Vertical Transversely Isotropic Media Research Articles

Truncated Gauss-Newton full-waveform inversion of pure quasi-P waves in vertical transverse isotropic media

Truncated Gauss-Newton full-waveform inversion of pure quasi-P waves in vertical transverse isotropic media

Viscoacoustic VTI media reverse time migration method in the complex-domain based on the staining algorithm

Underground media exhibit characteristics of viscosity and anisotropy, with vertical transversely isotropic (VTI) media being a common example of anisotropic media. Consequently, it is crucial to address the viscoacoustic VTI wave equation during forward modeling and migration imaging processes to attain highly precise imaging outcomes. However, conventional subsalt imaging techniques yield low accuracy and suffer from a low signal-to-noise ratio. To overcome this challenge, this study proposes a staining algorithm-based viscoacoustic vertical transversely isotropic reverse time migration (VTI RTM) in the complex-domain method by deriving the complex-domain viscoacoustic VTI equation. This method requires both the traditional real velocity field and the imaginary velocity field as inputs. The imaginary velocity field contains stained geological bodies and significant areas without data. Seismic waves propagate normally in the real wavefield, while in the imaginary wavefield, reflections occur only when the wavefront encounters stained geological bodies. The proposed method is assessed through testing on both a horizontally layered model and a salt model. Through comparative analysis, it has been verified that the method fully incorporates reflected waves with distinct structural features into the imaginary wavefield. Numerical experiments demonstrate that this method can accurately image subsalt structures.

Estimating the anisotropy of the vertical transverse isotropy coal seam by rock physics model–based inversion

AbstractCoal seams exhibiting nearly horizontal bedding, and fractures can be characterized as transversely isotropic media with a vertical axis of symmetry, known as vertical transverse isotropy coal seams. The resulting anisotropy cannot be overlooked in high‐precision seismic velocity analysis, migration imaging and pre‐stack inversion. Therefore, we estimate the anisotropy of the vertical transverse isotropy coal seam (using the anisotropic Thomsen's parameters ε, γ and δ) by inverting the horizontal P‐ and SH‐wave velocities and fracture density based on a rock physics model. The Mori–Tanaka model and Brown–Korringa formula were first used to quantify the anisotropy of the vertical transverse isotropy coal seams impacted by dry and fluid‐saturated fractures. Subsequently, we formulated an equation for the inversion of horizontal P‐ and SH‐wave velocities, considering the measured vertical P‐ and SH‐wave velocities as constrained parameters. This approach is generally applied in vertical drilling scenarios. We tested the inversion method using the ultrasonic test results of coal samples collected from the southern margin of the Qinshui Basin, China and then used it on the full waveform logging data from a vertical coalbed methane well. Both the inversion results of horizontal P‐ and SH‐wave velocities and the estimated anisotropic parameters (ε and γ) were in good agreement with the ultrasonic test results of coal samples, although the accuracy of δ was slightly lower. Therefore, we believe that the proposed method can be extended to estimate the anisotropy of vertical transverse isotropy medium (assuming suitable rock physics models) for the ultrasonic testing of rock samples and full waveform logging along the vertical direction in near‐horizontal formations.

A rock physics model in vertical transverse isotropy media and its application to Eagle Ford shale

AbstractShales are rocks with a complex structure. Shales contain high clay content, which constitutes a load‐bearing skeleton. In this study, we present a novel rock physics model to obtain elastic stiffness coefficients of both clays and shales. The robustness of the model is then verified by a field dataset from Eagle Ford shale. We utilize the extended Maxwell homogenization scheme as a rock physics model for transversely isotropic media, which honours the aspect ratio of each inhomogeneity embedded in an effective inclusion domain. Estimated anisotropy parameters ε, γ and δ, on average, are 0.19, 0.29 and 0.04, respectively, based on our modelling results in Eagle Ford shale. Anisotropic modelling results exhibit a good correlation with dipole sonic logs. Both dipole sonic log analysis and rock physics results demonstrate that clay content is the main driver of anisotropy in the field, and there is a direct relationship between clay volume and anisotropy parameters of ε and γ. The method shown here can be readily applied to other unconventional reservoirs.

