3D Earth Model Research Articles

Multilevel Algorithm for Large-Scale Gravity Inversion

Surface gravity inversion attempts to recover the density contrast distribution in the 3D Earth model for geological interpretation. Since airborne gravity is characterized by large data volumes, large-scale 3D inversion exceeds the capacity of desktop computing resources, making it difficult to achieve the appropriate depth/lateral resolution for geological interpretation. In addition, gravity data are finite and noisy, and their inversion is ill posed. Especially in the absence of a priori geological information, regularization must be introduced to overcome the difficulty of the non-uniqueness of the solutions to recover the most geologically plausible ones. Because the use of Haar wavelet operators has an edge-preserving property and can preserve the sensitivity matrix structure at each level of the multilevel method to obtain faster solvers, we present a multilevel algorithm for large-scale gravity inversion solved by the re-weighted regularized conjugate gradient (RRCG) algorithm to reduce the inversion computational resources and improve the depth/lateral resolution of the inversion results. The RRCG-based multilevel inversion was then applied to synthetic cases and airborne gravity data from the Quest-South project in British Columbia, Canada. Results from synthetic models and field data show that the RRCG-based multilevel inversion is suitable for obtaining density contrast distributions with appropriate horizontal and vertical resolution, especially for large-scale gravity inversions compared to Occam’s inversion.

On the Stability of Mantle‐Sensitive P‐Wave Interference During a Secondary Microseismic Event

AbstractBody wave extraction from oceanic secondary microseismic sources with seismic interferometry provides alternative information to better constrain the Earth's structure. However, sources' spatiotemporal variations raise concerns about travel time measurement robustness. Therefore, we study the cross‐correlations’ stability during a single oceanic event. This study focuses on 3 days of data and three seismic arrays' combinations between 8 and 11 December 2014 during storm Alexandra, a “weather bomb” event in southern Greenland. We use the WAVEWATCH III hindcast to model P‐wave noise sources and assess the impact of short‐term source variations on cross‐correlations. Model‐based cross‐correlations compared to data show coherent delays to reference 3D Earth models (∼0–3 s) confirming the robustness of the source model which could explain minor travel time variations (≤1 s).

Grounded source transient electromagnetic 3D forward modeling with the spectral-element method and its application in hydraulic fracturing monitoring

A long wire with large current source transient electromagnetic (TEM) monitoring, with a large detection depth, low cost, safety, and environmental protection, has unique advantages in the testing and identification of unconventional reservoir fluid and the evaluation of stimulated reservoir volume. So, the TEM 3D forward modeling method has become a research hotspot. Although the finite-element method (FEM) is a type of numerical algorithm that has been widely applied in three-dimensional (3D) electromagnetic field forward modeling, the efficiency and accuracy of FEM require further improvement in order to meet the demand of fast 3D inversion. By increasing the order of the basis function and adjusting the principle of mesh discretization, the precision of the mixed-order spectral-element (SEM) result will be increased. The backward Euler scheme is an unconditionally stable technique which can ignore the impact of the scale of the time step. To achieve a better description of the nonlinear electromagnetic (EM) response of the grounded source TEM method and to optimize the efficiency and accuracy/precision of the 3D TEM forward modeling method significantly, we proposed the use of 3D TEM forward modeling based on the mixed-order SEM and the backward Euler scheme, which can obtain more accurate EM results with fewer degrees of freedom. To check its accuracy and efficiency, the 1D and 3D layered models are applied to compare the SEM results with the semi-analytical and FEM solutions. In addition, we analyzed the accuracy and efficiency of the SEM method for different types of order basis functions. Finally, we calculated the long-wire source TEM response for a practical 3D earth model of a shale gas reservoir for fracturing monitoring and tested the feasibility of the TEM method in a hydraulic fracturing monitoring area to further demonstrate the flexibility of the SEM method.

