Abstract
A novel inter-disciplinary methodology for the generation of rock property and AVO feasibility maps or cubes to be used in subsurface characterization and prospect de-risking is presented. We demonstrate the workflow for 1D, 2D and 3D cases on data from the North Sea and the Barents Sea, offshore Norway. The methodology enables rapid extrapolation of expected rock physics properties away from well control along selected horizons, constrained by seismic velocity information, geological inputs (basin modeling, seismic stratigraphy and facies maps) and rock physics depth trend analysis. In this way, the expected rock physics properties of a reservoir sandstone (saturated with any pore fluid) can be predicted at any given location between or away from existing wells while honoring rock’s burial and thermal history at this same location. The workflow should allow for more rapid, seamless and geologically consistent subsurface mapping and de-risking of prospects in areas with complex geology and tectonic influence. The AVO feasibility results can furthermore be utilized to generate non-stationary training data for AVO classification.
Introduction
One of the key tasks within the field of geoscience is to obtain a better understanding of the subsurface using remote sensing techniques and/or selected modeling tools. Various geophysical data and observables are acquired to characterize or map the subsurface. In particular, seismic data have been utilized in great abundance for both petroleum exploitation and aquifer characterization (e.g., ; ; ). However, these data are often expensive to acquire, and the seismic data need to be converted to geological properties via rock physics relations. In this study, we propose a methodology to create a 3D subsurface feasibility model for rock properties constrained by local geology (e.g., available interpreted seismic stratigraphic horizons). This modeling can give valuable information before new or additional seismic data are acquired to decide whether certain types of data will be beneficial or not at a given depth (for instance, pre-stack data are only useful if we expect to see AVO signatures in a given area/target level). Furthermore, the feasibility modeling can constrain the pre-processing, imaging and inversion of seismic data. Finally, they can be used to help guide the quantitative seismic interpretation.
Another aspect that we would like to focus on in this study is that future oil and gas exploration will likely focus on increasingly more subtle stratigraphic and/or combination traps located down-flank or up-dip from drilled/explored structures (e.g., ; ). Quantitative seismic interpretation () will be essential in hunting for new prospects away from existing wells. A key challenge will be to do facies and fluid classification/prediction from seismic data away from existing well control, especially in areas characterized by complex tectonic history. Rock physics combined with stratigraphic interpretation and basin modeling can improve the understanding of expected seismic signatures and create augmented elastic training data for AVO classification using machine learning methods (e.g., ; ).
This study presents an innovative and seamless workflowwhere rock physics combined with burial history is used to create AVO feasibility maps away from well control. The methodology is a culmination of several studies conducted in the past few years. showed how to combine rock physics and diagenetic modeling to predict expected AVO signatures for a given burial history (1D), and and showed how this method could be combined with seismic velocities to obtain calibrated net-erosion (exhumation) maps, where net-erosion is the difference between maximum burial and present-day burial depth. , demonstrated a new workflow where rock physics combined with burial history, the latter determined from net erosion maps, was used to create AVO feasibility maps/cubes away from well control (i.e., in 2D and 3D). First, combined rock physics and compactional modeling are integrated with seismic velocities and basin modeling to create regional uplift and maximum burial maps for selected horizons/intervals. Next, geologically consistent AVO feasibility maps/cubes are created from these maximum burials and net erosion maps, while also honoring key uncertainties (rock texture, mineralogy, heterogeneity, anisotropy, temperature, etc.). This is possible because the uplift and maximum burial maps constrain the modeling of sand and shale depth trends at any given location. These depth trends are then used to estimate the expected AVO signatures for shale-sand interfaces at any given depth. The feasibility maps/cubes can be used directly during prospect maturation and de-risking. Furthermore, they can be used as a fundament to create augmented, non-stationary training data for AVO classification and seismic reservoir prediction in areas with poor well control (c.f. ).
In this paper, the focus is on how we go from 1D combined rock physics and burial modeling to 2D and 3D feasibility maps/cubes that can be created in real-time for multiple scenarios, where we honor variability and uncertainties in key geological parameters, including grain size, clay content, temperature history, etc. We provide an overview of the suggested workflow and demonstrate the potential of this methodology in selected areas of the Barents Sea, where the geology is complex due to spatially varying burial and uplift history. Finally, we suggest some best practices to validate the methodology and assess the uncertainties in the AVO feasibility maps.
Geologically Consistent Rock-Physics Modeling
One of the most common methodologies in rock physics is investigating the relationships between seismic velocities and rock texture (i.e., porosity, clay, cement, grain size, etc.). The goal is either to interpret observed data in terms of geological factors, like clay content, rock texture, pressure or pore fluid saturations, or to be able to extrapolate from the data observations to predict certain “what-if” scenarios.
Figure 1 shows some useful rock physics models for high porosity sands and sandstones (sst) (; , ) used to quantify geologic trends and rock texture in the velocity vs. porosity domain. The models in Figure 1 (black lines) are based on contact theory combined with modified Hashin-Shtrikman (see also ). A steep trend in this crossplot will indicate a diagenetic trend, as quartz cement at grain contacts will significantly stiffen the rock frame, even though porosity will not reduce much. This trend can be modeled using the Dvorkin-Nur contact cement model (). As cement is filling macro-porosity, the model can be extrapolated to lower porosities using modified upper Hashin-Shtrikman bound. The friable sand model is a combination of Hertz-Mindlin contact theory at high porosity end member and modified lower-bound Hashin-Shtrikman for decreasing porosities. The constant cement model is a combination of the contact cement model to a certain cement volume, and a lower-bound Hashin-Shtrikman. This is a useful model for a cemented sandstone reservoir at a given burial depth, assuming cement volume is more or less constant. In contrast, porosity at a given depth will vary as a function of depositional porosity. The model equations used in this study are found in or .
FIGURE 1
For unconsolidated sediments, mechanical compaction is handled via empirical relationships between porosity and burial depth (e.g.,
where ϕ is the porosity at burial depth z, ϕ0 is the depositional porosity (i.e., critical porosity) at the sea-floor (z = 0), and k is a compactional coefficient [m–1]. Both the depositional porosity and the constant k will vary depending on lithology and clay content. Equation 1 can be modified to include clay content in sandstones (see
Quartz cementation will typically start at temperatures around 70 °C, which generally corresponds to a burial depth of around 2 km.
where
- •
Vcemi, Vcem(i−1) [–]: cumulative quartz cement volume fraction precipitated from t = 0 s to t = ti, and from t = 0 s to t = t(i–1), respectively,
- •
ϕ0cc [–]: porosity at the start of cementation,
- •
M [g/mol]: molar mass; the value used for quartz is Mqz = 60.09 g/mol,
- •
A(i–1) [cm2]: cumulative quartz surface area at t = t(i–1),
- •
ρma [g/cm3]: (quartz) matrix density,
- •
a, b: constant with a = 1.98⋅10–22 mol/(cm2s) and b = 0.022 1/C,
- •
ci [°C/s]: heating rate of the i-th segment, estimated from burial/thermal history curves for different stratigraphic intervals,
- •
di [°C]: initial temperature of the i-th segment of the burial/thermal history curve under scope.
Figure 2 (
FIGURE 2

