Vertical Transverse Isotropy Research Articles

Characteristics of dispersion curves for Love channel waves in transversely isotropic media

Coal seams have a pronounced bedding structure with developed cracks and exhibit significant anisotropy. However, few studies have examined the frequency dispersion properties of channel waves in anisotropic coal seams. In this study, numerical solutions are calculated using the generalized reflection-transmission coefficient method for the dispersion curves of Love channel waves in vertical transversely isotropic (VTI) and horizontal transversely isotropic (HTI) medium models. Moreover, the frequency dispersion characteristics of Love channel waves in several typical transversely isotropic models are analyzed. We find that the dispersion curves for isotropic and VTI media differ significantly. In addition, the phase and Airy-phase velocities in VTI media are higher than those in isotropic media. Thus, neglecting this difference in practical channel wave detection will result in large detection errors. The dispersion curves for the isotropic and HTI media do not differ significantly, and the Airy-phase velocities of various modes are similar. The group-velocity curve for a coal seam model containing a dirt band is found to be extremely irregular. The fundamental-mode Airy phase is not pronounced, but the first-mode Airy phase can be clearly observed. Hence, first-mode channel waves are suitable for detecting dirt bands.

Elastic vertically transversely isotropic full-waveform inversion using cross-gradient constraints — An application toward high-level radioactive waste repository monitoring

Anisotropic seismic full-waveform inversion (FWI) is a challenging task. In the case of 2D vertically transversely isotropic (VTI) media, there are five independent model parameters. This relatively large number of different parameter types imposes significant trade-off issues and makes the inversion parameterization a challenging task. The problem is less severe in a crosshole configuration, in which a wider angular coverage of the region of interest is available. There exist many suggestions for suitable inversion parameterizations. We have determined that, for a crosshole configuration, a relatively simple velocity-based parameterization provides a good FWI reconstruction of the subsurface. Furthermore, considerable improvements of the tomographic images can be achieved by supplying structural similarity constraints using cross gradients to the inversion problem. With two synthetic data sets, we determine that a structurally constrained VTI FWI workflow produces sharper subsurface images without adversely affecting the parameter trade-off issue. With a second synthetic experiment, we find that structurally constrained VTI FWI is robust to major differences in anomaly locations for different parameter types. We successfully applied the methodology to a crosshole data set acquired to image a downscaled version of a high-level radioactive waste repository. The resulting tomograms allowed a narrow highly fractured zone to be imaged.

A non-balanced staggered-grid finite-difference scheme for the first-order acoustic VTI equation modeling

Numerically solving wave equation is widely used to seismic modeling, migration and inversion. It is important to improve the simulation efficiency while still preserving high accuracy. Different from the balanced staggered-grid finite-difference (SGFD) scheme for the first-order acoustic vertical transversely isotropic (VTI) equation modeling, we propose a non-balanced FD scheme which uses the second-order SGFD operator for part of the spatial derivatives in the first-order VTI wave equation to improve the simulation efficiency. Meanwhile, we compute the SGFD coefficient from the normal-grid FD coefficient. Compared with the balanced SGFD scheme, the non-balanced SGFD scheme could save simulation time. The efficiency and accuracy of the proposed SGFD scheme are demonstrated by the dispersion analysis and numerical simulation.

Traveltime computation and OBN seismic record simulation for rugged seafloor in VTI medium

ABSTRACT To improve the computational accuracy of seismic traveltime for complex structures in inhomogeneous media, a mesh generation method that is adaptive to a rugged seafloor or interface is presented. A hybrid mesh discrete velocity model consisting of conventional rectangular mesh and irregular quadrilateral mesh is also proposed. The local traveltime equations for the hybrid mesh are derived from the linear traveltime interpolation (LTI) method and are shown to be stable. The relationship between the group velocity and group angle is converted into that between group velocity and interpolated point coordinates, extending the LTI ray tracing algorithm to multiwave simulation in vertical transversely isotropic (VTI) medium by multi-stage partitioning. Computations of the first arrival, reflection, multiple reflection, multiple transmission conversion, and multiple reflection conversion seismic waves in the VTI medium with rugged seafloor and complex structural interfaces are realised. The results show that the proposed method can adapt to the rugged seafloor and velocity interfaces of complex structures, resulting in higher computational accuracy of the traveltime and ray paths for ocean bottom node (OBN) seismic wave simulation. The accuracy of the proposed method is verified by comparison with the finite-difference method. This method will be useful for modelling of seismic waves, wavefield identification, and study of seismic wave propagation in OBN seismic observations.

