Anisotropic Inversion Research Articles

Anisotropic full-waveform inversion with tilt-angle recovery

By allowing spatial variations in the direction of the anisotropic fast axis, tilted transverse isotropy (TTI) helps to image complex or steeply dipping structures. Without a priori geologic constraints, however, recovery of all the anisotropic parameters can be nontrivial and nonunique. We adopt two methods for TTI inversion with tilt-angle recovery: one based on the familiar Voigt parameters, and another based on the so-called Chen and Tromp parameters known from regional and global seismology. These parameterizations arise naturally in seismic wave propagation and facilitate straightforward recovery of the tilt angle and anisotropic strength. In numerical experiments with vertical transversely isotropic starting models and TTI target models, we find that the Voigt as well as the Chen and Tromp parameters allow quick and robust recovery of steeply dipping anticlinal structures.

Crustal Structure, Seismic Anisotropy and Deformations of the Ediacaran/Cambrian of the Ma\u0142opolska Block in SE Poland Based on Data from Two Seismic Wide-Angle Experiments

The area of SE Poland represents a complex contact of tectonic units of different consolidation age—from the Precambrian East European Craton, through Palaeozoic West European Platform (including Małopolska Block) to Cenozoic Carpathians and Carpathian Foredeep. In order to investigate the anisotropic properties of the upper crust of the Małopolska Block and their relation to tectonic evolution of the area, two seismic datasets were used: seismic wide-angle off-line recordings from POLCRUST-01 deep seismic reflection profile and recordings from active deep seismic experiment CELEBRATION 2000. During acquisition of deep reflection seismic profile POLCRUST-01 in 2010, a 35-km-long line of 14 recorders (PA-14), oriented perpendicularly to the profile, was deployed to record the refractions from the upper crust (Pg) at wide range of azimuths. These data were used for an analysis of the azimuthal anisotropy of the MB with the modified delay-time inversion method. The results of modelling of the off-line refractions from the MB suggest ~6% HTI anisotropy of the Cambrian/Ediacaran basement, with ~130º azimuth of the fast velocity axis and mean Vp of 4.9 km/s. To compare this result with previous, independent information about anisotropy at larger depth, a subset of previously modelled data from CELEBRATION 2000 experiment, recorded in the MB area, was also analysed by inversion. The recordings of Pg phase at up to 120 km offsets were analysed using anisotropic delay-time inversion, providing information down to ~12 km depth. The CELEBRATION 2000 model shows ~9% HTI anisotropy with ~126º orientation of the fast axis. Thus, local-scale anisotropy of this part of MB confirms the large-scale anisotropy suggested by previous studies based on data from a broader area and larger depth interval. The azimuthal anisotropy (i.e. HTI symmetry of the medium) is interpreted as a result of strong compressional deformation during the accretion of terranes to the EEC margin, leading to tight (sub-vertical) folding and fracturing of intrinsically anisotropic metasediments forming the MB basement. Obtained anisotropy models are compared with data about stratal dips of the MB sequences and implications of assuming more realistic TTI model are discussed. Wide-angle recordings from off-line measurements along a reflection profile provided new information about seismic velocity and anisotropy, not available from standard near-vertical profiling, and contributed to more complete image of the upper crustal structure of Małopolska Block.

Geoelectric models of the earth's crust of Ukraine by the results of the magnetotelluric studies using new methods of inversions

Application of 1D anisotropic inversion (using methods of stochastic and directional decomposition analysis) and 3D inversion (by thin layer) to magnetotelluric data in the territory of Ukraine allowed to prove quantitatively the existence of conductive objects located at different depths and extending in intersecting directions. The importance of the use of these methods has been demonstrated by examples, linking results in the Carpathians, the Dnieper-Donets Basin, the slope of the Voronezh massif, Ukrainian shield with accommodation areas and areas of specific minerals, seismic and geo- and hydrothermal resources