Combined burial (mechanical and chemical compaction) and rock physics modeling using contact theory. The end-points in red represent the present-day properties, whereas the light blue curves show the rock physics properties as a function of geological time. The modeled rock represents a Tertiary age sandstone deposited 60 Ma ago that reached the chemical compaction domain (>70°C) around 30 Ma ago, then maximum burial around 25 Ma ago before the rock was exposed to tectonic uplift (which would also erode a significant part of the overburden) and is presently buried at 2 km beneath the sedimentary surface. The various subplots show the combined burial and rock physics modeling sensitivity to various input geological parameters, comprising clay coating, grain size (D), and sorting (via varying critical porosity).
where
- •
f [–]— a fraction of detrital quartz
- •
V [cm3]—a unit volume of the sandstone
- •
D [cm]—a diameter (size) of the idealized sand sphere (grain)
- •
coat [–]—a fraction of coated quartz grains
Then, the quartz surface area, A, when Vcem volume fraction of quartz cement has precipitated, is calculated as:
Equation 4 mathematically expresses that the change in quartz surface area caused by precipitation of quartz cement is proportional to the porosity loss caused by quartz precipitation.
In particular, we see that grain size is an important parameter that will affect the cement volume, as it directly affects the specific surface area available for quartz overgrowths. Smaller grain size will have a larger specific surface area than larger grains (e.g.,
1D AVO Modeling Constrained by Burial History at Well Locations
The one-dimensional modeling of rock physics properties of sandstones and shales as a function of burial depth in continuously subsiding basins was first presented by
FIGURE 3