Automatic estimation of traveltime parameters in VTI media using similarity-weighted clustering

Compared with hyperbolic velocity estimation methods, nonhyperbolic methods (such as shifted hyperbola) are better choices for large offsets or vertical transverse isotropy (VTI) media. Since local seismic event slope contains subsurface information, they can be used to estimate zero-offset two-way traveltime and normal moveout velocity. The traditional velocity estimation methods require a great deal of manual work and are also prone to human error. In order to estimate the traveltime parameters for VTI media automatically, in this paper, we propose to use predictive painting and similarity-weighted clustering to obtain traveltime parameters. The predictive painting is used to estimate zero-offset two-way traveltime, and the shifted-hyperbola traveltime equation is used to obtain velocity and anisotropy attributes. We first map local slopes to zero-offset two-way traveltime and moveout-parameters domain and then use similarity-weighted k-means clustering to find the maximum likelihood anisotropy parameters of the main subsurface structures. In order to demonstrate that, we apply the similarity-weighted clustering method to synthetic and field data examples and the results are of higher accuracy when compared to the ones obtained using multiparameter semblance-based method. From estimation error section, it can be seen that the estimation error of multiparameter semblance-based method is about 3–5 times that of the proposed method.

A nonlinear and anisotropic data-driven litho-petroelastic inversion for single-loop subsurface characterization: Theory, uncertainties, and a case study

A new data assimilation algorithm for joint litho-petroelastic (LPE) inversion using nonlinear anisotropic Zoeppritz reflectivity operators, together with iterative sequential filtering, is used to provide joint elastic, lithology, and petrophysical estimates. The sequential filtering approach is an attractive choice because integration of petroelastic rock models with seismic data for multiparameter estimation can become quickly ill posed. Data assimilation techniques integrate the data and model in a manner that tracks uncertainties and manages the flow of data, which helps control this difficult, ill-posed estimation problem. For anisotropic formations, joint LPE inversion makes it possible to use anisotropy information associated with the lithology units or petrophysical parameters, either as fixed lithology-dependent trends by means of prior averages or as a direct function of the petrophysical parameters. This proves beneficial for amplitude variation with angle/amplitude variation with azimuth inversion where the azimuthal invariant anisotropic parameter space, containing the vertical transverse isotropy (VTI) components of the reflectivity operators, is not resolvable independently from shear and density information. In many cases, neglecting to account for anisotropy will lead to inferior characterization of anisotropic plays. Anisotropic LPE inversion enables anisotropic characterization by identifying the anisotropic formation as part of the inversion process. LPE inversion also provides estimates of the petrophysical parameter space and, therefore, honors the relation between the anisotropic elasticity, lithology, and petrophysical parameters. This study reviews the LPE inversion workflow and shows how anisotropic LPE inversion in VTI media is used to derive jointly elastic properties, lithology, and petrophysical parameters of the Wolfcamp Permian Basin shale play in Texas. We also demonstrate the importance of including anisotropy in the inversion and show that isotropic inversion poorly delineated the lithology of the play.

