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Full waveform inversion in transversely isotropic media with a vertical symmetry axis provides an opportunity to better match the data at the near and far offsets. However, multi-parameter full waveform inversion, in general, suffers from serious cycle-skipping and trade-off problems. Reflection waveform inversion can help us recover a background model by projecting the residuals of the reflected wavefield along the reflection wavepath. Thus, we extend reflection waveform inversion to acoustic transversely isotropic media with a vertical symmetry axis utilizing the proper parameterization for reduced parameter trade-off. From a radiation patterns analysis, an acoustic transversely isotropic media with a vertical symmetry axis is better described by a combination of the normal-moveout velocity and the anisotropic parameters η and δ for reflection waveform inversion applications. We design a three-stage inversion strategy to construct the optimal resulting model. In the first stage, we only invert for the background by matching the simulated reflected wavefield from the perturbations of and δ with the observed reflected wavefield. In the second stage, the background and η are optimized simultaneously and the far-offset reflected wavefield mainly contribute to their updates. We perform Born modelling to compute the reflected wavefield for the two stages of reflection waveform inversion. In the third stage, we perform full waveform inversion for the acoustic transversely isotropic media with a vertical symmetry axis to delineate the high-wavenumber structures. For this stage, the medium is described by a combination of the horizontal velocity , η and ε instead of , η and δ. The acoustic multi-parameter full waveform inversion utilizes the diving waves to improve the background as well as utilizes reflection for high-resolution information. Finally, we test our inversion algorithm on the modified Sigsbee 2A model (a salt free part) and a two-dimensional line from a three-dimensional ocean bottom cable dataset. The results demonstrate that the proposed reflection waveform inversion approach can recover the background model for acoustic transversely isotropic media with a vertical symmetry axis starting from an isotropic model. This recovered background model can mitigate the cycle skipping of full waveform inversion and help the inversion recover higher resolution structures. 相似文献
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Using both image and data domains to perform velocity inversion can help us resolve the long and short wavelength components of the velocity model, usually in that order. This translates to integrating migration velocity analysis into full waveform inversion. The migration velocity analysis part of the inversion often requires computing extended images, which is expensive when using conventional methods. As a result, we use pre‐stack wavefield (the double‐square‐root formulation) extrapolation, which includes the extended information (subsurface offsets) naturally, to make the process far more efficient and stable. The combination of the forward and adjoint pre‐stack wavefields provides us with update options that can be easily conditioned to improve convergence. We specifically use a modified differential semblance operator to split the extended image into a residual part for classic differential semblance operator updates and the image (Born) modelling part, which provides reflections for higher resolution information. In our implementation, we invert for the velocity and the image simultaneously through a dual objective function. Applications to synthetic examples demonstrate the features of the approach. 相似文献
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Analysis of the traveltime sensitivity kernels for an acoustic transversely isotropic medium with a vertical axis of symmetry 
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下载免费PDF全文 In anisotropic media, several parameters govern the propagation of the compressional waves. To correctly invert surface recorded seismic data in anisotropic media, a multi‐parameter inversion is required. However, a tradeoff between parameters exists because several models can explain the same dataset. To understand these tradeoffs, diffraction/reflection and transmission‐type sensitivity‐kernels analyses are carried out. Such analyses can help us to choose the appropriate parameterization for inversion. In tomography, the sensitivity kernels represent the effect of a parameter along the wave path between a source and a receiver. At a given illumination angle, similarities between sensitivity kernels highlight the tradeoff between the parameters. To discuss the parameterization choice in the context of finite‐frequency tomography, we compute the sensitivity kernels of the instantaneous traveltimes derived from the seismic data traces. We consider the transmission case with no encounter of an interface between a source and a receiver; with surface seismic data, this corresponds to a diving wave path. We also consider the diffraction/reflection case when the wave path is formed by two parts: one from the source to a sub‐surface point and the other from the sub‐surface point to the receiver. We illustrate the different parameter sensitivities for an acoustic transversely isotropic medium with a vertical axis of symmetry. The sensitivity kernels depend on the parameterization choice. By comparing different parameterizations, we explain why the parameterization with the normal moveout velocity, the anellipitic parameter η, and the δ parameter is attractive when we invert diving and reflected events recorded in an active surface seismic experiment. 相似文献