Combined burial and rock physics modeling for a Jurassic sandstone with continuous subsidence. Note the drastic change in rock-physics, and seismic properties as the burial goes from mechanical to chemical compaction domain (>ca. 70°C).
Figure 4 shows another synthetic example, where the burial history includes an uplift episode. Note that the maximum burial happens around 35 Ma ago, at ca. 2.1 km below the sea-floor. The dashed horizontal line in all five upper subplots indicates the 70°C thermocline where we assume that quartz cementation commences. The cementation happens both during subsidence and exhumation as long as the temperatures are higher than ca. 70°C (
FIGURE 4

Combined burial and rock physics modeling for a Cretaceous sandstone with Cenozoic tectonic uplift. Note the drastic change in rock physics, and seismic properties as the burial goes from mechanical to chemical compaction domain (>ca. 70°C indicated by the dashed horizontal line).
Figure 5 shows a real data example of 1D AVO feasibility modeling performed at a well (15/5-5) in the Glitne Field, North Sea (see
FIGURE 5

Combined burial and rock physics modeling for Paleocene sandstones in Well 15/5-5 in the Glitne Field, North Sea. Note the change in elastic properties as we go from mechanical to chemical compaction at around 2,000 m burial depth (indicated by dashed brown horizontal line). The expected AVO signatures change drastically as we go from the Top Heimdal Fm horizon (upper) to the slightly deeper Top Ty Fm horizon (lower). The expected oil response for the Ty Formation is similar to the expected brine response of the Heimdal Formation. This shows the importance of burial history as a key constraint in AVO analysis.
2D AVO Feasibility Modeling (Barents Sea Demonstration)
Deriving Burial History and Net Erosion From Seismic Velocities
The same approach, as described above, can be used to model expected AVO signatures along a given seismic horizon. The burial history can be derived from seismic velocities where a normal compaction curve is defined for an area, and the deviation from this reference trend at a given location will provide information about maximum burial (e.g.,
FIGURE 6

Left: Present-day Base Cretaceous Unconformity (BCU) horizon (which is close to the Top Stø Fm sandstone horizon) in the selected area in the southern Barents Sea (offshore Norway), and selected well locations used in the calibration study (black circles). Right: Estimated net erosion map derived from seismic velocities relative to a normal compaction trend (Adapted from
Temperature gradients vary both spatially and with time. Temperature gradient maps can be used directly as input in the modeling (
Burial-Constrained Modeling of Sandstone Properties
Next, forward modeling of the expected rock physics properties and associated AVO responses for selected scenarios is performed, given the input burial history (Figure 7). The methodology introduced by
FIGURE 7

Combined burial and rock physics modeling for clean sandstone of a Jurassic sandstone with varying burial history at different locations of the map shown in Figure 6. Walderhaug model predicts the cement volume (subplot 2) for a given burial/temperature history (subplot 1), and the porosities are updated accordingly (subplot 3). Eventually, the seismic velocities are predicted using rock physics models (subplot 4). Note that the lighter burial history curves seen in subplot 1 are those that do not enter the cementation window (i.e., the T = 70 oC lower limit), not even at the time of their maximum burial. The corresponding end-points in porosity and VP subplots are marked by lighter orange color to discern them from the (majority of darker) orange points that have been at least slightly cemented. Note also that since the Tgrad varies from point-to-point, the depth of cementation onset can change from one X–Y point to another: this transition from a mechanical compaction domain to a chemical compaction domain for each curve is seen as a horizontal (gray) line in each subplot.
Empirical Shale Trends
Before we can conduct the AVO modeling at any given depth, we also need to establish shale depth trends. The rock physics modeling of shale depth trends is a challenging task. Several rock physics models have been used to model shale depth trends (e.g.,
As of today, there is no good holistic rock physics model to mimic all these complex geologic processes. Hence, we select to estimate empirical regression models for the shales from the well log data. Figure 8 shows the resulting empirical trends for separate key shale intervals and a regression model for all key shale intervals lumped together. We have plotted well log data corrected for uplift, according to the analysis above (i.e., against the maximum burial). We have also superimposed well-known regression models for Norwegian shelf shales published in the literature, including the model by
FIGURE 8