Anisotropic geophysics and vector field

It has been proved that the physical anisotropies of earth medium, such as resistivity, electric susceptibility, velocity, and quality factor, et al., exist and can’t be ignored. For this reason, researches on anisotropy began tens of years ago and now become a hotspot in the field of seismology and geo-electromagnetism in recent years. Promoted by development of information sciences and technology, especially driven by technological progresses of sensor, storage and communication of big dataset, the observations of geophysical field have been upgraded to 2- and 3-dimensional, multi-component vector and tensor measurements at different elevations and spatial sizes, such as 6-component seismic and 5-component MT acquisition provided the possibilities of anisotropic inversion and more precise prediction on physical parameters in geosciences. However, serious challenges have been faced by the traditional geophysics, just because the theoretical principles, methods and techniques of geophysics were built on the basis of scalar observation, and massive vector data are observed and their sharing and utilization become an incontrovertible trend. Thus, in this No.567 Xiangshan-Science Conferences, the progresses and problems in the study of anisotropic geophysics and vector field were introduced and analyzed according to 4 sections. First, different scale and types of vibrations from 6-component earthquake, 3-component seismic exploration and micro-seismic monitoring, and the relations in between are presented and discussed. Secondly, numerical simulations and inversions of resistivity anisotropy are given more discussions; especially on the non-uniqueness of anisotropic inversions for apparent resistivity, tensor observation and azimuthal acquisition were also addressed. Thirdly, the joint geophysical measurements from different altitudes, including well logging, underground geophysical prospecting, airborne and satellite geophysical observations are expected to be used on land, in the ocean and in the air. Finally, instruments of vector seismic sensing and tensor MT and CSAMT, processing techniques of vector signals and software system, communication and storage of big geophysical datasets, including advanced technologies on compressed sensing, were introduced respectively. All these presentations could not be covered in detail within one paper, though, the basic scientific and technological problems about computational geophysics, active or passive seismology, and anisotropic electromagnetism will be focused on, while the detailed discussions on different geophysical fields will follow in other papers, so that the issues on the fundaments and generality of anisotropic geophysics could be studied extensively in the future.

Bayesian Markov chain Monte Carlo inversion for anisotropy of PP- and PS-wave in weakly anisotropic and heterogeneous media

A single set of vertically aligned cracks embedded in a purely isotropic background may be considered as a long-wavelength effective transversely isotropy (HTI) medium with a horizontal symmetry axis. The crack-induced HTI anisotropy can be characterized by the weakly anisotropic parameters introduced by Thomsen. The seismic scattering theory can be utilized for the inversion for the anisotropic parameters in weakly anisotropic and heterogeneous HTI media. Based on the seismic scattering theory, we first derived the linearized PP- and PS-wave reflection coefficients in terms of P- and S-wave impedances, density as well as three anisotropic parameters in HTI media. Then, we proposed a novel Bayesian Markov chain Monte Carlo inversion method of PP- and PS-wave for six elastic and anisotropic parameters directly. Tests on synthetic azimuthal seismic data contaminated by random errors demonstrated that this method appears more accurate, anti-noise and stable owing to the usage of the constrained PS-wave compared with the standards inversion scheme taking only the PP-wave into account.

Improving Global Radial Anisotropy Tomography: The Importance of Simultaneously Inverting for Crustal and Mantle Structure

Observed seismic anisotropy gives the most direct information on mantle flow, but it is challenging to image it robustly at global scales. Difficulties in separating crustal from mantle structures in particular can have a strong influence on the imaging. Here we carry out several resolution tests using both real and synthetic data, which show that unconstrained crustal structure can strongly contaminate retrieved radial anisotropy at 100–150 km depth. To efficiently reduce crustal effects, we perform whole‐mantle radially anisotropic tomographic inversions including crustal thickness perturbations as model parameters. Our data set includes short‐period group velocity data, which are sensitive to shallow structure. We perform a series of tests that highlight the advantages of our approach and show that to properly constrain thin oceanic crust in global radially anisotropic inversions, group velocity data with wave periods of at least T ∼20 s or shorter are required. Our Moho perturbation model shows thicker crust along subduction zones and beneath the Ontong Java plateau in the southwestern Pacific than in the global crustal model CRUST2.0. These features agree well with other crustal models as well as with refraction survey data and tectonic features in these regions.