Spectral-infinite-element simulations of seismic wave propagation in self-gravitating, rotating 3-D Earth models

SUMMARY Although observation of gravity perturbations induced by earthquakes is possible, simulation of seismic wave propagation in a self-gravitating, rotating Earth model with 3-D heterogeneity is challenging due to the numerical complexities associated with the unbounded Poisson/Laplace equation that governs gravity perturbations. Therefore, gravity perturbations are generally omitted, and only the background gravity is taken into account using the so-called Cowling approximation. However, gravity perturbations may be significant for large earthquakes (Mw ≥ 6.0) and long-period responses. In this study, we develop a time-domain solver based on the spectral-infinite-element approach, which combines the spectral element method inside the Earth domain with a mapped-infinite-element method in the infinite space outside. This combination allows us to solve the complete, coupled momentum-gravitational equations in a fully discretized domain while accommodating complex 3-D Earth models. We compute displacement and gravity perturbations considering various Earth models, including Preliminary Reference Earth Model and S40RTS and conduct comprehensive benchmarks of our method against the spherical harmonics normal-mode approach and the direct radial integration method. Our 3-D simulations accommodate topography, bathymetry, rotation, ellipticity and oceans. Results show that our technique is accurate and stable for long simulations. Our method provides a new scope for incorporating earthquake-induced gravity perturbations into source and adjoint tomographic inversions.

Bridging Computational Stratigraphy and Reservoir Simulation for Geologically Realistic High-Resolution Reservoir Modeling

Summary Computational stratigraphy (CompStrat) is a state-of-the-art Earth-modeling method that captures the key heterogeneities in subsurface reservoirs through modeling of the detailed flow and sediment transportation processes in various depositional environments. The method is fully based on physics and generates high-resolution 3D Earth models that are much more geologically realistic than those generated by traditional Earth-modeling methods. It can accurately predict and preserve those spatially continuous but vertically thin and volumetrically insignificant layers, such as shale layers, thus enabling a much more accurate representation of natural reservoir connectivity. In the past few years, CompStrat has been studied mainly within the Earth science community and has not been broadly applied yet in reservoir simulation research and practices. Our objective is to bridge this gap and allow this frontier technology to offer geologically realistic Earth models for reservoir simulation to better understand how various geological features contribute and control subsurface flow patterns and performance, subsequently leading to better integration among Earth modeling, flow simulation, and more reliable reservoir performance predictions. CompStrat models often have large numbers of cells (hundreds of millions or more). A large proportion of them are related to thin shale layers. These thin cells can often cause convergence difficulties in reservoir simulations. We developed a grid coarsening method to dramatically reduce the cell number and the simulation time with minimal alteration of the overall model connectivity characteristics. The method reduces the cell number by 85% (to 93%) and the simulation time by 94% (to 99%) with limited loss of accuracy for representative examples. Without this method, the simulation may take impractically long time to run for large models with complex multiphase flow dynamics. The successful removal of the computational bottleneck enables the application of this frontier Earth-modeling method in high-fidelity reservoir simulation. It also facilitates a detailed understanding of the connection between geology and flow to offer valuable insight for reservoir modeling, production forecast uncertainty analysis, and history matching. We developed a method to label, evaluate, and rank geological features based on their influence on flow performance, with shale layers being the specific focus. The labeling is performed semiautomatically, and the evaluation and ranking are done efficiently with a reduced-physics solver. The result is statistically consistent across multiple realizations. The fluvial-deltaic CompStrat sector model on which our grid coarsening and shale analysis methods were tested is shared in the Supplementary Materials.

