3-D moveout velocity analysis and parameter estimation for orthorhombic media

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 820-837 ◽  
Author(s):  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Parameter Estimation ◽  
Numerical Study ◽  
Symmetry Plane ◽  
P Wave ◽  
Inversion Method ◽  
Orthorhombic Symmetry ◽  
Data Set ◽  
Anisotropic Models ◽  
Wave Data ◽  
Time Migration

Orthorhombic symmetry describes several azimuthally anisotropic models typical for fractured formations, such as those containing two orthogonal crack systems or parallel vertical cracks in a VTI (transversely isotropic with a vertical symmetry axis) background. Here, we present a methodology for inverting multiazimuth P-wave reflection traveltimes for the parameters of vertically inhomogeneous orthorhombic media. Our approach is based on the general analytic representation of normal‐moveout (NMO) velocity as an ellipse in the horizontal plane. A minimum of three differently oriented common‐midpoint (CMP) lines (or a “wideazimuth” 3-D survey) is needed to reconstruct the ellipse and thus obtain NMO velocity in any azimuthal direction. Then, the orientation and the semiaxes of the NMO ellipse, which are dependent on both anisotropy and heterogeneity, can be inverted for the medium parameters. Our analytic and numerical study shows that for the model of a homogeneous orthorhombic layer above a dipping reflector, the exact P-wave NMO velocity is determined by the symmetry‐plane orientation and five parameters: the NMO velocities from a horizontal reflector measured in the symmetry planes [[Formula: see text]] and three anisotropic coefficients η(1,2,3) introduced by analogy with the Alkhalifah‐Tsvankin parameter η for VTI media. The importance of the medium parameterization in terms of the η coefficients goes well beyond the NMO-velocity function. By generating migration impulse responses, we demonstrate that the parameters [Formula: see text] and η(1,2,3) are sufficient to perform all time processing steps (normal‐moveout and dip‐moveout corrections, prestack and poststack time migration) in orthorhombic models. The velocities [Formula: see text] and the orientation of the vertical symmetry planes can be found using the azimuthally dependent NMO velocity from a horizontal reflector. Then the NMO ellipse of at least one dipping event is additionally needed to obtain the coefficients η(1,2,3) that control the dip dependence of normal moveout. We discuss the stability of the inversion procedure and specify the constraints on the dip and azimuth of the reflector; for instance, for all three η coefficients to be resolved individually, the dip plane of the reflector should not coincide with either of the symmetry planes. To carry out parameter estimation in vertically inhomogeneous orthorhombic media, we apply the generalized Dix equation of Grechka, Tsvankin and Cohen, which operates with the matrices responsible for interval NMO ellipses rather than with the NMO velocities themselves. Our algorithm is designed to find the interval values of [Formula: see text] and η(1,2,3) using moveout from horizontal and dipping reflectors measured at different vertical times (i.e., only surface P-wave data are needed). Application to a synthetic multiazimuth P-wave data set over a layered orthorhombic medium with depth‐varying orientation of the symmetry planes verifies the accuracy of the inversion method.

3-D description of normal moveout in anisotropic inhomogeneous media

Geophysics ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 1079-1092 ◽  
Author(s):  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Fractured Reservoirs ◽  
Symmetry Plane ◽  
Transversely Isotropic ◽  
Inhomogeneous Media ◽  
P Wave ◽  
Orthorhombic Symmetry ◽  
Azimuthal Variation ◽  
Anisotropic Models ◽  
Transversely Isotropic Media ◽  
Isotropic Media

We present a new equation for normal‐moveout (NMO) velocity that describes azimuthally dependent reflection traveltimes of pure modes from both horizontal and dipping reflectors in arbitrary anisotropic inhomogeneous media. With the exception of anomalous areas such as those where common‐midpoint (CMP) reflection time decreases with offset, the azimuthal variation of NMO velocity represents an ellipse in the horizontal plane, with the orientation of the axes determined by the properties of the medium and the direction of the reflector normal. In general, a minimum of three azimuthal measurements is necessary to reconstruct the best‐fit ellipse and obtain NMO velocity in all azimuthal directions. This result provides a simple way to correct for the azimuthal variation in stacking velocity often observed in 3-D surveys. Even more importantly, analytic expressions for the parameters of the NMO ellipse can be used in the inversion of moveout data for the anisotropic coefficients of the medium. For homogeneous transversely isotropic media with a vertical axis of symmetry (VTI media), our equation for azimuthally dependent NMO velocity from dipping reflectors becomes a relatively simple function of phase velocity and its derivatives. We show that the zero‐dip NMO velocity Vnmo(0) and the anisotropic coefficient η are sufficient to describe the P-wave NMO velocity for any orientation of the CMP line with respect to the dip plane of the reflector. Using our formalism, Vnmo(0) and η (the only parameters needed for time processing) can be found from the dip‐dependent NMO velocity at any azimuth or, alternatively, from the azimuthally dependent NMO for a single dipping reflector. We also apply this theory to more complicated azimuthally anisotropic models with the orthorhombic symmetry used to describe fractured reservoirs. For reflections from horizontal interfaces in orthorhombic media, the axes of the normal moveout ellipse are aligned with the vertical symmetry planes. Therefore, azimuthal P-wave moveout measurements can be inverted for the orientation of the symmetry planes (typically determined by the fracture direction) and the NMO velocities within them. If the vertical velocity is known, symmetry‐plane NMO velocities make it possible to estimate two anisotropic parameters equivalent to Thomsen’s coefficient δ for transversely isotropic media.