Viscoacoustic anisotropic full waveform inversion

A viscoacoustic vertical transverse isotropic (VTI) quasi-differential wave equation, which takes account for both the viscosity and anisotropy of media, is proposed for wavefield simulation in this study. The finite difference method is used to solve the equations, for which the attenuation terms are solved in the wavenumber domain, and all remaining terms in the time-space domain. To stabilize the adjoint wavefield, robust regularization operators are applied to the wave equation to eliminate the high-frequency component of the numerical noise produced during the backward propagation of the viscoacoustic wavefield. Based on these strategies, we derive the corresponding gradient formula and implement a viscoacoustic VTI full waveform inversion (FWI). Numerical tests verify that our proposed viscoacoustic VTI FWI can produce accurate and stable inversion results for viscoacoustic VTI data sets. In addition, we test our method's sensitivity to velocity, Q, and anisotropic parameters. Our results show that the sensitivity to velocity is much higher than that to Q and anisotropic parameters. As such, our proposed method can produce acceptable inversion results as long as the Q and anisotropic parameters are within predefined thresholds.

Imaging fracture permeability using magnetotellurics

We present 1D anisotropic inversions of magnetotelluric data in two regions of the Otway Basin; Koroit, Victoria, and Penola, South Australia. In the Koroit region we have delineated an electrically anisotropic layer at approximately 2.5 to 3.5 km depth; this corresponds to the upper part of the Lower Cretaceous Crayfish Group, a known reservoir unit. The anisotropy strike is consistent between stations at approximately 160° east of north. We interpret the anisotropy at Koroit as resulting from pervasive NNW oriented, fluid-filled fractures, resulting in enhanced bulk electrical and hydraulic conductivity. This interpretation is consistent with permeability data from well formation tests. It is also consistent with the orientation of mapped faults in the area, which are favourably oriented for reactivation in the current stress field. In Penola, no persistent anisotropic layer has been defined even though the areas are geologically similar. The difference in the resistivity structure may reflect differences in the density of fractures or their fill material. Alternatively, it may reflect small differences in the amount by which the fractures are open, resulting from differences in the stress field and fracture orientation in each area.

Multiparameter estimation with acoustic vertical transverse isotropic full-waveform inversion of surface seismic data

Obtaining accurate depth-migrated images demands an anisotropic representation of the earth. As a prominent tool for building high-resolution earth models, full-waveform inversion (FWI) therefore must not only account for anisotropy during wavefield simulation but also reconstruct the anisotropy fields. We have developed an inversion strategy to perform acoustic multiparameter FWI of surface seismic data in transversely isotropic media with a vertical axis of symmetry (VTI). During the early era of FWI practice, most studies only invert for the most dominant parameter, that is, the vertical velocity, and the rest of the model parameters are either ignored or kept constant. Recently, more and more emphases focus on inverting for more parameters, such as for the vertical velocity and the anisotropy fields; these are referred to as multiparameter inversion. Due to the dominant influence of the vertical velocity on the kinematics of surface seismic data, we have developed a hierarchical approach to invert for the vertical velocity first, but we kept the anisotropy fields unchanged and only switched to joint inversion of the vertical velocity and the anisotropy fields when the inversion for the vertical velocity approaches convergence. In addition, we have illustrated the necessity of incorporating the diving and reflection energy during inversion to mitigate the nonuniqueness of the solutions caused by the coupling between the vertical velocity and the anisotropy fields. We also demonstrate the success of our method for VTI FWI using synthetic and real data examples based on marine surface seismic acquisition. Our results show that incorporation of multiparameter anisotropy inversion produced better focused migration images.

Large-scale seismically guided anisotropic inversion of towed-streamer EM data in the Barents Sea

This paper presents a fast and efficient large-scale anisotropic inversion technique for towed streamer electromagnetic (EM) data, which incorporates seismic constraints. The inversion algorithm is based on the 3D contraction integral equation method and utilizes a reweighted regularized conjugate gradient technique to minimize the objective functional (Zhdanov et al. 2014a, b). We have also introduced the concept of a moving sensitivity domain for seismically guided EM inversion, originally developed for airborne EM surveys (Zhdanov and Cox, 2013), which makes it possible to invert the entire large-scale towed streamer EM survey data while keeping the accuracy of the computation of the EM fields. The developed algorithm and software can take into account the constraints based on seismic and well-log data, and provide the inversion guided by these constraints. To demonstrate the practical effectiveness of this approach for large-scale inversion of marine EM data, as well as integration with seismic data, we apply the method to the inversion of about 2000 line-km of towed streamer EM data. The data form part of a larger survey in the Norwegian Barents Sea (McKay et al., 2016). We show that the technique produces a single resistivity model that is consistent with both the measured EM data and the main seismically defined structures. Thus, the resistivity model is ready to be interpreted and used in further quantitative interpretation studies.