Hypocenter, Fault Plane, and Rupture Characterization of Australian Earthquakes: Application to the September 2021 Mw 5.9 Woods Point Earthquake

AbstractThe Australian Seismometers in Schools (AuSIS) network operates 50 broadband seismic stations across Australia that are hosted at schools. The instruments augment the Australian National Seismograph Network providing valuable data from urban and regional Australia. The network coverage is quite sparse, but these vital records of rare, moderate Australian earthquakes can improve our understanding of the deformation within the stable continental region of Australia, especially for events with no surface rupture. In this study, we present the feasibility of identifying the fault plane of moderate earthquakes on the Australian continent, using data from the AuSIS network. We examine the fault plane of the September 2021 Mw 5.9 Woods Point earthquake that occurred about 130 km northeast of the Melbourne metropolitan area. We estimate the hypocenter and the centroid moment tensor (CMT) to identify the fault plane from the auxiliary plane in the focal mechanism. We explore a range of 1D models and a 3D Earth model to simulate seismic arrivals and full waveform data. The hypocenter is resolved using P- and S-wave arrivals in a probabilistic framework and the CMT is derived from full waveform modeling through grid search over a set of trial points around the hypocenter. Our solution suggests the mainshock ruptured the depth of 15 ± 4 km, with a strike-slip mechanism striking 348° north on a nearly vertical plane. The high double-couple percentage of this event indicates a simple rupture that propagated from the south (hypocenter) toward the north (centroid) and remained subsurface. This indicates that the causative fault had a deeper structure than the previously known shallow, northwest–southeast-striking faults of the region. The P and T axes deduced from our fault model are notably aligned with the maximum horizontal crustal stress in the region.

The Influence of Sediments, Lithosphere and Upper Mantle (Anelastic) With Lateral Heterogeneity on Ocean Tide Loading and Ocean Tide Dynamics

AbstractOcean tide loading (OTL) and ocean tide dynamics (OTD) are known to be affected by Earth's internal structures, with the latter being affected by the self‐attraction and loading (SAL) potential. Combining the 3D earth models Lyon and LITHO1.0, we construct a hybrid model to quantify the coupled effect of sediments, oceanic and continental lithosphere, and anelastic upper mantle on OTL and OTD. Compared to PREM, this more realistic 3D model produces significantly larger vertical OTL displacement by up to 3.9, 2.6, and 0.1 mm for the M2, K1, and Mf OTL, respectively. Moreover, it shows a smaller vector difference of 0.1 mm and a smaller amplitude difference of 0.2 mm than PREM with OTL observations at 663 Global Navigation Satellite System stations, a confirmation of the cumulative effect due to these earth features. On the other hand, we find a resonant impact of wider extent and larger magnitude on OTD, especially for the M2 and K1 tides. Specifically, this impact is concentrated in the ranges 0–6 mm and 0–1.5 mm for M2 and K1, respectively, which is considerably larger than the impact on SAL (mostly in the ranges 0–2 mm and 0–1.0 mm, respectively). Since the effect on vertical displacement is at a similar level compared to the accuracy of modern data‐constrained ocean tide models that require correction of the geocentric tide by loading induced vertical displacements, we regard its consideration to be potentially beneficial in OTD modeling.

Forward calculation of 3D controlled-source electromagnetic responses based on joint application of secondary field and coupled potential formulations

In the traditional framework of 3D controlled-source electromagnetic (CSEM) modeling, either the field formulation or the coupled potential formulation is implemented. We have developed an improved algorithm that can calculate the 3D CSEM responses based on a joint application of the secondary field and secondary coupled potential formulations. The vector finite-element method is implemented for the discretization of the curl-curl equation of the secondary field. The vector and nodal elements are implemented simultaneously for the discretization of the coupled potential formulation. We use the stiffness matrix resulting from the coupled potential formulation to construct an efficient preconditioner, which is used for the solution of the linear system of equations obtained based on the secondary field formulation. The linear system of the equations could be solved efficiently by the quasiminimum residual method within several hundred iterations with the constructed preconditioner. We compare different modeling schemes to calculate the CSEM responses for a horizontally layered earth model excited by an electric dipole and find that the iteration process of the improved algorithm converges faster on average than other modeling schemes for the frequency band considered. Thus, the least computation time can be obtained over the frequency band for the improved algorithm compared with other modeling schemes, with the same level of accuracy reached. We further verify the efficiency of the algorithm through a small-scale 3D earth model excited by a magnetic dipole. Finally, we illustrate the performance of the algorithm with two 3D subsurface models, including a land-based model and a marine disk model. By comparison with published work, it is illustrated that our algorithm can efficiently calculate accurate land-based and marine CSEM responses with the new constructed preconditioner implemented.