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3D anisotropic waveform inversion could provide high-resolution velocity models and improved event locations for microseismic surveys. Here we extend our previously developed 2D inversion methodology for microseismic borehole data to 3D transversely isotropic media with a vertical symmetry axis. This extension allows us to invert multicomponent data recorded in multiple boreholes and properly account for vertical and lateral heterogeneity. Synthetic examples illustrate the performance of the algorithm for layer-cake and ‘hydraulically fractured’ (i.e. containing anomalies that simulate hydraulic fractures) models. In both cases, waveform inversion is able to reconstruct the areas which are sufficiently illuminated for the employed source-receiver geometry. In addition, we evaluate the sensitivity of the algorithm to errors in the source locations and to band-limited noise in the input displacements. We also present initial inversion results for a microseismic data set acquired during hydraulic fracturing in a shale reservoir. 相似文献
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In multi-parameter ray-based anisotropic migration/inversion, it is essential that we have an understanding of the scattering mechanism corresponding to parameter perturbations. Because the complex nonlinearity in the anisotropic inversion problem is intractable, the construction of true-amplitude linearized migration/inversion procedures is needed and important. By using the acoustic medium assumption for transversely isotropic media with a vertical axis of symmetry and representing the anisotropy with P-wave normal moveout velocity, Thomsen parameter δ and anelliptic parameter η, we formalize the linearized inverse scattering problem for three-dimensional pseudo-acoustic equations. Deploying the single-scattering approximation and an elliptically anisotropic background introduces a new linear integral operator that connects the discontinuous perturbation parameters with the multi-shot/multi-offset P-wave scattered data. We further apply the high-frequency asymptotic Green's function and its derivatives to the integral operator, and then the scattering pattern of each perturbation parameter can be explicitly presented. By naturally establishing a connection to generalized Radon transform, the pseudo-inverse of the integral operator can be solved by the generalized Radon transform inversion. In consideration of the structure of this pseudo-inverse operator, the computational implementation is done pointwise by shooting a fan of rays from the target imaging area towards the acquisition system. Results from two-dimensional numerical tests show amplitude-preserving images with high quality. 相似文献
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Tilted transversely isotropic formations cause serious imaging distortions in active tectonic areas (e.g., fold‐and‐thrust belts) and in subsalt exploration. Here, we introduce a methodology for P‐wave prestack depth imaging in tilted transversely isotropic media that properly accounts for the tilt of the symmetry axis as well as for spatial velocity variations. For purposes of migration velocity analysis, the model is divided into blocks with constant values of the anisotropy parameters ε and δ and linearly varying symmetry‐direction velocity VP0 controlled by the vertical (kz) and lateral (kx) gradients. Since determination of tilt from P‐wave data is generally unstable, the symmetry axis is kept orthogonal to the reflectors in all trial velocity models. It is also assumed that the velocity VP0 is either known at the top of each block or remains continuous in the vertical direction. The velocity analysis algorithm estimates the velocity gradients kz and kx and the anisotropy parameters ε and δ in the layer‐stripping mode using a generalized version of the method introduced by Sarkar and Tsvankin for factorized transverse isotropy with a vertical symmetry axis. Synthetic tests for several models typical in exploration (a syncline, uptilted shale layers near a salt dome and a bending shale layer) confirm that if the symmetry‐axis direction is fixed and VP0 is known, the parameters kz, kx, ε and δ can be resolved from reflection data. It should be emphasized that estimation of ε in tilted transversely isotropic media requires using nonhyperbolic moveout for long offsets reaching at least twice the reflector depth. We also demonstrate that application of processing algorithms designed for a vertical symmetry axis to data from tilted transversely isotropic media may lead to significant misfocusing of reflectors and errors in parameter estimation, even when the tilt is moderate (30°). The ability of our velocity analysis algorithm to separate the anisotropy parameters from the velocity gradients can be also used in lithology discrimination and geologic interpretation of seismic data in complex areas. 相似文献
8.