Anisotropy evolution during early maturation of organic-rich carbonates

The organic-rich Late Cretaceous carbonates of the Ghareb and Mishash formations are potentially both self-sourced unconventional reservoirs and high quality source rocks for conventional petroleum systems in the eastern Mediterranean region. In this study we use cores from depths ranging from 340 to 1290 m in the Shefela and Golan Heights basins in Israel, which records the diagenesis and transformation phases of organic-rich chalk into limestone. Understanding such source rocks is complicated by the fact that each formation is unique and heterogeneity is common within each formation. Moreover, in situ samples at various stages of maturation are rarely available. We apply the three-plug measuring technique for a vertical transversely isotropic (VTI) medium to investigate the ultrasonic wave velocity and permeability anisotropies of organic-rich chalks (ORC) within the tested sequence.We propose that in ORC diagenesis, the characteristics and distribution of the organic matter in the rock matrix change significantly throughout burial and thermal maturation, strongly affecting the velocities. Measuring the velocity hysteresis under varying confining pressures revealed that development of soft porosity with preferred orientation plays a crucial role in the early maturation stage (TMAX of 428–434°C), particularly under low effective stresses, while it is absent in the immature stage (TMAX of 403–415°C). The sensitivity of the wave velocities at low effective stresses results in variations in velocity anisotropy, which may potentially be utilized in seismic exploration to delineate the highly-pressured ‘sweet spots’ in unconventional organic-rich carbonates.

Efficient acoustic-elastic FD coupling method for anisotropic media

Pre-salt discoveries are among the most important in the world over the last decade and ultra-deep water offshore exploration targets became common in oil industry. In these cases, the water layer typically compounds 30–40% of the whole geophysical region of interest. The most successful numerical schemes to model seismic waves in these regions are based on ordinary staggered-grid schemes (OSG). Nevertheless, these formulations have the drawback of requiring higher memory storage, since they need to save both velocity and stress components. Recently, we presented equivalent staggered-grid schemes (ESG) that allow memory storage reduction and/or higher computational efficiency depending on the specific case. Specially, the acoustic ESG has lower memory requirement and is the most efficient one. In order to improve the efficiency and reduce memory storage requirement in offshore regions, the present paper develops an explicit direct acoustic-elastic coupling to solve anisotropic wave equations. A domain decomposition is used, where the geophysical medium is divided in two different subdomains, one acoustic, related to water layer, and the other elastic, related to rock layers, considered as vertical-transverse isotropic (VTI) media. The best computational efficiency is achieved by choosing a flat-horizontal interface to couple the two subdomains. The former subdomain is modeled using the acoustic ESG and the second subdomain is modeled using the OSG for VTI media. Both schemes have the same stability properties and the resulting coupling algorithm has the same stability and accuracy as the original OSG applied to the whole model. The proposed method applies to 3D case up to orthorhombic case. To validate the method, it was applied to the Hess VTI model with water layer extended to compound 35% of the model. The reduction observed was near to 25% in memory and in CPU time and grows with percentage of water in the model.

Non-Hyperbolic Velocity Analysis of Seismic Data from Jequitinhonha Basin, Northeastern Brazil.

Normal moveout (NMO) velocity is used in seismic data processing to correct the data from the moveout effect. This velocity depends on the medium above the reflector and it is estimated from the adjustment of a hyperbolic function that approximates the reflection time. This approximation is reasonable for media formed by isotropic layers. For deeper exploration targets, which effectively behave as anisotropic media, the NMO velocity estimate from the hyperbolic approximation becomes imprecise. One possibility is the use of non-hyperbolic approximations for the reflection time and deeming the medium to be anisotropic. However, these approximations make the NMO velocity estimation a more complex problem, since the anisotropic parameters are unknown. In this study the NMO velocities for a vertical transverse isotropy medium are estimated using two non-hyperbolic reflection time approaches. For comparing the two methodologies that estimate NMO velocity, a 2-D dataset from Jequitinhonha Basin is used and it presents anisotropic behavior. The results show that this approach produces more consistent results than the conventional approach, which ignores the anisotropy of the medium.