A GNSS velocity field for crustal deformation studies: The influence of glacial isostatic adjustment on plate motion models

SUMMARYThe two main causes of global-scale secular deformation of the Earth are tectonic plate motion and glacial isostatic adjustment (GIA). We create a bespoke global 3D GNSS surface velocity field ‘NCL20’ to investigate tectonic plate motion and the effect of GIA on plate motion models (PMMs), drawing on a set of 1D and 3D GIA model predictions. The main motivation for creating NCL20 is to include a larger number of GNSS sites in the most GIA-affected areas of investigation, namely North America, Europe, and Antarctica. We do this using the IGS repro2 data and other similarly processed GNSS data sets. Our final GNSS velocity field has horizontal uncertainties mostly within ±0.5 mm yr–1 and vertical uncertainties mostly within ±1 mm yr–1 (at 95 per cent confidence), which make it suitable for testing GIA models. We generate a suite of 117 global GIA model predictions by combining three different ice history models (ICE-5G, ICE-6G and W12) with a range of 1D and 3D Earth models. By subtracting this ensemble from the GNSS velocity field, we identify and compare a range of PMMs which are expected to be unaffected by GIA. Our method allows us to include GNSS sites that are typically excluded from PMM estimations due to their location in GIA-affected regions. We demonstrate that significant GIA-related horizontal motion outside of the rapidly uplifting regions may bias PMMs if left uncorrected. Based on their ability to explain the observed surface velocity field, a group of best-performing GIA models is selected for three regions of interest: North America, Europe and Antarctica. The range of GIA predictions in each best-performing group is assumed to represent the uncertainty in regional GIA modelling insofar as it can be constrained by present-day geodetic velocities. In the horizontal component, we note that 3D GIA models show more variation in the direction of predicted velocities than 1D GIA models, confirming that horizontal velocities are strongly sensitive to lateral variations in Earth structure. Furthermore, for Antarctica the variation in predicted GIA vertical velocities suggests that the total GIA contribution to annual gravimetric mass change ranges from –3 to 22 Gt yr–1 depending on which of the best-performing GIA models is used.

Frequency domain electromagnetic and electrical resistivity geophysical investigation of tar sands deposits in the Ijebu Waterside area, Eastern Dahomey Basin, southwestern Nigeria

The use of electromagnetic conductivity and electrical resistivity geophysical techniques has been employed in this study to investigate the occurrence, thickness, and spatial distribution of bitumen deposit around Makun-Omi in the Ijebu Waterside area of southwestern Nigeria. Subsurface apparent conductivity distribution data obtained using Geonic 34-3 equipment along fifteen traverses which sounded from different depths of 7.5, 15, 30 and 60 m at inter-coil separation of 10, 20 and 40 m in vertical and horizontal coupling modes and ground resistivity distribution measurements, obtained using Geopulse Tiger Allied resistivity meter at fourteen Vertical Electrical Sounding (VES) stations, were processed and employed to characterize the subsurface in terms of tar sands distribution. The conductivity and resistivity distribution in the form of a 3D earth model, iso-depth maps, 2D sections generated from the processed conductivity and resistivity data indicate relatively low conductivity <20 mS/m and high resistivity >1300 Ωm values around tar/bitumen impregnated sands which mostly occurred in the southern part of the study area. Clearly defined conductivity and resistivity anomalies which delineate the lateral and vertical occurrence of tar impregnated sands underscore the efficacy of integrating electromagnetic and electrical resistivity geophysical techniques to identify occurrence of economic deposits of tar sands in parts of southwestern Nigeria.