The horizontal transversely isotropic model, with arbitrary symmetry axis orientation, is the simplest effective representative that explains the azimuthal behaviour of seismic data. Estimating the anisotropy parameters of this model is important in reservoir characterisation, specifically in terms of fracture delineation. We propose a travel‐time‐based approach to estimate the anellipticity parameter η and the symmetry axis azimuth ? of a horizontal transversely isotropic medium, given an inhomogeneous elliptic background model (which might be obtained from velocity analysis and well velocities). This is accomplished through a Taylor's series expansion of the travel‐time solution (of the eikonal equation) as a function of parameter η and azimuth angle ?. The accuracy of the travel time expansion is enhanced by the use of Shanks transform. This results in an accurate approximation of the solution of the non‐linear eikonal equation and provides a mechanism to scan simultaneously for the best fitting effective parameters η and ?, without the need for repetitive modelling of travel times. The analysis of the travel time sensitivity to parameters η and ? reveals that travel times are more sensitive to η than to the symmetry axis azimuth ?. Thus, η is better constrained from travel times than the azimuth. Moreover, the two‐parameter scan in the homogeneous case shows that errors in the background model affect the estimation of η and ? differently. While a gradual increase in errors in the background model leads to increasing errors in η, inaccuracies in ?, on the other hand, depend on the background model errors. We also propose a layer‐stripping method valid for a stack of arbitrary oriented symmetry axis horizontal transversely isotropic layers to convert the effective parameters to the interval layer values. 相似文献
9.
Diffractions play a vital role in seismic processing as they can be utilized for high‐resolution imaging applications and analysis of subsurface medium properties like velocity. They are particularly valuable for anisotropic media as they inherently possess a wide range of dips necessary to resolve the angular dependence of velocity. However, until recently, the focus of diffraction imaging or inversion algorithms have been only on the isotropic approximation of the subsurface. Using diffracted waves, we develop a framework to invert for the effective η model. This effective model is obtained through scanning over possible effective η values and selecting the one that best fits the observed moveout curve for each diffractor location. The obtained effective η model is then converted to an interval η model using a Dix‐type inversion formula. The inversion methodology holds the potential to reconstruct the true η model with sufficiently high accuracy and resolution properties. However, it relies on an accurate estimation of diffractor locations, which in turn requires good knowledge of the background velocity model. We test the effectiveness and applicability of our method on the vertical transverse isotropic Marmousi model. The inversion results yield a reasonable match even for the complex Marmousi model. 相似文献
10.
Integrating migration velocity analysis and full waveform inversion can help reduce the high non‐linearity of the classic full waveform inversion objective function. The combination of inverting for the long and short wavelength components of the velocity model using a dual objective function that is sensitive to both components is still very expensive and have produced mixed results. We develop an approach that includes both components integrated to complement each other. We specifically utilize the image to generate reflections in our synthetic data only when the velocity model is not capable of producing such reflections. As a result, we get the migration velocity analysis working when we need it, and we mitigate its influence when the velocity model produces accurate reflections (possibly first for the low frequencies). This is achieved using a novel objective function that includes both objectives. Applications to a layered model and the Marmousi model demonstrate the main features of the approach. 相似文献
11.
Pure-mode wave propagation is important for applications ranging from imaging to avoiding parameter tradeoff in waveform inversion. Although seismic anisotropy is an elastic phenomenon, pseudo-acoustic approximations are routinely used to avoid the high computational cost and difficulty in decoupling wave modes to obtain interpretable seismic images. However, such approximations may result in inaccuracies in characterizing anisotropic wave propagation. We propose new pure-mode equations for P- and S-waves resulting in an artefact-free solution in transversely isotropic medium with a vertical symmetry axis. Our approximations are more accurate than other known approximations as they are not based on weak anisotropy assumptions. Therefore, the S-wave approximation can reproduce the group velocity triplications in strongly anisotropic media. The proposed approximations can be used for accurate modelling and imaging of pure P- and S-waves in transversely isotropic media. 相似文献
12.