Frequency-domain elastic wave modeling for vertical transversely isotropic media with an average-derivative optimal method

Based on an average-derivative method (ADM), it is feasible to develop an optimal elastic wave finite-difference nine-point scheme for vertical transversely isotropic (VTI) media in the frequency domain. The optimization coefficients of ADM can be determined by minimizing phase-velocity dispersion error. Nevertheless, for the complex VTI media, the point-by-point optimization, which only considers a single anisotropic parameter pair, will require high computational cost. To address this issue, we take into account the other two low-cost schemes: the overall simultaneous optimization in terms of various anisotropy parameter pairs and the interpolation based on the completely computed optimization coefficients. Applying the 58 measured anisotropy parameter pairs of sedimentary rocks, we test the performances of point-by-point optimization, the overall optimization, interpolation, and classical nine-point method (CM). The results indicate that the number of grid points per qS wavelength of the interpolation scheme is closest to that of the point-by-point optimization scheme and much lower than that of the overall optimization scheme and CM. In addition, the surface of solid earth is a strong impedance-discontinuity surface (free surface), resulting in the more complicated wavefields. To realize the full-waveform simulation for elastic VTI media, it is necessary to implement the free-surface boundary condition in detail. Based on the equivalence between the stress-image and adaptive parameter-modified schemes for implementing the free-surface boundary condition in the time domain, we give a new frequency-domain free-surface expression for the VTI media. We still call this expression the stress-image scheme. Numerical experiments demonstrate that (1) the optimal ADM can produce more accurate results than CM at almost the same computational cost, (2) the interpolation scheme has almost identical accuracy with the point-by-point optimization scheme, and (3) the stress-image scheme is feasible for the implementation of free-surface boundary condition in a VTI medium.

Acoustoelastic Mori-Tanaka model for third-order elastic constants of fractured rocks

Insights into the stress-dependent elastic moduli of fractured rocks are important in monitoring geopressure and tectonic stress. This can be addressed by the theory of acoustoelasticity that describes elastic nonlinearity due to the cubic strain-energy function through third-order elastic constants (TOECs). The acoustoelastic TOECs are strictly valid for an isotropic homogeneous medium. The extension to fractured rocks remains largely unaddressed. A group of fractures (ellipses) is embedded into a homogeneous background medium subjected to a uniform confining pressure. We formulate an acoustoelastic Mori-Tanaka (MT) model for the effective TOECs of fractured rocks which can be defined as the weighted average of individual TOECs between the background and fractures in terms of respective volume fractions and stiffnesses. For homogeneously distributed fractures, the stress-induced strains are isotropic in the background and in the fractures. For aligned fractures, the resulting anisotropic strains over the background and fractures make the rock a vertical transverse isotropic medium. The effective elastic moduli and TOECs of fractured rocks depend on background elastic moduli, fracture contents, aspect ratios, and fracture orientations. The prestressed aligned fractures induce nonlinear effects on the effective TOECs that increase with increasing fracture contents and decreasing aspect ratios. We validate the acoustoelastic MT model by experimental data and investigate its limitation by comparing it with finite-element simulations.

Anisotropic elastic least-squares reverse time migration with density variations in vertical transverse isotropic media

Anisotropic elastic least-squares reverse time migration with density variations in vertical transverse isotropic media

A fast anisotropic decoupled operator of elastic wave propagation in the space domain for P-/S-wave-mode decomposition and angle calculation, with its application to elastic reverse time migration in a TI medium

The conventional anisotropic P-/S-wave-mode decomposition and angle calculation usually are performed in the wavenumber domain and require multiple Fourier transforms and rely on strong model assumptions. Therefore, it is difficult to use in production due to the prohibitively high computational cost. To tackle this problem, we develop a fast anisotropic P-/S-wave-mode decomposition approach in the space domain and further apply this decomposition to the vertical transversely isotropic (VTI)/tilted transversely isotropic (TTI) elastic reverse time migration (ERTM) and the associated angle-domain common-image gathers (ADCIGs). To start with, we solve the Christoffel equation of the VTI media and obtain an anisotropic-Helmholtz (AH) operator that represents the P- and S-wave polarizations in the wavenumber domain. The decoupled operators for the P-/S-wave decomposition are then derived in terms of the AH operator. To improve the efficiency and model adaptability, we convert the decoupled operators from the wavenumber domain to the space domain as a function of the model parameters and phase angle. By further eliminating the phase-angle term, such space-domain decoupled operators lead to the approximate P- and S-wave components which are proven to achieve the same effect as the accurate P and S wavefields applied in the angle calculation and ERTM images. A fast space-domain AH decomposition approach is thus obtained and can be used for P-/S-wave-mode decomposition, ADCIGs, and ERTM. In addition, we extend our approach to the TTI media by using the coordinate transform. Three examples are used to demonstrate the effectiveness and feasibility of our method.