Three-dimensional controlled-source electromagnetic forward modeling by edge-based finite element with a divergence correction

We have developed an edge-based finite-element (FE) modeling algorithm with a divergence correction for calculating the controlled-source electromagnetic (CSEM) responses of a 3D conductivity earth model. We solve a curl-curl equation to directly calculate the secondary electric field to eliminate the source singularity. The choice of the edge-based FE method enables us to properly handle the discontinuity of the normal component of electric fields across conductivity boundaries. Although we can solve the resulting complex-symmetric linear system of equations efficiently by a quasiminimal residual (QMR) method preconditioned with an incomplete Cholesky decomposition for the high-frequency band, the iterative solution process encounters a common problem in the field formulation and does not converge within a practically feasible number of iterations for low frequencies. To overcome this difficulty and to accelerate the iterative solution process in general, we combine a divergence correction technique with the secondary field solution using the QMR solver. We have found that applying the divergence correction intermittently during the iterative solution process ensures the calculation of sufficiently accurate electric and magnetic fields and can significantly speed up the solution process by more than an order of magnitude. We have tested the efficiency and accuracy of our algorithm with 1D and 3D models, and we have found that the divergence correction technique is able to guide the electric field to satisfy the boundary conditions across conductivity interfaces. Although there is a computational overhead required for applying the divergence correction, that cost is significantly offset by the substantial gains in the solution accuracy and speed-up. The work makes the field-based curl-curl formulation using edge elements an efficient and practical method for CSEM simulations.

Deterministic 3D Ground-Motion Simulations (0–5 Hz) and Surface Topography Effects of the 30 October 2016 Mw 6.5 Norcia, Italy, Earthquake

ABSTRACT The Mw 6.5 Norcia, Italy, earthquake occurred on 30 October 2016 and caused extensive damage to buildings in the epicentral area. The earthquake was recorded by a network of strong-motion stations, including 14 stations located within a 5 km distance from the two causative faults. We used a numerical approach for generating seismic waves from two hybrid deterministic and stochastic kinematic fault rupture models propagating through a 3D Earth model derived from seismic tomography and local geology. The broadband simulations were performed in the 0–5 Hz frequency range using a physics-based deterministic approach modeling the earthquake rupture and elastic wave propagation. We used SW4, a finite-difference code that uses a conforming curvilinear mesh, designed to model surface topography with high numerical accuracy. The simulations reproduce the amplitude and duration of observed near-fault ground motions. Our results also suggest that due to the local fault-slip pattern and upward rupture directivity, the spatial pattern of the horizontal near-fault ground motion generated during the earthquake was complex and characterized by several local minima and maxima. Some of these local ground-motion maxima in the near-fault region were not observed because of the sparse station coverage. The simulated peak ground velocity (PGV) is higher than both the recorded PGV and predicted PGV based on empirical models for several areas located above the fault planes. Ground motions calculated with and without surface topography indicate that, on average, the local topography amplifies the ground-motion velocity by 30%. There is correlation between the PGV and local topography, with the PGV being higher at hilltops. In contrast, spatial variations of simulated PGA do not correlate with the surface topography. Simulated ground motions are important for seismic hazard and engineering assessments for areas that lack seismic station coverage and historical recordings from large damaging earthquakes.