James G. Berryman 《Geophysical Prospecting》2009,57(2):193-208
Certain crack-influence parameters of Sayers and Kachanov are shown to be directly related to Thomsen's weak-anisotropy seismic parameters for fractured reservoirs when the crack/fracture density is small enough. These results are then applied to the problem of seismic wave propagation in polar reservoirs, i.e., those anisotropic reservoirs having two axes that are equivalent but distinct from the third axis), especially for horizontal transversely isotropic seismic wave symmetry due to the presence of aligned vertical fractures and resulting in azimuthal seismic wave symmetry at the Earth's surface. The approach presented suggests one method of inverting for fracture density from wave speed data. A significant fraction of the technical effort in the paper is devoted to showing how to predict the angular location of the true peak (or trough) of the quasi-SV-wave for polar media and especially how this peak is related to another angle that is very easy to compute. The axis of symmetry is always treated here as the x 3 -axis for either vertical transversely isotropic symmetry (due, for example, to horizontal cracks), or horizontal transversely isotropic symmetry (due to aligned vertical cracks). Then, the meaning of the stiffnesses is derived from the fracture analysis in the same way for vertical transversely isotropic and horizontal transversely isotropic media, but for horizontal transverse isotropy the wave speeds relative to the Earth's surface are shifted by 90o in the plane perpendicular to the aligned vertical fractures. Skempton's poroelastic coefficient B is used as a general means of quantifying the effects of fluids inside the fractures. Explicit Biot-Gassmann-consistent formulas for Thomsen's parameters are also obtained for either drained or undrained fractures resulting in either vertical transversely isotropic or horizontal transversely isotropic symmetry of the reservoir. 相似文献
13.
Yang Zhang Leo Eisner William Barker Michael C. Mueller Kevin L. Smith 《Geophysical Prospecting》2013,61(5):919-930
We develop a methodology to obtain a consistent velocity model from calibration shots or microseismicity observed on a buried array. Using a layered 1D isotropic model derived from checkshots as an initial velocity model, we invert P‐wave arrival times to obtain effective anisotropic parameters with a vertical axis of symmetry (VTI). The nonlinear inversion uses iteration between linearized inversion for anisotropic parameters and origin times or depths, which is specific to microseismic monitoring. We apply this technique to multiple microseismic events from several treatments within a buried array. The joint inversion of selected events shows a largely reduced RMS error indicating that we can obtain robust estimates of anisotropic parameters, however we do not show improved source locations. For joint inversion of multiple microseismic events we obtained Thomsen anisotropic parameters ε of 0.15 and δ of 0.05, which are consistent with values observed in active seismic surveys. These values allow us to locate microseismic events from multiple hydraulic fracture treatments separated across thousands of metres with a single velocity model. As a result, we invert the effective anisotropy for the buried array region and are able to provide a more consistent microseismicity mapping for past and future hydraulic fracture stimulations. 相似文献
14.
Anisotropy is often observed due to the thin layering or aligned micro‐structures, like small fractures. At the scale of cross‐well tomography, the anisotropic effects cannot be neglected. In this paper, we propose a method of full‐wave inversion for transversely isotropic media and we test its robustness against structured noisy data. Optimization inversion techniques based on a least‐square formalism are used. In this framework, analytical expressions of the misfit function gradient, based on the adjoint technique in the time domain, allow one to solve the inverse problem with a high number of parameters and for a completely heterogeneous medium. The wave propagation equation for transversely isotropic media with vertical symmetry axis is solved using the finite difference method on the cylindrical system of coordinates. This system allows one to model the 3D propagation in a 2D medium with a revolution symmetry. In case of approximately horizontal layering, this approximation is sufficient. The full‐wave inversion method is applied to a crosswell synthetic 2‐component (radial and vertical) dataset generated using a 2D model with three different anisotropic regions. Complex noise has been added to these synthetic observed data. This noise is Gaussian and has the same amplitude f?k spectrum as the data. Part of the noise is localized as a coda of arrivals, the other part is not localized. Five parameter fields are estimated, (vertical) P‐wave velocity, (vertical) S‐wave velocity, volumetric mass and the Thomsen anisotropic parameters epsilon and delta. Horizontal exponential correlations have been used. The results show that the full‐wave inversion of cross‐well data is relatively robust for high‐level noise even for second‐order parameters such as Thomsen epsilon and delta anisotropic parameters. 相似文献
15.
Based on the theory of anisotropic elasticity and observation of static mechanic measurement of transversely isotropic hydrocarbon source rocks or rock‐like materials, we reasoned that one of the three principal Poisson's ratios of transversely isotropic hydrocarbon source rocks should always be greater than the other two and they should be generally positive. From these relations, we derived tight physical constraints on c13, Thomsen parameter δ, and anellipticity parameter η. Some of the published data from laboratory velocity anisotropy measurement are lying outside of the constraints. We analysed that they are primarily caused by substantial uncertainty associated with the oblique velocity measurement. These physical constraints will be useful for our understanding of Thomsen parameter δ, data quality checking, and predicting δ from measurements perpendicular and parallel to the symmetrical axis of transversely isotropic medium. The physical constraints should also have potential application in anisotropic seismic data processing. 相似文献
16.