Imaging the lithospheric structure beneath the Indian continent

AbstractWe present a high‐resolution 3‐D lithospheric model of the Indian plate region down to 300 km depth, obtained by inverting a new massive database of surface wave observations, using classical tomographic methods. Data are collected from more than 550 seismic broadband stations spanning the Indian subcontinent and surrounding regions. The Rayleigh wave dispersion measurements along ~14,000 paths are made in a broad frequency range (16–250 s). Our regionalized surface wave (group and phase) dispersion data are inverted at depth in two steps: first an isotropic inversion and next an anisotropic inversion of the phase velocity including the SV wave velocity and azimuthal anisotropy, based on the perturbation theory. We are able to recover most of the known geological structures in the region, such as the slow velocities associated with the thick crust in the Himalaya and Tibetan plateau and the fast velocities associated with the Indian Precambrian shield. Our estimates of the depth to the Lithosphere‐Asthenosphere boundary (LAB) derived from seismic velocity Vsv reductions at depth reveal large variations (120–250 km) beneath the different cratonic blocks. The lithospheric thickness is ~120 km in the eastern Dharwar, ~160 km in the western Dharwar, ~140–200 km in Bastar, and ~160–200 km in the Singhbhum Craton. The thickest (200–250 km) cratonic roots are present beneath central India. A low velocity layer associated with the midlithospheric discontinuity is present when the root of the lithosphere is deep.

Constraining a 3D anisotropic tomography inversion with 800 wells – A Canadian oil sands case history

This Canadian oil-sands case history is a very shallow play with a complex geology that includes Quaternary thrusting at surface, sinkholes, and highly karsted Devonian carbonates at the base of the notoriously complex McMurray reservoir. Despite this challenging environment, we were able to demonstrate that Depth Imaging brought significant improvements as compared to the routinely used time imaging. Recent developments in Anisotropic Pre-Stack Depth Imaging technologies provided a better focused and better positioned 3D subsurface image that accurately tied several hundreds of wells. These results were achieved using steering filters, solver bounds and simultaneous multi-parameter tomography inversion while constraining the tomography updates with the well top picks from over 800 wells. Surveys of different vintages, geometries, orientations and shooting directions were regularized using 5D interpolation and merged together. Besides a better imaging of the subsurface, one of main objective of the project was the characterization of the McMurray reservoir. To that aim, the Anisotropic Pre-Stack Depth Migration (APSDM) generated better conditioned Offset Vector Tile gathers for subsequent pre-stack inversion work. The Alberta oil sands are one of the largest bituminous hydrocarbon reserves in the world (Alberta Energy Regulator, 2015). At reservoir temperature, the bitumen is so viscous that it can almost be considered as a solid. In situ thermal recovery processes such as steam-assisted gravity drainage (SAGD) that lower viscosity and increase mobility are required to extract the bitumen from the reservoir. SAGD operations consist of horizontal well pairs that are drilled into the base of the reservoir. In each pair, one well is drilled about 5 m directly above the other well. The top well is injected with steam to melt the bitumen. The bitumen seeps down towards the bottom producing well, which pumps the bitumen to the surface. The well pairs are generally configured to about ten parallel horizontal well pairs that are around 100 m apart horizontally and are 1000 m long, which constitute a 1-km2 pad.

Direct elastic properties to resistivity transforms

Numerous publications have dealt with estimations of resistivity from elastic parameters and vice versa. Attempts have been made in the cross-property relationship of elastic and electric properties, in particular, velocity to resistivity using different parameters, such as porosity and water saturation. These types of transforms are currently used to predict background seismic velocities and resistivities, or even start models for seismic or controlled source electromagnetic (CSEM) inversions. However, they are not reliable predictors because they depict the regional elastic or electric variations with limited accuracy. We present a novel approach for the development of models capable of estimating the regional subsurface resistivity based on information from regional wells and seismic inversions. We apply multivariate nonlinear regression on data derived from regional wells and seismic inversions and subsequently produced an estimation of subsurface horizontal resistivity that could be either used as a direct hydrocarbon indicator or provide a constraint on the horizontal resistivity in anisotropic CSEM inversions. We have verified the validity of the approach using two data sets from the Norwegian continental shelf. We found very good agreement between the borehole-measured and predicted resistivity.