Moveout inversion of P-wave data for horizontal transverse isotropy

Geophysics ◽  
1999 ◽  
Vol 64 (4) ◽  
pp. 1219-1229 ◽  
Author(s):  
Pedro Contreras ◽  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Vertical Velocity ◽  
Symmetry Axis ◽  
Transverse Isotropy ◽  
P Wave ◽  
Orthorhombic Symmetry ◽  
Anisotropic Parameter ◽  
Data Set ◽  
Velocity Models ◽  
Wave Data ◽  
Hti Media

The transversely isotropic model with a horizontal symmetry axis (HTI media) has been extensively used in seismological studies of fractured reservoirs. In this paper, a parameter‐estimation technique originally developed by Grechka and Tsvankin for the more general orthorhombic media is applied to horizontal transverse isotropy. Our methodology is based on the inversion of azimuthally‐dependent P-wave normal‐moveout (NMO) velocities from horizontal and dipping reflectors. If the NMO velocity of a given reflection event is plotted in each azimuthal direction, it forms an ellipse determined by three combinations of medium parameters. The NMO ellipse from a horizontal reflector in HTI media can be inverted for the azimuth β of the symmetry axis, the vertical velocity [Formula: see text], and the Thomsen‐type anisotropic parameter δ(V). We describe a technique for obtaining the remaining (for P-waves) anisotropic parameter η(V) (or ε(V)) from the NMO ellipse corresponding to a dipping reflector of arbitrary azimuth. The interval parameters of vertically inhomogeneous HTI media are recovered using the generalized Dix equation that operates with NMO ellipses for horizontal and dipping events. High accuracy of our method is confirmed by inverting a synthetic multiazimuth P-wave data set generated by ray tracing for a layered HTI medium with depth‐varying orientation of the symmetry axis. Although estimation of η(V) can be carried out by the algorithm developed for orthorhombic media, for more stable results the HTI model has to be used from the outset of the inversion procedure. It should be emphasized that P-wave conventional‐spread moveout data provide enough information to distinguish between HTI and lower‐symmetry models. We show that if the medium has the orthorhombic symmetry and is sufficiently different from HTI, the best‐fit HTI model cannot match the NMO ellipses for both a horizontal and a dipping event. The anisotropic coefficients responsible for P-wave moveout can be combined to estimate the crack density and predict whether the cracks are fluid‐filled or dry. A unique feature of the HTI model that distinguishes it from both vertical transverse isotropy and orthorhombic media is that moveout inversion provides not just zero‐dip NMO velocities and anisotropic coefficients, but also the true vertical velocity. As a result, reflection P-wave data acquired over HTI formations can be used to build velocity models in depth and perform anisotropic depth processing.

scholarly journals Fluid prediction of a deep carbonate reservoir using walkaround 3D-3C vertical seismic profiling data

2019 ◽  
Author(s):  
Haohao Zhang ◽  
Jun Lu ◽  
Benchi Chen ◽  
Xuejun Ma ◽  
Zhidong Cai
Keyword(s):  
Poisson’S Ratio ◽  
Wave Impedance ◽  
Carbonate Reservoir ◽  
P Wave ◽  
Poisson's Ratio ◽  
Inversion Method ◽  
Seismic Profiling ◽  
Tahe Oilfield ◽  
Vertical Seismic Profiling ◽  
Time Migration

Abstract The considerable depth and complicated structure of the Tahe Oilfield in the Tuofutai area of China make it very difficult to delineate its Ordovician carbonate fracture-cavity reservoir. The resolution of conventional ground seismic data is inadequate to satisfy current exploitation requirements. To further improve the understanding of the carbonate fracture-cavity reservoir of the Tahe Oilfield and to provide predictions of reservoir properties that are more accurate, a walkaround 3D-3C vertical seismic profiling (VSP) survey was conducted. First, we preprocessed raw VSP data and developed a method of joint PP- and PSV-wave prestack time migration. In contrast to ground seismic imaging profiles, VSP imaging profiles have a higher resolution and wider spectrum range that provide more detailed strata information. Then, using the joint PP- and PSV-wave prestack inversion method, we obtained the PP- and PSV-wave impedance and Poisson's ratio parameters of the Ordovician carbonate reservoir. Compared with the P-wave impedance of the ground seismic inversion, we found the VSP inversion results had higher accuracy, which enabled clearer identification of the internal characteristics of the carbonate reservoir. Finally, coupled with the Poisson's ratio attribute, we predicted the distribution of favorable reservoirs and interwell connectivity. The prediction results were verified using both logging and production data. The findings of this study demonstrate the applicability of the proposed technical method for the exploration of deep carbonate fracture-cavity reservoirs.