Sequential Seismic Anisotropic Inversion for VTI Media with Simulated Annealing Algorithm Aided by Adaptive Setting of Optimization Parameters

As an important geophysical data processing technique, seismic inversion estimates subsurface rock properties with seismic observations. However, anisotropic inversion, intended for a vertical transverse isotropy (VTI) media that primarily describes shale gas/oil resources, suffers from high nonlinearity. Simulated annealing is a widely used global optimization algorithm for solving nonlinear seismic inverse problems, but it involves multiple optimization parameters (e.g., initial temperature, search limit, and perturbation range). The importance of such parameters has been proven whilst the relevant analysis is limited in seismic inversion studies. This work hereby proposes a sequential anisotropic inversion method for VTI media, wherein we combine Bayesian linear and simulated annealing nonlinear inversion schemes. The simulated annealing is featured by adaptive optimization parameters aided by the linear result. Rather than the conventional method, the adaptive setting can be implemented trace by trace for complex reservoirs, which endows the method with enhanced stability and extended applicability. Synthetic tests and practical application demonstrate the validity of the method, wherein the obtained stiffness parameters facilitate the characterization of potential shale reservoirs with an improved accuracy.

Semi-analytical solution for the elastic wave propagation due to a dislocation source in a transversely isotropic half-space

SUMMARY In this paper, the 3-D theoretical seismogram at the free surface of an elastic half-space with ‘vertical transverse isotropy (VTI)’ and an ‘elliptic anisotropy‘ is synthesized via semi-analytical formulation. To this end, the time-domain solution is obtained via the Hankel and Laplace integral transforms and the Cagniard contour integration scheme. The formulations include complete Green's functions expressed in compact and elegant formulations in terms of some elementary line integrals over the finite interval (0, π/2), due to the general point force and point double-couple source of arbitrary orientation, varying with time as Heaviside step function. This solution is further implemented to model seismic waves generated from moment tensor source with a ramp-type slip function. The solution clearly delineates compressional P waves, shear SV waves and SH waves, diffracted SPwaves and surface Rayleigh waves, with two critical distances in which the mode conversion happens. The first marks the conversion of the total reflection of SV wave into the diffracted SPwave travelling on the free surface with the velocity of compressional wave. The second, however, marks a location where the order of arrival times of SP and SH waves is reversed. The interesting phenomenon of shear wave splitting by the apparent time lag between the arrivals of SV and SHwaves is further demonstrated. Studied also is the effect of non-double-couple (non-DC) components of the moment tensor of the shear fault. Particularly, it is shown that non-DC components may lead to large amplitude of the P wave in the presence of anisotropy, resulting in the changed polarity of P wave at the onset of the motion. It is found that for the elliptic anisotropy, and for oblique-thrust faults, the isotropic moment (ISO) is always negative if the elastic constants satisfy C11 > C33 and C44 > C66, whereas it is always positive if C11 < C33 and C44 < C66 (for oblique-reverse faults, the situation is reversed). It is shown that for some sedimentary rocks, the decomposition of moment tensor in the general VTI and in its elliptic approximation are close to each other, and that the moment tensor decomposition in VTI media is very sensitive to the elastic coefficients, such that a small change in the elastic constants may lead to a remarkable change in the moment tensor decomposition. Particularly, the effect of elastic constant C13 is shown to be significant. While the time-domain solution obtained in this paper can be also degenerated to the solution in the corresponding isotropic half-space, the Mathematica code of the solution provided can be served as benchmark to other numerical solutions, applicable for the computation of the theoretical seismogram in the involved media.