Empirical shale trends. Models for separate shale intervals are shown from left to right, comprising Kolje, Fuglen, and Fruholmen Fm-s. Regression lines are also made for all shale intervals together (rightmost subplot). Published trends by
Elastic Property Feasibility Maps
From the burial-constrained rock physics modeling, we create forward-modeled maps of elastic properties for the Fuglen Fm cap-rock shale and the Stø Fm reservoir sandstones (Figure 9). We test out various scenarios and the sensitivity of important input parameters. Figure 9 shows a scenario where the dominating grain size of sandstones is 0.3 mm (i.e., medium grain size), the pore-filling clay content is 0.1, the temperature gradient is 38°C/km, and the pore fluid is oil. Note the significant imprint of geologic structures and tectonics. This is geologic information brought into the modeling from the seismic velocity data and stratigraphic interpretations. The area in the west has the largest maximum burial, which explains the very high acoustic impedance values (>10 g/cm3⋅km/s). This is an area where we expect very low seismic fluid sensitivity. Eastward, the maximum burial is lower, and in some areas the rocks have not even been cemented (T < ca. 70°C at maximum burial). Here, the impedance values are significantly lower (<10 g/cm3⋅km/s), and we would expect better seismic detectability of oil.
FIGURE 9

Elastic property feasibility maps for a given geological scenario. Upper: Expected acoustic impedance and VP/VS of cap-rock Fuglen Fm shale; Lower: Expected acoustic impedance and VP/VS for brine-filled reservoir sandstone of Stø Fm. Note that these maps are modeled values for shales and sandstones constrained by the burial maps (i.e., net erosion) in Figure 6, which are again derived from the seismic velocity data.
AVO Feasibility Maps
Next, we create the AVO feasibility maps (Figure 10) from the elastic property maps, using full Zoeppritz modeling (
FIGURE 10

AVO feasibility maps, including AVO classes for brine saturated sandstones (left) and oil-saturated sandstones (right). Regional AVO feasibility maps that show significant geologic imprint on the expected AVO classes of different fluid scenarios.
3D AVO Feasibility Cubes (Barents Sea Demonstration)
Finally, we perform a full 3D modeling of rock physics properties and associated AVO feasibility cubes. We extrapolate between 2D maps using compaction/depth trends honoring the burial history at any given location. In this way, we can forecast the expected rock physics properties of a given rock, sandstone or shale, at any given location of a 3D cube, while honoring the burial (and thermal) history of the rock at this same location. By combining the elastic properties of sandstone and shale cubes, we can generate the so-called AVO feasibility cubes (in 3D) that predict the expected AVO response for a given pore fluid at any location in the cube.
Figure 11 shows a 3D AVO feasibility cube and associated rock properties, and we focus on a Tertiary age target interval, the Intra Torsk Fm sandstones of Paleocene/Eocene age, in a selected area in the Barents Sea. These sands are located in a deep-marine setting. As Figure 11 shows, we expect no quartz cementation in these sands toward the top of the formation, based on our modeling. This is because the sands have never reached a depth where temperatures are large enough (greater than ca. 70°C) to form quartz cement. However, we need to honor the mechanical compaction with porosity reduction and increasing effective stress with depth. The shale depth trends used for the AVO feasibilities in the Torsk Fm interval, are empirical trends derived from intra Torsk shales in nearby wells. We see that mainly AVO class 3 is expected for oil-filled Torsk Fm sands, whereas brine sands (not shown here) will give a class 1.
FIGURE 11

