters are consistent with those used in Figure 2. Similarly, we compare the original model equipped with LVZ at 3% with the models inverted using the theoretical dispersion curves (Figure 9D). It is observed that the LVZ at 2% (red line in Figure 9C) can be recovered mostly only under the constraint of the fundamental mode dispersion curve (green line in Figure 9C), and the LVZ and shallow structures can be further recovered after the addition of the first higher-mode (blue line in Figure 9C). The same conclusions are obtained for the LVZ at 3%. Therefore, these tests suggest that it can distinguish the LVZ at 3%, especially under the joint constraints of the first two mode dispersion curves.
FIGURE 9

Crustal LVZ and model recovery tests of the Icelandic average Vs model. (A) Original model with an LVZ at 3% (red line), a new model with an LVZ at 2% (blue line), and an increasing model (green line). (B) Theoretical dispersion curves computed from the original (blue dots) and increasing models (green dots) are projected on the average F-J spectrum. (C) Comparisons among the new model with an LVZ at 2% (red line) and the models inverted by its theoretical dispersion curves of the fundamental mode (green line) and first two modes (blue line). (D) It is the same as Figure 9C; however, the model has an LVZ at 3%.
4.2 Icelandic average crust and low-velocity anomalies
The upper crust exhibits high-velocity gradients of up to ∼0.17 until the depth of ∼10 km. Nevertheless, the comparison between low-velocity gradients of 0.03 in the mid-lower crust and those of 0.008 in the top 30 km of the uppermost mantle defines the boundary between the crust and the mantle (BCM) at a depth of ∼32 km. In addition, we refer to our average model at 10–22 km depths as the middle crust including an LVZ. The high-velocity gradients of the Icelandic upper crust are generally considered to be due to the reduction of porosity caused by the closure of fractures under lithostatic pressure and the infilling of secondary minerals, as well as the dense parts of unconsolidated lava piles in the upper crust (e.g.,
Abundant receiver function works in Iceland (e.g.,
5 Conclusion
Based on ambient noise analysis, we use the F-J method to successfully extract Rayleigh phase velocity dispersion curves of the fundamental mode (0.020–0.285 Hz) and first higher-mode (0.343–0.403 Hz) from the continuous broadband ambient noise data recorded at the XD array and some supplement stations in Iceland. Following this, we obtain the average structure down to 120 km depth in Iceland by using multimode dispersion measurements. We observe a crustal LVZ at a depth of 12–22 km, which supplements the characteristics of the Icelandic average crust. We also image the crustal structures in a volcanic zone and a non-volcanic zone, which reveals similar crustal LVZs in both subregions. Considering the gabbro of the middle crust with a lower velocity than that of ultrabasic cumulates at the base, acid intrusion bodies, and high-velocity layer in the upper crust of Iceland, the crustal LVZ may be caused by the lithological composition variations of the crust and the high temperature under the central volcanoes.
Using the changes of the Vs gradient, we also divide the average structure into three parts: upper crust above 10 km depth; middle crust down to 22 km depth, including an LVZ; and the lower crust in the depth range of 22–32 km. The LVZ at 55 km depth below the lithosphere can be regarded as the beginning of the asthenosphere. In addition, we conduct systematic tests to verify the reliability of the crustal LVZ in our average model, which further reveals that the minimum of LVZ is approximately 3% slower than that at the beginning depth of this LVZ. Furthermore, the residual of the predicted primary wave travel time by our model relative to the observed data is smaller than those of other average models, which better supports our average model.
Statements
Data availability statement
Datasets for this research are provided by the Incorporated Research Institutions for Seismology (IRIS) from the XD Array (HOTSPOT experiment) (https://doi.org/10.7914/SN/XD_1996, Nolet, 1996), Z7 Array (Northern Volcanic Zone) (https://doi.org/10.7914/SN/Z7_2010, White, 2010), BORG GSN (https://doi.org/10.7914/SN/II, Scripps Institution of Oceanography, 1986), and YA Array (Torfajökull 2005) (http://www.fdsn.org/networks/detail/YA_2005/, Nordic Volcanological Institute, 2005). The earthquake parameters used in this study are supported by IRIS (http://ds.iris.edu/wilber3/find_event). The packages for the F-J method, inversion, and seismic travel time calculation are available in the following references: Li et al. (2021) (https://doi.org/10.1785/0220210042), Pan et al. (2019) (https://doi.org/10.1093/gji/ggy479), and
Author contributions
The specific contributions of each author can be described as follows. Conceptualization: SZ, GZ, XF, and XC; methodology: ZL, LP, JW, and XC; formal analysis: SZ, GZ, XF, and XC; investigation: SZ, GZ, XF, and XC; resources: XC; data curation: SZ and GZ; writing—original draft preparation: SZ; writing—review and editing: XF, ZL, and XC; visualization: SZ, XF, LP, and JW; supervision: XC; project administration: XC; funding acquisition: XC. All authors read and approved the final manuscript.
Funding
This research was supported by National Natural Science Foundation of China (Grant Nos. 41790465 and 92155307), Key Special Project for Introduced Talents Team of Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou) (GML2019ZD0203), Shenzhen Science and Technology Program (Grant No. KQTD20170810111725321), and Shenzhen Key Laboratory of Deep Offshore Oil and Gas Exploration Technology (Grant No. ZDSYS20190902093007855).
Conflict of interest
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.
Publisher’s note
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.
Supplementary material
The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/feart.2022.1008354/full#supplementary-material
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Summary
Keywords
Iceland, crust, S-wave low-velocity zone, ambient noise tomography, frequency-Bessel transform method
Citation
Zhang S, Zhang G, Feng X, Li Z, Pan L, Wang J and Chen X (2022) A crustal LVZ in Iceland revealed by ambient noise multimodal surface wave tomography. Front. Earth Sci. 10:1008354. doi: 10.3389/feart.2022.1008354
Received
31 July 2022
Accepted
16 August 2022
Published
28 September 2022
Volume
10 - 2022
Edited by
Weijia Sun, Institute of Geology and Geophysics (CAS), China
Reviewed by
Xiaoming Xu, China Earthquake Administration, China
Shaolin Liu, Ministry of Emergency Management, China
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Copyright
© 2022 Zhang, Zhang, Feng, Li, Pan, Wang and Chen.
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.
*Correspondence: Xiaofei Chen, chenxf@sustech.edu.cn
This article was submitted to Solid Earth Geophysics, a section of the journal Frontiers in Earth Science
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