Decoupled wave equation and forward modeling of qP wave in VTI media with the new acoustic approximation

Acoustic approximation has received wide attention in modeling and inversion for the anisotropic wave equation to avoid high computational cost and parameter trade-off in seismic inversion. However, it also is limited by the stability condition, such as the instability for the qP-wave equation in transversely isotropic media with [Formula: see text]. We have developed a new approach that decoupled wave equation and forward modeling of the qP wave in vertical transversely isotropic (VTI) media with the new acoustic approximation. To keep dispersion relations ([Formula: see text]) of the qSV wave in each direction equal to zero, we formulate the vertical S-wave velocity ([Formula: see text]) to be a function of the model parameters and wavenumber component ([Formula: see text]), rather than setting it to zero. Then, the corresponding dispersion relation of pure qP for the new acoustic approximation is derived. According to this decoupled dispersion relation, we obtain the decoupled wave equation of pure qP wave in VTI media by inverse Fourier transform. To solve the wave equation in the space domain efficiently, the operator [Formula: see text] in the wave equation is characterized in the space domain by its asymptotic approximation operator [Formula: see text]. From the qP wave equation in the time-space domain, we realize the forward modeling of the pure qP wave in VTI media with the finite-difference method. The dispersion relation analysis and numerical examples find that the decoupled qP-wave equation with the new acoustic approximation does not contain the degenerate qSV wave and is a pure qP-wave equation, which is in good agreement with the simulation results of the elastic wave equation and has high accuracy and is stable in VTI media with [Formula: see text] or [Formula: see text].

Generalization of Bayesian inversion with application to PP reflection in a vertical transverse isotropy medium

ABSTRACTSeismic inversion of amplitude variation with offset is an ill‐conditioned problem, in which small errors in the observed data result in large errors in the estimates, and therefore regularization functions are necessary. The Bayes' theorem regularizes ill‐posed problems using the statistical properties of the model parameters of interest; however, our knowledge of these statistical properties is poor. Meanwhile, the Bayesian framework is limited to particular forms of a priori probability distributions, due to poor knowledge of the statistical properties of individual probability distributions. Moreover, each particular a priori probability distribution requires a reformulation of the inversion under a Bayesian framework, which is not practically preferred. Here, we construct a Bayesian framework that enables the use of various types of a priori probability distributions without the need to reformulate the problem and to obtain well‐established statistical information on the model parameters of interest, specifically a lower bound on the variance of the a priori model, for example. Fisher information. Consequently, different probability distributions that best address the parameters of interest are first fitted using the maximum likelihood estimator . A lower bound on the variance of each a priori model is then estimated, which provides adequate statistical information between different model parameters; hence, it is ideally suited for the Bayesian framework. Thereafter, an iterative approach is proposed that utilizes the Hessians of the data and model spaces, and an adaptive learning rate to compute the optimal directions for model updates. The approach is applied to synthetic and real seismic data to estimate the elastic and seismic anisotropy parameters of shale formations. The regularization from the a priori probability density successfully stabilizes the updates of the variant‐sensitivity parameters by imposing the correlation information in the optimization process.

NMO stretch in vertical transverse isotropic media presented by nonhyperbolic approximations

Normal-moveout (NMO) correction is an inevitable part of routine seismic data processing and imaging. NMO correction suffers from an undesirable phenomenon called NMO stretching, which is more pronounced in larger emerging angles. Frequency distortions caused by NMO stretching for isotropic media have fully been studied in the literature. We express the distortions for the simplest case of anisotropy, which is vertical transverse isotropic media. This is done through different nonhyperbolic approximations, including shifted-hyperbola approximation, rational approximation, and generalized moveout approximation (GMA). To evaluate the predicted distortions, we define a trace-muting threshold and use it in the trace-muting procedure for synthetic data, as well as a field recorded example. Comparison between the results proves that the GMA has the highest accuracy among the other presented approximations. The proposed approach has an immediate potential to be used in industry and also to help to develop innovative nonstretch NMO correction workflows.

A novel and efficient engine for P-/S-wave-mode vector decomposition for vertical transverse isotropic elastic reverse time migration