MARE2DEM: a 2-D inversion code for controlled-source electromagnetic and magnetotelluric data

This work presents MARE2DEM, a freely available code for 2-D anisotropic inversion of magnetotelluric (MT) data and frequency-domain controlled-source electromagnetic (CSEM) data from onshore and offshore surveys. MARE2DEM parametrizes the inverse model using a grid of arbitrarily shaped polygons, where unstructured triangular or quadrilateral grids are typically used due to their ease of construction. Unstructured grids provide significantly more geometric flexibility and parameter efficiency than the structured rectangular grids commonly used by most other inversion codes. Transmitter and receiver components located on topographic slopes can be tilted parallel to the boundary so that the simulated electromagnetic fields accurately reproduce the real survey geometry. The forward solution is implemented with a goal-oriented adaptive finite-element method that automatically generates and refines unstructured triangular element grids that conform to the inversion parameter grid, ensuring accurate responses as the model conductivity changes. This dual-grid approach is significantly more efficient than the conventional use of a single grid for both the forward and inverse meshes since the more detailed finite-element meshes required for accurate responses do not increase the memory requirements of the inverse problem. Forward solutions are computed in parallel with a highly efficient scaling by partitioning the data into smaller independent modeling tasks consisting of subsets of the input frequencies, transmitters and receivers. Non-linear inversion is carried out with a new Occam inversion approach that requires fewer forward calls. Dense matrix operations are optimized for memory and parallel scalability using the ScaLAPACK parallel library. Free parameters can be bounded using a new non-linear transformation that leaves the transformed parameters nearly the same as the original parameters within the bounds, thereby reducing non-linear smoothing effects. Data balancing normalization weights for the joint inversion of two or more data sets encourages the inversion to fit each data type equally well. A synthetic joint inversion of marine CSEM and MT data illustrates the algorithm's performance and parallel scaling on up to 480 processing cores. CSEM inversion of data from the Middle America Trench offshore Nicaragua demonstrates a real world application. The source code and MATLAB interface tools are freely available at http://mare2dem.ucsd.edu.

A new parameter set for anisotropic multiparameter full-waveform inversion and application to a North Sea data set

Parameterization lies at the center of anisotropic full-waveform inversion (FWI) with multiparameter updates. This is because FWI aims to update the long and short wavelengths of the perturbations. Thus, it is important that the parameterization accommodates this. Recently, there has been an intensive effort to determine the optimal parameterization, centering the fundamental discussion mainly on the analysis of radiation patterns for each one of these parameterizations, and aiming to determine which is best suited for multiparameter inversion. We have developed a new parameterization in the scope of FWI, based on the concept of kinematically equivalent media, as originally proposed in other areas of seismic data analysis. Our analysis is also based on radiation patterns, as well as the relation between the perturbation of this set of parameters and perturbation in traveltime. The radiation pattern reveals that this parameterization combines some of the characteristics of parameterizations with one velocity and two Thomsen’s parameters and parameterizations using two velocities and one Thomsen’s parameter. The study of perturbation of traveltime with perturbation of model parameters shows that the new parameterization is less ambiguous when relating these quantities in comparison with other more commonly used parameterizations. We have concluded that our new parameterization is well-suited for inverting diving waves, which are of paramount importance to carry out practical FWI successfully. We have demonstrated that the new parameterization produces good inversion results with synthetic and real data examples. In the latter case of the real data example from the Central North Sea, the inverted models show good agreement with the geologic structures, leading to an improvement of the seismic image and flatness of the common image gathers.