Tutorial — time conversion of depth migrated data: part II, TTI preSDM

Contemporary depth imaging projects often require final pre-Stack Depth-Migrations (preSDM) to be converted to time for comparison to vintage pre-Stack Time-Migrations (preSTM), or to facilitate conversion to ‘geological’ depth through calibration to well and check-shot data. Here, I consider the situation of having performed an anisotropic Tilted Transverse Isotropy (TTI) preSDM and wanting to convert it to time via vertical stretch in order to compare it, say, to an anisotropic preSTM. Such a comparison is inherently invalid, as time-migration will explicitly treat any anisotropy as if it were Vertical Transverse Isotropy (VTI), and, in addition, the lateral positioning error inherent in preSTM will render such comparisons questionable on steeply dipping structures. I show here that the most appropriate type of ‘velocity’ to use for conversion to time of TTI preSDM reflection events should be the vertical component of the phase velocity. Conversely, if we are considering point-to-point measurements, such as the direct arrival travel time, a down-hole or check-shot measurement, then the group velocity should be used, as it is with this speed that energy travels. In addition, subsequent depth conversion of any time product for interpretational purposes would best be accomplished using a velocity calibrated to well check-shots.

Anisotropic P-wave travel-time tomography implementing Thomsen's weak approximation in TOMO3D

Abstract. We present the implementation of Thomsen's weak anisotropy approximation for vertical transverse isotropy (VTI) media within TOMO3D, our code for 2-D and 3-D joint refraction and reflection travel-time tomographic inversion. In addition to the inversion of seismic P-wave velocity and reflector depth, the code can now retrieve models of Thomsen's parameters (δ and ε). Here, we test this new implementation following four different strategies on a canonical synthetic experiment in ideal conditions with the purpose of estimating the maximum capabilities and potential weak points of our modeling tool and strategies. First, we study the sensitivity of travel times to the presence of a 25 % anomaly in each of the parameters. Next, we invert for two combinations of parameters (v, δ, ε and v, δ, v⊥), following two inversion strategies, simultaneous and sequential, and compare the results to study their performance and discuss their advantages and disadvantages. Simultaneous inversion is the preferred strategy and the parameter combination (v, δ, ε) produces the best overall results. The only advantage of the parameter combination (v, δ, v⊥) is a better recovery of the magnitude of v. In each case, we derive the fourth parameter from the equation relating ε, v⊥ and v. Recovery of v, ε and v⊥ is satisfactory, whereas δ proves to be impossible to recover even in the most favorable scenario. However, this does not hinder the recovery of the other parameters, and we show that it is still possible to obtain a rough approximation of the δ distribution in the medium by sampling a reasonable range of homogeneous initial δ models and averaging the final δ models that are satisfactory in terms of data fit.

Enhancing subsurface imaging and reservoir characterization in the Marcellus Shale play, northeast Pennsylvania, through advanced reprocessing of wide-azimuth 3D seismic data

The Marcellus Shale sits in a geologically complicated region, characterized by faults and salt-cored compressional folds. Large lateral velocity variations associated with this complex geology make seismic imaging difficult. Recently acquired 3D seismic with wide azimuthal coverage and long offsets have poorly imaged folds and faults within the Marcellus Shale. Wells drilled using the existing 3D seismic volumes often encounter incorrect bed dips and folds mistakenly interpreted as faults (or vice versa) because of the poor imaging quality. We carefully examined each processing step in the seismic processing and imaging workflow and identified a few key drivers that could potentially lead to improvements in subsurface imaging. Starting from field seismic records, we identified and corrected geometry errors. To improve signal-to-noise ratio, we applied advanced noise attenuation practices including land surface-related multiple elimination. We carefully tested and validated an extension patch in the 5D seismic data interpolation that improved the offset coverage in the crossline direction. Furthermore, we performed orthorhombic prestack time migration (PSTM). An orthorhombic velocity model fits the geology better than the traditional vertical transverse isotropic (VTI) model for layered subsurface because a dominant set of orthogonal fracture sets is present in the basin. We achieved a significant improvement of subsurface imaging by implementation of these processing steps as key drivers. The new orthorhombic PSTM correctly images steeply dipping (75° and above) faults that were elusive or absent on the previous VTI migration. Additionally, previously interpreted faults are now clearly imaged as folds, small and large in scale. These imaging improvements have enabled the accurate drilling of lateral wells in the target that otherwise would have been drilled out of zone. Some large faults, which pass through the Marcellus, Mahantango, and Tully Formations, are now well-imaged but were previously barely visible. Successful imaging of such large faults helps identify and avoid geohazards. The dramatic improvement in the subsurface imaging and amplitude-preserving processing enhance the reservoir description of the Marcellus Shale.