Wave-mode decomposition plays a very important role in elastic reverse time migration (ERTM). Improved imaging quality can be achieved due to reduced wave-mode crosstalk artifacts. The current state-of-the-art methods for anisotropic wavefield separation are based on either splitting model strategy, low-rank approximation, or lower-upper (LU) factorization. Most of these involve expensive matrix computation and Fourier transforms with strong model assumptions. Based on the anisotropic-Helmholtz (ani-Helmholtz) decomposition operator and decoupled formulations, we develop a novel and efficient P-/S-wave-mode vector decomposition method in vertical transverse isotropic (VTI) media with application in ERTM. We first review the basics of classical Helmholtz decomposition and isotropic decoupled formulations. In addition, the ani-Helmholtz decomposition operator is built from the P- and S-wave polarizations of the Christoffel equation in VTI media. We then derive novel decoupled formulations of anisotropic P-/S-waves based on the obtained ani-Helmholtz operator. Moreover, we use the first-order Taylor expansion to approximate the normalization term from the derived decoupled formulations and obtain an efficient ani-Helmholtz decomposition approach, which produces vector P- and S-wavefields with correct units, phases, and amplitudes. Compared with the previous studies, our approach mitigates model assumptions, avoids intricate calculations, such as LU factorization or low-rank approximation, and only needs three fast Fourier transforms at each time step. In addition, the graphic processing unit technique is used to dramatically accelerate various functions of ERTM, such as wavefields extrapolation, decomposition, and imaging. Three synthetic examples demonstrate the effectiveness and feasibility of our proposed approach.

Viscoacoustic wave equation for qP-wave in transversely isotropic media

The wave equation acts a pivotal part in seismic data processing. We derived two time-domain pure qP viscoacoustic wave equations suitable for attenuation anisotropic media, providing a choice for pure qP-wave forward modeling and inversion in attenuation anisotropic media. Our new qP-wave equation in vertical transversely isotropic (VTI) media are based on the dispersion relation for qP-wave in VTI media and obtained by the relaxation functions of the standard linear solid model and the Kjartansson's constant Q model respectively. Anelasticity including amplitude attenuation and phase dispersion can be dealt with by the proposed wave equation separately. With the coordinate transform, the corresponding two pure qP-wave viscoacoustic anisotropic wave equations for titled transversely isotropic media also are derived. Different from the common viscoacoustic anisotropic wave equation (a coupled second-order partial differential equations system), the new wave equations are simplified by decomposing the original pseudo-differential operator into a differential and a scalar opera- tors. For numerical calculation, the new wave equations can be solved more efficiently than the coupled wave equations. Meanwhile the new wave equations could simulate pure qP-wave steadily in attenuation anisotropic media without quasi-SV wave artifacts. Some synthetic examples, including attenuation Hess and Marmousi-2 models, demonstrate the feasibility of the derived pure qP-wave viscoacoustic wave equations in transversely isotropic media.

Amplitude-Preserving Imaging Condition for Scattering-Based RTM in Acoustic VTI Media

Conventional seismic imaging methods rely on reflected waves to obtain the interfaces of geologic variations and the normal-incidence reflectivity at the interfaces. However, the scattering phenomena affect the imaging quality, especially in anisotropic media. Most of the current techniques which neglect the scattering effects are insufficient to acquire accurate images. To correct such scattering effects and reduce the image artifacts, we have derived a new, scattering-based, amplitude-preserving imaging condition with anisotropic background assumption in acoustic vertical transverse isotropic (VTI) media. In addition, we present a correlation-type representation for this imaging condition to avoid the problem of being divided by small numbers during reverse-time migration (RTM). Based on this proposed imaging condition, the amplitude of imaging result has the specific physical meaning of the velocity perturbation, and can be retrieved by RTM accurately. Numerical experiments on synthetic data show that our inverse-scattering imaging condition can produce more accurate amplitudes on images than cross-correlation imaging condition.

Oriented NMO correction of VTI data in the absence of near-offset traces

Calculating an accurate seismic velocity model serves an important role in many seismic imaging techniques. The process of velocity model building is often time-consuming, specifically for anisotropic areas, where more than a single parameter is involved in the process. In the past few years, more time-efficient approaches have been considered to estimate seismic velocity as well as anellipticity parameter or heterogeneity factor using local event slopes. Nevertheless, some of these techniques are not practical due to curvature-dependency, or due to the lack of near-offset data. To address such limitations, we have used a curvature-independent approach for normal-moveout correction as well as parameter estimation in vertical transverse isotropic media, which is based on local estimation of vertical traveltime using a shifted-hyperbola approximation in the absence of near-offset data. The performance of our approach is tested on synthetic and field common-midpoint gathers. It is also assessed in different signal-to-noise ratios and different missing-near-offset situations. Our findings are consistent with the results achieved by the previous methods that were not developed for sparse data.