Four Years of Earthquake Early Warning in Southern Iberia: 2016–2019

The performance of an earthquake early warning system (EEWS) for southern Iberia during the period of 2016–2019 is analyzed. The software PRESTo (PRobabilistic and Evolutionary early warning SysTem; the University of Naples Federico II, Italy) operating at the Universidad Complutense de Madrid has detected 728 events (2 < Mw < 6.3), with 680 earthquakes occurring in southern Iberia. Differences between the EEWS origin time and epicenter and those of the Instituto Geográfico Nacional (IGN) catalog are less than 2 s and 20 km, respectively, for 70% of the detected earthquakes. The main differences correspond to the EEWS magnitude that is underestimated for earthquakes that occurred at the west of the Gibraltar Strait (Mw differences larger than 0.3 for 70%). To solve this problem, several relationships have been tested, and a modification to those that currently use PRESTo is proposed. Other improvements, such as to densify the network or to use 3D Earth models, are proposed to decrease the time needed to issue the alert and avoid the false alerts (19 events over a total of 728 events). The EEWS has estimated the depth for 680 events and compared to those from the IGN (491 events). The performance of PRESTo during the 2020–2021 Granada swarm is analyzed. The hypocentral locations for the three largest earthquakes are close to those from the IGN (differences from 1 to 7 km for the epicenter and 0 s for the time origin), although there are some differences in their magnitude estimations that varies from 0.2 to 0.5. The PRESTo first times are 17, 25, and 41 s after the origin time. This study shows that the actual PRESTo EEWS configured for the southern Iberia may generate effective warnings despite the low seismicity rate in this region. To decrease the warning time, the geometry and density of the seismic network must be improved together with the use of 3D Earth models and on-site system approaches.

Full-Wavefield, Full-Domain Deterministic Modeling of Shallow Low-Magnitude Events for Improving Regional Ground-Motion Predictions

ABSTRACT At the fundamental level, seismic risk analysis relies on good modeling tools for predicting the ground motion resulting from hypothetical earthquake events, which is traditionally approximated using many variations of ground-motion prediction equations (GMPEs). The main benefit of these equations lies in their low computational cost, allowing one to run Monte Carlo simulations in which event probabilities are dictated by regional catalogs comprising historical observations. These equations, however, rely on approximations that are only accurate in a statistical sense. In this study, we consider cases in which regional high-resolution 3D earth models are available from exploration reflection seismology. These high-fidelity velocity models allow us to perform deterministic elastic ground-motion simulations at local distances, given a prescribed synthetic earthquake event, and compare the results with those predicted by GMPEs. This full-wavefield full-domain modeling approach is significantly more costly and particularly challenging due to the slow shear-wave velocity at the near surface, which requires fine spatial and temporal discretizations. With the aid of powerful computational resources, we use an adaptive mesh generator and an efficient wave solver to model the 3D elastic and anelastic wave propagation from the hypocenter all the way to the ground surface. This approach can simultaneously account for 3D subsurface structures, near-surface site effects, topographic relief, and the radiation pattern of the source. In areas where observations are sparse, the modeling results can fill the gap between stations and provide a test bed that can be used for improving the development and accuracy of GMPEs. This approach is well suited for areas where shallow low-magnitude-induced seismic events can occur. Lastly, to demonstrate our approach, we consider an observed seismic event at the Groningen gas field and compare the recorded ground motions with both—those predicted by our approach and those predicted by GMPEs.

3D mechanical earth model for optimized wellbore stability, a case study from South of Iraq

Wellbore instability issues represent the most critical problems in Iraq Southern fields. These problems, such as hole collapse, tight hole and stuck pipe result in tremendous increasing in the nonproductive time (NPT) and well costs. The present study introduced a calibrated three-dimensional mechanical earth model (3DMEM) for the X-field in the South of Iraq. This post-drill model can be used to conduct a comprehensive geomechanical analysis of the trouble zones from Sadi Formation to Zubair Reservoir. A one-dimensional mechanical earth model (1DMEM) was constructed using Well logs, mechanical core tests, pressure measurements, drilling reports, and mud logs. Mohr–Coulomb and Mogi–Coulomb failure criteria determined the possibility of wellbore deformation. Then, the 1DMEMs were interpolated to construct a three-dimensional mechanical earth model (3DMEM). 3DMEM indicated relative heterogeneity in rock properties and field stresses between the southern and northern of the studied field. The shale intervals revealed prone to failure more than others, with a relatively high Poisson's ratio, low Young's modulus, low friction angle, and low rock strength. The best orientation for directional Wells is 140° clockwise from the North. Vertical and slightly inclined Wells (less than 40°) are more stable than the high angle directional Wells. This integration between 1 and 3DMEM enables anticipating the subsurface conditions for the proactive design and drilling of new Wells. However, the geomechanics investigations still have uncertainty due to unavailability of enough calibrating data, especially which related with maximum horizontal stresses magnitudes.