Permian Basin: Use of In-Situ Mechanical Rock Properties Improves Completions

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 191406, “Using In-Situ Mechanical Rock Properties To Target Landing Zones and Improve Completions in the Permian Basin,” by E.L. Scott, A.M. Hildick, and C. Glaser, Fracture ID, and E. Petre, Hunt Oil, prepared for the 2018 SPE International Hydraulic Fracturing Technology Conference and Exhibition, Muscat, Oman, 16–18 October. The paper has not been peer reviewed. Optimizing horizontal well placement is not limited to identifying the most-favorable reservoir, but also involves identifying the ideal target window within that reservoir. Gathering drill-bit geomechanics data provides a lower-cost and lower-risk method to acquire mechanical rock properties in long horizontal wellbores. By integrating data sets with mechanical rock properties recorded while drilling, operators can have significantly higher confidence in choosing a target landing zone and improving completions. The complete paper presents two detailed case studies from the Permian Basin. Introduction In this paper, the authors combine the characterization of petrophysical and geomechanical properties into what they call a petromechanical work flow. Typically, petrophysical and geomechanical properties are characterized using data acquired by wireline logs. In vertical wells, wireline logs represent, traditionally, the least-intrusive manner of acquiring high-resolution data. With additional cost and rig time, cores of the formation rock can be exhumed to analyze its properties on surface. In horizontal wells, both wireline logs and conventional cores are costly and operationally challenging. Because of the economic and operational burden, operators typically avoid collecting geomechanical data in horizontal wells. Besides these traditional measurements, the novel technique of using drill-bit geomechanics can enable measurement of geomechanical properties while drilling. Compared with wireline logs and core analysis, this technique is less costly and has a lower risk in long horizontal wells. Drill-Bit Geomechanics Drill-bit geomechanics provides mechanical properties through continuous, high-resolution measurements of drilling-induced vibrations. Triaxial accelerometers, which sample at 1 kHz, record the vibrations while positioned directly behind the drill bit. Earthquake seismology models allow a transformation of the high-frequency, triaxial, drilling-induced vibrations into mechanical rock•properties. The drill-bit geomechanics method determines mechanical properties by using stress-strain relationships and isotropic stiffness coefficients. Additionally, the method describes anisotropy by solving for transversely isotropic (TI) interpretations of the rock matrix. Typically, a vertically transverse isotropic (VTI) matrix contains high shale content or other laminar bedding, while a horizontally transverse isotropic (HTI) matrix contains vertical bedding or fractures. In this paper, the authors define VTI anisotropy as bedding and HTI anisotropy as fracture intensity.

Frequency‐dependent PP and PS reflection coefficients in fractured media

ABSTRACTWhen a porous layer is permeated by mesoscale fractures, wave‐induced fluid flow between pores and fractures can cause significant attenuation and dispersion of velocities and anisotropy parameters in the seismic frequency band. This intrinsic dispersion due to fracturing can create frequency‐dependent reflection coefficients in the layered medium. In this study, we derive the frequency‐dependent PP and PS reflection coefficients versus incidence angle in the fractured medium. We consider a two‐layer vertical transverse isotropy model constituted by an elastic shale layer and an anelastic sand layer. Using Chapman's theory, we introduce the intrinsic dispersion due to fracturing in the sand layer. Based on the series coefficients that control the behaviour of velocity and anisotropy parameters in the fractured medium at low frequencies, we extend the conventional amplitude‐versus‐offset equations into frequency domain and derive frequency‐dependent amplitude‐versus‐offset equations at the elastic–anelastic surface. Increase in fracture length or fracture density can enlarge the frequency dependence of amplitude‐versus‐offset attributes of PP and PS waves. Also, the frequency dependence of magnitude and phase angle of PP and PS reflection coefficients increases as fracture length or fracture density increases. Amplitude‐versus‐offset type of PP and PS reflection varies with fracture parameters and frequency. What is more, fracture length shows little impact on the frequency‐dependent critical phase angle, while the frequency dependence of the critical phase angle increases with fracture density.