Rock property and AVO feasibility cubes in a selected area of the Barents Sea. Oil-filled Tertiary sands show mostly class 3 AVO response in the area, and cement volume is 0, as the sands are not buried deep enough to be cemented (figure adapted from
Validation and Uncertainty Assessment of AVO Feasibilities
The resulting AVO feasibility maps/cubes should be validated against real data observations, if available. The water-saturated signatures are often well constrained by the fact that most of the subsurface is indeed water-filled. The observed brine-filled AVO response in a down-flank area of a prospective structure, where one knows there must be water-filled sandstones, should match the modeled AVO brine response for this location. Furthermore, blind-well validations of expected rock properties and AVO signatures should be conducted if there are several wells inside the area of interest. If there is a mismatch with the observed (pre-stack seismic or well log) data, the AVO feasibility modeling input must be updated. In a scenario-based modeling, geological parameters like facies, grain size, temperature gradient, clay content, etc., can be edited. This exercise should be done in integrated teams with input from domain experts covering a range of different geological constraints (basin modeling, sedimentology, geochemistry). Note that the AVO feasibility maps could also highlight the poor quality or insufficient pre-conditioning of the seismic data.
Regardless of any validation, there are uncertainties associated with the AVO feasibility maps related to both geological variability and modeling bias/ambiguities (i.e., input parameters and model assumptions). The key geological uncertainties include uncertainties in burial history and net erosion from seismic velocities, both associated with the choice of shale reference trend and the seismic interval velocities. However, this information is better than no information and linear interpolation between wells. Furthermore, we can test uncertainties in uplift and how they will affect the AVO feasibility maps. Another key geological uncertainty is associated with the assumed sandstone texture for different intervals, including grain size, clay volume, sorting, and clay coating. Temperature gradients and their variation in space and time can also significantly impact the AVO feasibility maps/cubes. This variation can be associated with distances to the basement craton. It could also be related to tectonic uplift processes and the timing of uplift. One of the best ways to mitigate temperature-gradient-related uncertainties is to perform a probabilistic tectonic heat flow modeling (
In the 2D AVO feasibility map generated above, we focused on a scenario with a spatially constant temperature gradient of 38°C/km. Figure 12 shows a test where we simulate AVO feasibility maps for several cases where we vary the temperature gradient. Then, we test how this will affect the AVO classification for different fluid scenarios. Interestingly, we see that the classes stay constant regardless of temperature gradient in some parts of the map, but will change in other parts.
FIGURE 12

Uncertainty assessment of AVO feasibility maps testing a range of constant temperature gradients. The white areas in the three lower subplots indicate where AVO classes do not change (i.e., low uncertainty). In contrast, the gray areas indicate where AVO classes will change within this temperature range (i.e., higher uncertainty).
It should also be mentioned that we have used default values for brine, oil and gas in this study. These may indeed vary spatially and with burial depth (fluid pressure effect that will change with burial depth is accounted for already). Variability in salinity, oil API/GOR and gas gravity represents uncertainties that could be handled via scenarios or sensitivity studies, but in this study, we consider the variability of these properties to be second-order compared to other geological uncertainties.
Conclusion
We have demonstrated a new integrated workflow for generating AVO feasibility maps/cubes with data from the Barents Sea. The methodology enables rapid extrapolation of expected rock physics properties away from well control, along selected horizons, constrained by seismic velocity information, geological inputs (basin modeling, seismic stratigraphy and facies maps) and rock physics depth trend analysis. The workflow should allow for more rapid, seamless and geologically consistent DHI de-risking of prospects in areas with complex geology and tectonic influence. The AVO feasibility maps can furthermore be utilized to generate non-stationary training data for AVO classification.
Statements
Data availability statement
The data analyzed in this study is subject to the following licenses/restrictions: Confidential seismic velocity data have been used to generate maps/cubes. Well log data used in this study are released through Norwegian Petroleum Directorate, but permission requires membership of their Diskos database. Requests to access these datasets should be directed to www.npd.no/en/diskos.
Author contributions
PA did concept and rock physics. IL did coding and implementation. Both authors have contributed equally.
Acknowledgments
We thank Spirit Energy and partners of license PL962 on the Norwegian Continental Shelf for data and financial support for this study.
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.
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Summary
Keywords
rock physics, subsurface characterization, AVO modeling, exploration, basin analysis/modeling
Citation
Avseth P and Lehocki I (2021) 3D Subsurface Modeling of Multi-Scenario Rock Property and AVO Feasibility Cubes—An Integrated Workflow. Front. Earth Sci. 9:642363. doi: 10.3389/feart.2021.642363
Received
15 December 2020
Accepted
23 February 2021
Published
15 March 2021
Volume
9 - 2021
Edited by
Jing Ba, Hohai University, China
Reviewed by
José M. Carcione, National Institute of Oceanography and Experimental Geophysics (OGS), Italy; Da Shuai, China University of Petroleum, China
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Copyright
© 2021 Avseth and Lehocki.
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: Per Avseth, per.avseth@digsciene.no; per.aage.avseth@gmail.com
This article was submitted to Solid Earth Geophysics, a section of the journal Frontiers in Earth Science
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