Seismic Driven Geomechanical Modeling of Uplifted and Subsided Wells in Mumbai Offshore and Its Engineering Implications

Seismic data provide evidence about hydrocarbon deposition, geological and geophysical subsurface information, including geomechanical aspects. Deriving and understanding geomechanical properties is crucial for reservoir management as it can avoid drilling and production-related problems that cause environmental impacts associated with land subsidence and uplift. The Poison's ratio (PR), Young Modulus (YM), and elastic moduli for a reservoir block were estimated using 3D seismic pre-stack data and well data. 3D Mechanical Earth Models (MEM) were also developed using the well logs, seismic horizons, and drilling data. Seismic data-derived geomechanical properties were compared with the mechanical earth models for the first time for this field. Well-tie analysis was used for inversion of 3D seismic data to extract detailed waveform and amplitude information. The brittleness index of the subsurface layers was estimated, which is a critical rock property that provides information about rock hardness and fragility phenomenon. The brittleness index has a diverse range from 5-35%, with significant contrast at shallow zones. PR and YM models generated from 3D MEM and seismic data have average values of 0.2 -0.6 and 5 - 28 GPa with significant contrast from shales and carbonates. The study recommends that the drilling through these problematic zones should be avoided to avoid wellbore problems that cause challenges in maintaining wellbore integrity and reservoir management in the North-Heera field, Mumbai Offshore Basin.

Basis function choice for trans-dimensional models in geophysical inference

Inference methods depend on parametrization choices. Over-parametrized, under-parametrized, and trans-dimensional (trans-D) models are routinely chosen. Over-parametrization employs space discretization below the resolution power of the data and includes regularization (e.g. Tikhonov) to control the amount of model structure. Under-parametrized models employ fewer parameters, and practitioners choose model complexity (e.g. the number of seabed layers) that is consistent with data information, often based on incomplete prior information. Trans-D models assign model complexity based on data information in an automated, data-driven procedure. The success of trans-D models depends on the choice of basis function for space partitioning. We review existing trans-D approaches and present new ones for 2D and 3D Earth models. Existing approaches include Voronoi partitioning, wavelet decomposition, and polynomial shapes, which can produce inadequate results. New approaches use various degrees of prior information when assigning the basis. The approaches include multiple nested Voronoi diagrams, a combination of grid data and alpha shapes, and partitioning of Voronoi diagrams with horizontal and vertical lines and planes. Since the computational burden is significant for 2D and 3D Earth models, we study various algorithms to carry out partitioning and show that approximate nearest neighbours are sufficiently accurate and outperform other methods.

Regional-Scale 3D Ground-Motion Simulations of Mw 7 Earthquakes on the Hayward Fault, Northern California Resolving Frequencies 0–10 Hz and Including Site-Response Corrections

ABSTRACTLarge earthquake ground-motion simulations in 3D Earth models provide constraints on site-specific shaking intensities but have suffered from limited frequency resolution and ignored site response in soft soils. We report new regional-scale 3D simulations for moment magnitude 7.0 scenario earthquakes on the Hayward Fault, northern California with SW4. Simulations resolved significantly broader band frequencies (0–10 Hz) than previous studies and represent the highest resolution simulations for any such earthquake to date. Seismic waves were excited by a kinematic rupture following Graves and Pitarka (2016) and obeyed wave propagation in a 3D Earth model with topography from the U.S. Geological Survey (USGS) assuming a minimum shear wavespeed, VSmin, of 500 m/s. We corrected motions for linear and nonlinear site response for the shear wavespeed, VS, from the USGS 3D model, using a recently developed ground-motion model (GMM) for Fourier amplitude spectra (Bayless and Abrahamson, 2018, 2019a). At soft soil locations subjected to strong shaking, the site-corrected intensities reflect the competing effects of linear amplification by low VS material, reduction of stiffness during nonlinear deformation, and damping of high frequencies. Sites with near-surface VS of 500 m/s or greater require no linear site correction but can experience amplitude reduction due to nonlinear response. Averaged over all sites, we obtained reasonable agreement with empirical ergodic median GMMs currently used for seismic hazard and design ground motions (epsilon less than 1), with marked improvement at soft sedimentary sites. At specific locations, the simulated shaking intensities show systematic differences from the GMMs that reveal path and site effects not captured in these ergodic models. Results suggest how next generation regional-scale earthquake simulations can provide higher spatial and frequency resolution while including effects of soft soils that are commonly ignored in scenario earthquake ground-motion simulations.