Ho Seuk Bae Changsoo Shin Young Ho Cha Yunseok Choi Dong‐Joo Min 《Geophysical Prospecting》2010,58(6):997-1010
Although waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the time‐ and frequency‐domain waveform inversion algorithms still have critical limitations in their applications to field data. This may be attributed to the highly non‐linear objective function and the unreliable low‐frequency components. To overcome the weaknesses of conventional waveform inversion algorithms, the acoustic Laplace‐domain waveform inversion has been proposed. The Laplace‐domain waveform inversion has been known to provide a long‐wavelength velocity model even for field data, which may be because it employs the zero‐frequency component of the damped wavefield and a well‐behaved logarithmic objective function. However, its applications have been confined to 2D acoustic media. We extend the Laplace‐domain waveform inversion algorithm to a 2D acoustic‐elastic coupled medium, which is encountered in marine exploration environments. In 2D acoustic‐elastic coupled media, the Laplace‐domain pressures behave differently from those of 2D acoustic media, although the overall features are similar to each other. The main differences are that the pressure wavefields for acoustic‐elastic coupled media show negative values even for simple geological structures unlike in acoustic media, when the Laplace damping constant is small and the water depth is shallow. The negative values may result from more complicated wave propagation in elastic media and at fluid‐solid interfaces. Our Laplace‐domain waveform inversion algorithm is also based on the finite‐element method and logarithmic wavefields. To compute gradient direction, we apply the back‐propagation technique. Under the assumption that density is fixed, P‐ and S‐wave velocity models are inverted from the pressure data. We applied our inversion algorithm to the SEG/EAGE salt model and the numerical results showed that the Laplace‐domain waveform inversion successfully recovers the long‐wavelength structures of the P‐ and S‐wave velocity models from the noise‐free data. The models inverted by the Laplace‐domain waveform inversion were able to be successfully used as initial models in the subsequent frequency‐domain waveform inversion, which is performed to describe the short‐wavelength structures of the true models. 相似文献
17.
We develop a two‐dimensional full waveform inversion approach for the simultaneous determination of S‐wave velocity and density models from SH ‐ and Love‐wave data. We illustrate the advantages of the SH/Love full waveform inversion with a simple synthetic example and demonstrate the method's applicability to a near‐surface dataset, recorded in the village ?achtice in Northwestern Slovakia. Goal of the survey was to map remains of historical building foundations in a highly heterogeneous subsurface. The seismic survey comprises two parallel SH‐profiles with maximum offsets of 24 m and covers a frequency range from 5 Hz to 80 Hz with high signal‐to‐noise ratio well suited for full waveform inversion. Using the Wiechert–Herglotz method, we determined a one‐dimensional gradient velocity model as a starting model for full waveform inversion. The two‐dimensional waveform inversion approach uses the global correlation norm as objective function in combination with a sequential inversion of low‐pass filtered field data. This mitigates the non‐linearity of the multi‐parameter inverse problem. Test computations show that the influence of visco‐elastic effects on the waveform inversion result is rather small. Further tests using a mono‐parameter shear modulus inversion reveal that the inversion of the density model has no significant impact on the final data fit. The final full waveform inversion S‐wave velocity and density models show a prominent low‐velocity weathering layer. Below this layer, the subsurface is highly heterogeneous. Minimum anomaly sizes correspond to approximately half of the dominant Love‐wavelength. The results demonstrate the ability of two‐dimensional SH waveform inversion to image shallow small‐scale soil structure. However, they do not show any evidence of foundation walls. 相似文献
18.