Seismic shear wave anisotropy of an anisotropic rock containing aligned cracks: theory and applications to experiment and field data

SUMMARY Cracks universally exist in Earth's crustal rocks. Many rocks are intrinsically anisotropic, which, when coupled with crack-induced anisotropy, significantly affect seismic wave propagation through the rocks. Using the method of sphere equivalency of effective scattering, we have developed a technique to model the effective moduli of transversely isotropic (TI) media containing cracks. The modelling results show that the wave characteristics are significantly affected by the interaction of the two anisotropy mechanisms. To validate the validity and accuracy, the theory was applied to a recent experiment made with a vertical transverse isotropy (VTI) medium containing cracks and shows significantly better agreement with the data. For a more realistic situation, the new modelling was applied to interpret the borehole acoustic anisotropy measurement results from a fractured VTI formation, showing that the theory can adequately explain the anisotropic characteristics of the field data. With the validation and testing, the theoretical results advocated in this study can be used with confidence.

Analysis of Eshelby-Cheng’s model in anisotropic porous cracked medium: An ultrasonic physical modeling approach

Many effective medium theories are designed to describe the macroscopic properties of a medium (the rock, or reservoir in this case) in terms of the properties of its constituents (the background matrix of the rock and the inclusions, for our scenario). A very well known effective medium theory is the Eshelby-Cheng model, which was studied by us in previous work, being tested for the case where the background medium was weakly-anisotropic and porous. The analysis was done testing elastic velocities and Thomsen parameters - as a function of crack density for fixed values of aspect ratio - predicted by the model with data acquired from synthetic rock samples. In this work, we aim to complete the analysis of the Eshelby-Cheng model capabilities when applied to rocks with porous and vertical transversely isotropic (VTI) backgrounds, testing the model for the elastic velocities as functions of aspect ratio - for fixed values of crack density - against experimental data. The data used to test the model were obtained from 17 synthetic rock samples, one uncracked and 16 cracked, the latter divided into four groups of four samples each, each group with cracks having the same aspect ratio, but with the samples having different crack densities. In these samples, ultrasonic pulse transmission measurements were performed to obtain the experimental velocities used to test the model. As was not possible to acquire data for velocity as a function of aspect ratio for fixed values of crack density, we performed interpolations of the experimental data to estimate these velocities. Eshelby-Cheng model effective velocities and Thomsen parameters were calculated using three formulations proposed for the crack porosity: one proposed by Thomsen, the second one proposed in our previous work (which depends only on the crack density) and the third one proposed in this work (which depends on the crack porosity and the aspect ratio, just like Thomsen’s proposal). The comparisons between elastic velocities and Thomsen parameters - as function of crack aspect ratio, for fixed values of crack density - predicted by the model and estimated from the data via interpolation showed that the third formulation produced better fittings (lower root-mean-square errors) between model and experimental data for all ranges of aspect ratio and crack density.

Elastic least-squares reverse time migration in vertical transverse isotropic media

Using adjoint-based elastic reverse time migration, it is difficult to produce high-quality reflectivity images due to the limited acquisition apertures, band-limited source time function, and irregular subsurface illumination. Through iteratively computing the Hessian inverse, least-squares migration enables us to reduce the point-spread-function effects and improve the image resolution and amplitude fidelity. By incorporating anisotropy in the 2D elastic wave equation, we have developed an elastic least-squares reverse time migration (LSRTM) method for multicomponent data from the vertically transversely isotropic (VTI) media. Using the perturbed stiffness parameters [Formula: see text] and [Formula: see text] as PP and PS reflectivities, we linearize the elastic VTI wave equation and obtain a Born modeling (demigration) operator. Then, we use the Lagrange multiplier method to derive the corresponding adjoint wave equation and reflectivity kernels. With linearized forward modeling and adjoint migration operators, we solve a linear inverse problem to estimate the subsurface reflectivity models for [Formula: see text] and [Formula: see text]. To reduce the artifacts caused by data over-fitting, we introduce total-variation regularization into the reflectivity inversion, which promotes a sparse solution in terms of the model derivatives. To accelerate the convergence of LSRTM, we use source illumination to approximate the diagonal Hessian and use it as a preconditioner for the misfit gradient. Numerical examples help us determine that our elastic VTI LSRTM method can improve the spatial resolution and amplitude fidelity in comparison to adjoint migration.