A new parameterization for waveform inversion in acoustic orthorhombic media

Orthorhombic anisotropic model inversion is extra challenging because of the multiple parameter nature of the inversion problem. The high number of parameters required to describe the medium exerts considerable trade-off and additional nonlinearity to a full-waveform inversion (FWI) application. Choosing a suitable set of parameters to describe the model and designing an effective inversion strategy can help in mitigating this problem. Using the Born approximation, which is the central ingredient of the FWI update process, we have derived radiation patterns for the different acoustic orthorhombic parameterizations. Analyzing the angular dependence of scattering (radiation patterns) of the parameters of different parameterizations starting with the often used Thomsen-Tsvankin parameterization, we have assessed the potential trade-off between the parameters and the resolution in describing the data and inverting for the parameters. The analysis led us to introduce new parameters [Formula: see text], [Formula: see text], and [Formula: see text], which have azimuthally dependent radiation patterns, but keep the scattering potential of the transversely isotropic parameters stationary with azimuth (azimuth independent). The novel parameters [Formula: see text], [Formula: see text], and [Formula: see text] are dimensionless and represent a measure of deviation between the vertical planes in orthorhombic anisotropy. Therefore, these deviation parameters offer a new parameterization style for an acoustic orthorhombic medium described by six parameters: three vertical transversely isotropic (VTI) parameters, two deviation parameters, and one parameter describing the anisotropy in the horizontal symmetry plane. The main feature of any parameterization based on the deviation parameters, is the azimuthal independency of the modeled data with respect to the VTI parameters, which allowed us to propose practical inversion strategies based on our experience with the VTI parameters. This feature of the new parameterization style holds for even the long-wavelength components of the model constrained by traveltimes.

Inversion of absorption anisotropy and bowing of crystal field splitting in wurtzite MgZnO

The anisotropic optical properties of wurtzite MgxZn1−xO thin films (0≤x≤0.45) grown on m-plane ZnO substrates by plasma assisted molecular beam epitaxy are studied using spectroscopic ellipsometry at room temperature. The data analysis provides the dielectric functions for electric field polarizations perpendicular and parallel to the optical axis. The splitting between the absorption edges of the two polarization directions decreases between x = 0 and x = 0.24, while an inverted absorption anisotropy is found at higher Mg content, indicating a sign change of the crystal field splitting Δcr as for the spin orbit parameter. The characteristic energies such as exciton binding energies and band gaps are determined from the analysis of the imaginary parts of the dielectric functions. In particular, these data reveal a bowing parameter of b=−283 meV for describing the compositional dependence of the crystal field splitting and indicate Δcr=−327 meV for wurtzite MgO. The inverted valence band ordering of ZnO (Γ7-Γ9-Γ7) is found to be preserved with increasing Mg content, while the optical selection rules interchange.

A joint inversion for shear velocity and anisotropy: the Woodlark Rift, Papua New Guinea

A joint inversion for shear velocity and anisotropy: the Woodlark Rift, Papua New Guinea

Integrated Interpretation and Simultaneous Joint Inversion of 3D Marine CSEM and Seismic Datasets

One of the most complex seismic challenges is the imaging of thick salt bodies, the detection of their base and flanks, and imaging underlying units. To achieve good seismic imaging, the complementary use of non-seismic methods is one of the recommended solutions. Electromagnetic (EM) methods, such as magnetotellurics (MT) and controlled source electromagnetics (CSEM) are sensitive to the presence of salt bodies thanks to the high resistivity contrast with respect to sedimentary units. We present an integrated workflow applied to re-image wide azimuth (WAZ) seismic data acquired by Schlumberger using EM data acquired by EMGS over 35 blocks in the Keathley Canyon, in the Gulf of Mexico to reduce risk in exploration decisions and improve seismic deliverables. Seismic and EM data are utilized first in a cooperative workflow through localized seismic imaging reverse time migration (LSI RTM) to validate new salt structures highlighted by the single domain 3D anisotropic CSEM and MT inversions. They are then fed into a simultaneous joint inversion (SJI) to update a multi-property earth model (velocity and resistivity) by jointly minimizing the CSEM data misfit, the seismic residual move-outs and a relationship between the two properties.

Application of prestack orthotropic AVAz inversion for fracture characterization of a deep carbonate reservoir in northern Kuwait

Prestack anisotropic (orthotropic symmetry) AVAz inversion of full-azimuth 3D seismic data for fracture characterization of the upper Najmah Formation in northern Kuwait was conducted. This formation comprises a thin, tight, naturally fractured carbonate overlying a kerogen-rich shale source rock. The inversion methodology uses an orthotropic system of symmetry that is appropriate for analysis of vertical transverse isotropic (VTI) anisotropic rock layers containing swarms of aligned vertical fractures. Measured seismic amplitudes show good agreement with synthetic models created at different well locations, indicating reliable representation of fractures in amplitude data. Inversion results show good agreement with well and drilling data. Rock-physics modeling shows a relationship between elastic properties and seismic anisotropy and between elastic properties and reservoir properties, such as porosity and fracture density.