A major complication caused by anisotropy in velocity analysis and imaging is the uncertainty in estimating the vertical velocity and depth scale of the model from surface data. For laterally homogeneous VTI (transversely isotropic with a vertical symmetry axis) media above the target reflector, P‐wave moveout has to be combined with other information (e.g. borehole data or converted waves) to build velocity models for depth imaging. The presence of lateral heterogeneity in the overburden creates the dependence of P‐wave reflection data on all three relevant parameters (the vertical velocity VP0 and the Thomsen coefficients ε and δ) and, therefore, may help to determine the depth scale of the velocity field. Here, we propose a tomographic algorithm designed to invert NMO ellipses (obtained from azimuthally varying stacking velocities) and zero‐offset traveltimes of P‐waves for the parameters of homogeneous VTI layers separated by either plane dipping or curved interfaces. For plane non‐intersecting layer boundaries, the interval parameters cannot be recovered from P‐wave moveout in a unique way. Nonetheless, if the reflectors have sufficiently different azimuths, a priori knowledge of any single interval parameter makes it possible to reconstruct the whole model in depth. For example, the parameter estimation becomes unique if the subsurface layer is known to be isotropic. In the case of 2D inversion on the dip line of co‐orientated reflectors, it is necessary to specify one parameter (e.g. the vertical velocity) per layer. Despite the higher complexity of models with curved interfaces, the increased angle coverage of reflected rays helps to resolve the trade‐offs between the medium parameters. Singular value decomposition (SVD) shows that in the presence of sufficient interface curvature all parameters needed for anisotropic depth processing can be obtained solely from conventional‐spread P‐wave moveout. By performing tests on noise‐contaminated data we demonstrate that the tomographic inversion procedure reconstructs both the interfaces and the VTI parameters with high accuracy. Both SVD analysis and moveout inversion are implemented using an efficient modelling technique based on the theory of NMO‐velocity surfaces generalized for wave propagation through curved interfaces. 相似文献
19.
The well‐known asymptotic fractional four‐parameter traveltime approximation and the five‐parameter generalised traveltime approximation in stratified multi‐layer transversely isotropic elastic media with a vertical axis of symmetry have been widely used for pure‐mode and converted waves. The first three parameters of these traveltime expansions are zero‐offset traveltime, normal moveout velocity, and quartic coefficient, ensuring high accuracy of traveltimes at short offsets. The additional parameter within the four‐parameter approximation is an effective horizontal velocity accounting for large offsets, which is important to avoid traveltime divergence at large offsets. The two additional parameters in the above‐mentioned five‐parameter approximation ensure higher accuracy up to a given large finite offset with an exact match at this offset. In this paper, we propose two alternative five‐parameter traveltime approximations, which can be considered extensions of the four‐parameter approximation and an alternative to the five‐parameter approximation previously mentioned. The first three short‐offset parameters are the same as before, but the two additional long‐offset parameters are different and have specific physical meaning. One of them describes the propagation in the high‐velocity layer of the overburden (nearly horizontal propagation in the case of very large offsets), and the other characterises the intercept time corresponding to the critical slowness that includes contributions of the lower velocity layers only. Unlike the above‐mentioned approximations, both of the proposed traveltime approximations converge to the theoretical (asymptotic) linear traveltime at the limit case of very large (“infinite”) offsets. Their accuracy for moderate to very large offsets, for quasi‐compressional waves, converted waves, and shear waves polarised in the horizontal plane, is extremely high in cases where the overburden model contains at least one layer with a dominant higher velocity compared with the other layers. We consider the implementation of the proposed traveltime approximations in all classes of problems in which the above‐mentioned approximations are used, such as reflection and diffraction analysis and imaging. 相似文献
20.
Tariq Alkhalifah 《Geophysical Prospecting》2014,62(2):397-403
Reflections in seismic data induce serious non‐linearity in the objective function of full‐ waveform inversion. Thus, without a good initial velocity model that can produce reflections within a half cycle of the frequency used in the inversion, convergence to a solution becomes difficult. As a result, we tend to invert for refracted events and damp reflections in data. Reflection induced non‐linearity stems from cycle skipping between the imprint of the true model in observed data and the predicted model in synthesized data. Inverting for the phase of the model allows us to address this problem by avoiding the source of non‐linearity, the phase wrapping phenomena. Most of the information related to the location (or depths) of interfaces is embedded in the phase component of a model, mainly influenced by the background model, while the velocity‐contrast information (responsible for the reflection energy) is mainly embedded in the amplitude component. In combination with unwrapping the phase of data, which mitigates the non‐linearity introduced by the source function, I develop a framework to invert for the unwrapped phase of a model, represented by the instantaneous depth, using the unwrapped phase of the data. The resulting gradient function provides a mechanism to non‐linearly update the velocity model by applying mainly phase shifts to the model. In using the instantaneous depth as a model parameter, we keep track of the model properties unfazed by the wrapping phenomena. 相似文献