Land seismic multiparameter full waveform inversion in elastic VTI media by simultaneously interpreting body waves and surface waves with an optimal transport based objective function

SUMMARY Land seismic multiparameter full waveform inversion in anisotropic media is challenging because of high medium contrasts and surface waves. With a data-residual least-squares objective function, the surface wave energy usually masks the body waves and the gradient of the objective function exhibits high values in the very shallow depths preventing from recovering the deeper part of the earth model parameters. The optimal transport objective function, coupled with a Gaussian time-windowing strategy, allows to overcome this issue by more focusing on phase shifts and by balancing the contributions of the different events in the adjoint-source and the gradients. We first illustrate the advantages of the optimal transport function with respect to the least-squares one, with two realistic examples. We then discuss a vertical transverse isotropic (VTI) example starting from a quasi 1-D isotropic initial model. Despite some cycle-skipping issues in the initial model, the inversion based on the windowed optimal transport approach converges. Both the near-surface complexities and the variations at depth are recovered.

Modeling 3D elastic VTI wave propagation using an optimal k-space operator-based temporal high-accuracy staggered-grid finite-difference scheme

It is difficult to extend the present time-space-domain or temporal high-order finite-difference (FD) stencils to model anisotropic wave equations owing to anisotropy parameters and spatial derivatives are mutually coupled. Thus, high-order spatial and second-order temporal FDs are commonly used to discretize anisotropic wave equations. To improve temporal modeling accuracy, we develop an efficient temporal high-accuracy staggered-grid FD (SG-FD) scheme to solve the first-order elastic wave equations in 3D vertical transversely isotropic (VTI) media. Through combining the spatial dispersion relation of the original SG-FD stencil with the first-order k (wavenumber)-space operator, we construct a modified SG-FD dispersion relation and determine FD coefficients using least-squares (LS). We adopt the modified LS-based SG-FD scheme using k-space operator compensation to simulate 3D elastic VTI wave propagation. Dispersion analysis and numerical examples demonstrate that our optimal k-space operator-based SG-FD scheme can achieve high temporal accuracy without compromising spatial accuracy compared with the traditionally uncompensated Taylor-series expansion- and LS-based SG-FD methods. Moreover, the stability of our proposed FD scheme is superior to the conventional ones.

Two‐dimensional elastic full‐waveform inversion of Love waves in shallow vertically transversely isotropic media: synthetic reconstruction tests

ABSTRACTIn most shallow‐seismic applications of full‐waveform inversion, the subsurface is assumed to be isotropic, although near‐surface materials may exhibit strong seismic anisotropy. Ignoring anisotropy will lead to inexact solutions when simulating wave propagation or imaging the subsurface using full‐waveform inversion. For shallow structures, vertically transversely isotropic media provide a suitable approximation due to the fine horizontal layering of the sediments. We investigate the effects of anisotropy on surface waves and on shallow‐seismic full‐waveform inversion in vertically transversely isotropic media. The comparisons of seismograms calculated in isotropic and vertically transversely isotropic models show that the sensitivity of full‐waveform inversion towards anisotropy is significantly higher for Love waves than for Rayleigh waves. This observation indicates that it is more promising to perform full‐waveform inversion on Love waves rather than on Rayleigh waves to identify anisotropy of near‐surface materials. Therefore, we performed synthetic two‐dimensional reconstruction tests of anisotropic full‐waveform inversion using only shallow‐seismic Love waves. These tests revealed that the parameters describing vertical transverse isotropy can be accurately reconstructed by full‐waveform inversion. Although the inversion for density is still problematic, this does not affect the results for the seismic velocities in a significant way. The tests on synthetic data thus prove the general applicability and the benefits of an anisotropic inversion of shallow‐seismic Love waves, which can provide a more comprehensive subsurface characterization in shallow anisotropic media.