3D borehole-to-surface and surface electromagnetic modeling and inversion in the presence of steel infrastructure

The borehole-to-surface electromagnetic (EM) method is a viable imaging and monitoring tool for energy reservoirs, geologic storage, geothermal exploration, fault zones, and other subsurface targets. Data interpretation typically requires considering steel-casing effects, but it is difficult and impractical to directly discretize arbitrarily oriented hollow steel-cased wells in a 3D reservoir-scale earth model because of their extremely high electrical conductivity and long hollow geometry. We have considered a borehole-to-surface EM configuration in which an electric dipole source is placed below the bottom of a steel-cased well. To practically simulate the casing effects on EM measurements, we develop a novel 3D finite-element EM algorithm using an unstructured tetrahedral mesh. To avoid excessive use of fine grids for modeling a steel-cased well, the well is replaced with the combination of a short solid conductive prism and a long linewise perfect electric conductor. We find that this combined structure can approximate casing effects at a small fraction of the computational cost required for modeling a complete hollow casing because the linewise structure is volumeless and does not require an excessive number of small elements. We also find that steel-cased wells distant from sources and receivers can be modeled as simple linewise perfect electric conductors, further improving the computational efficiency. Using this approximation, the 3D EM algorithm presented here is well-suited to modeling many arbitrarily oriented steel-cased wells. After verifying the accuracy and efficiency of this approach using various examples, we performed a 3D borehole-to-surface/surface-to-borehole and surface EM inversion and determine that the inversion can image a deep localized target in the presence of steel infrastructure.

An integrated petrophysical and geomechanical characterization of Sembar Shale in the Lower Indus Basin, Pakistan, using well logs and seismic data

Shale gas reservoirs are generally exploited through horizontal drilling and hydraulic fracturing. Petrophysical and geomechanical parameters help to determine horizontal well orientation, to select drilling mud densities for stable drilling operations, to assess the suitability of specific zones in a formation for hydraulic fracturing, and to assess required hydraulic fracturing pressures. The primary objective of this work was to characterize a shale interval in the Early Cretaceous-age Sembar Formation in the Lower Indus Basin of Pakistan, using only readily available data. A workflow was developed for the estimation and mapping of geomechanical properties using logs from multiple wells and relevant post-stack seismic reflection data. Mineralogy data from well cuttings, core testing results for elastic properties and hydraulic fracturing test data (mostly obtained from one key well) were utilized to constrain the values of the properties estimated from geophysical data. The following results obtained at the well-scale suggest that the Sembar Shale is favorable for development: high gas saturation, good porosity (up to 10%), moderate quantity of thermally mature organic matter (2%–4% TOC), a number of brittle intervals separated by thicker intervals that fall slightly below the brittle-ductile threshold, and a strike-slip stress regime. At the scale of the study area, robust statistical techniques were used to invert seismic stacks and develop a 3D mechanical earth model. This model shows a trend of increasing shale brittleness towards the northeastern portion of the study area, hence suggesting that this area might be most prospective for initial shale gas development. The results of sensitivity analyses are presented, which illustrate the potential errors in the estimated geomechanical properties. Future work to improve confidence in the shale gas potential of the Sembar Formation is given, including extensive coring and laboratory testing, in-situ stress and natural fracture characterization, and better delineation of shale thickness.