A fast sweeping method for calculating qP-wave traveltimes in 3-D vertical transversely isotropic media using a quadratic equation

SUMMARY Traveltime computations are an important aspect of seismic data processing applications such as traveltime tomography, migration and seismic source localization. Seismic anisotropy is a widespread feature of the Earth. Solutions to the eikonal equation that account for such anisotropy are needed for high-resolution seismic imaging and inversion. The fast sweeping method (FSM) has been widely used in computing the first-arrival traveltimes for anisotropic media because it does not need to expand the wave front from the point of the smallest traveltime. To apply FSM on strong anisotropic media, one has to solve the slowness equation derived from the Christoffel equation. All the previous developed FSM methods transform the quartic coupled slowness surface equation of quasi-P (qP) and quasi-SV (qSV) waves to the quartic equation in terms of the unknown traveltime, then numerically solve this quartic equation to compute the first-arrival traveltimes of the qP waves. However, the computational cost is significantly increased due the numerically solving the quartic equation, especially for the 3-D problems. In this study, we find a way to transform the quartic slowness equation into a quadratic one if a specific triangular-pyramid stencil around a target point is used. As the quadratic equation has the analytical solution and does not need a numerical solver, the computational efficiency of the scheme is greatly improved. We apply this methodology to develop an efficient 3-D FSM to compute the first-arrival traveltimes for qP waves in 3-D vertical transversely isotropic (VTI) media. We use both layered VTI model and complex VTI model to demonstrate the efficiency of the proposed method to obtain accurate traveltimes in 3-D VTI media involving strong anisotropy.

Decoupled approximation and separate extrapolation of P- and SV-waves in transversely isotropic media

Characterizing the kinematics of seismic waves in elastic vertical transversely isotropic (VTI) media involves four independent parameters. To reduce the complexity, the acoustic approximation for P-waves reduces the number of required parameters to three by setting the vertical S-wave velocity to zero. However, because only the SV-wave phase velocities parallel or perpendicular to the symmetry axis are indirectly set to zero, the acoustic approximation leads to coupled P-wave components and SV-wave artifacts. The new acoustic approximation suggests setting the vertical S-wave velocity as a phase angle-dependent variable so that the SV-wave phase velocity is zero at all phase angles. We find that manipulating this parameter is a valid approach for P-wave approximation but doing so inevitably leads to zero- or nonzero-valued spurious SV-wave components. Thus, we have developed a novel approach to efficiently approximate and thoroughly separate the two wave modes in VTI media. First, the exact P- and SV-wave phase velocity expressions are rewritten by introducing an auxiliary function. After confirming the insensitivity of this function, we construct a new expression for it and obtain simplified P- and SV-wave phase velocity expressions, which are three and four parameters, respectively. This approximation process leads to the same reasonable error for both wave modes. Accuracy analysis indicates that, for the P-wave, the overall accuracy performance of our approach is comparable to that of some existing three-parameter approximations. We then derive the corresponding P- and SV-wave equations in tilted transversely isotropic (TTI) media and provide two available solutions, the hybrid finite-difference/pseudospectral scheme and the low-rank approach. Numerical examples illustrate the separability and high accuracy of the proposed P- and SV-wave simulation methods in TTI media.

Determination of the elastic parameters of a VTI medium from sonic logging data using deep learning

Inversion of sonic logging data becomes a non-trivial problem for anisotropic media, especially for the case of vertical transverse isotropic (VTI) formation, when a well is parallel to its axis of symmetry. Most modern processing techniques use only the kinematic characteristics of the wavefield. Thus, they are incapable of determining all formation elastic parameters (density, compressional and shear wave velocities, and Thomsen parameters) that fully describe such a case unless some rigorous assumptions are made or the well has deviated sections. A sensitivity analysis based on modeled seismic response to the elastic parameters illustrates the fact that sufficient information is contained in the amplitudes of different sonic modes. To retrieve this information, we perform a method of the sonic data inversion using a machine learning algorithm such as the convolutional neural network. Powerful computing resources are needed only for synthetic seismograms generation by the spectral element method for the range of geologically admissible parameters (training dataset) and optimization of the neural network weights by minimizing a misfit function. The inversion process consists simply of applying the optimized neural network to the sonic data to retrieve the elastic parameters that fully describe the VTI medium. We generated a series of synthetic sonic data different from the training one (test dataset) and compared the outcome of the inversion to the actual parameters. The results show good agreement within a few per cent for all elastic parameters illustrating the feasibility of the proposed method.