Feasibility of nonhyperbolic moveout inversion in transversely isotropic media

Geophysics ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 957-969 ◽  
Author(s):  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Vertical Velocity ◽  
Transverse Isotropy ◽  
Horizontal Velocity ◽  
P Wave ◽  
Vacuum Field ◽  
Percentage Error ◽  
Correlated Errors ◽  
Data Set ◽  
Time Migration ◽  
Quartic Term

Inversion of reflection traveltimes in anisotropic media can provide estimates of anisotropic coefficients required for seismic processing and lithology discrimination. Nonhyperbolic P-wave moveout for transverse isotropy with a vertical symmetry axis (VTI media) is controlled by the parameter η (or, alternatively, by the horizontal velocity Vhor), which is also responsible for the influence of anisotropy on all time‐processing steps, including dip‐moveout (DMO) correction and time migration. Here, we recast the nonhyperbolic moveout equation, originally developed by Tsvankin and Thomsen, as a function of Vhor and normal‐moveout (NMO) velocity Vnmo and introduce a correction factor in the denominator that increases the accuracy at intermediate offsets. Then we apply this equation to obtain Vhor and η from nonhyperbolic semblance analysis on long common midpoint (CMP) spreads and study the accuracy and stability of the inversion procedure. Our error analysis shows that the horizontal velocity becomes relatively well‐constrained by reflection traveltimes if the spreadlength exceeds twice the reflector depth. There is, however, a certain degree of tradeoff between Vhor and Vnmo caused by the interplay between the quadratic and quartic term of the moveout series. Since the errors in Vhor and Vnmo have opposite signs, the absolute error in the parameter η (which depends on the ratio Vhor/Vnmo) turns out to be at least two times bigger than the percentage error in Vhor. Therefore, the inverted value of η is highly sensitive to small correlated errors in reflection traveltimes, with moveout distortions on the order of 3–4 ms leading to errors in η up to ±0.1—even in the simplest model of a single VTI layer. Similar conclusions apply to vertically inhomogeneous media, in which the interval horizontal velocity can be obtained with an accuracy often comparable to that of the NMO velocity, while the interval values of η are distorted by the tradeoff between Vhor and Vnmo that gets amplified by the Dix‐type differentiation procedure. We applied nonhyperbolic semblance analysis to a walkaway VSP data set acquired at Vacuum field, New Mexico, and obtained a significant value of η = 0.19 indicative of nonnegligible anisotropy in this area. Then we combined moveout inversion results with the known vertical velocity to resolve the anisotropic coefficients ε and δ. However, in agreement with our modeling results, η estimation was significantly compounded by the scatter in the measured traveltimes. Certain instability in η inversion has no influence on the results of anisotropic poststack time migration because all kinematically equivalent models obtained from nonhyperbolic moveout give an adequate description of long‐spread reflection traveltimes. Also, inversion of nonhyperbolic moveout provides a relatively accurate horizontal‐velocity function that can be combined with the vertical velocity (if it is available) to estimate the anisotropic coefficient ε. However, η represents a valuable lithology indicator that can be obtained from surface P-wave data. Therefore, for purposes of lithology discrimination, it is preferable to find η by means of the more stable DMO method of Alkhalifah and Tsvankin.

Quartic moveout coefficient for a dipping azimuthally anisotropic layer

Geophysics ◽  
2004 ◽  
Vol 69 (3) ◽  
pp. 699-707 ◽  
Author(s):  
Andrés Pech ◽  
Ilya Tsvankin
Keyword(s):  
Reservoir Characterization ◽  
Fractured Reservoirs ◽  
Symmetry Plane ◽  
Exact Expression ◽  
Naturally Fractured Reservoirs ◽  
P Wave ◽  
Orthorhombic Symmetry ◽  
Fracture Density ◽  
Weak Anisotropy ◽  
Velocity Anisotropy

Interpretation and inversion of azimuthally varying nonhyperbolic reflection moveout requires accounting for both velocity anisotropy and subsurface structure. Here, our previously derived exact expression for the quartic moveout coefficient A4 is applied to P‐wave reflections from a dipping interface overlaid by a medium of orthorhombic symmetry. The weak‐anisotropy approximaton for the coefficient A4 in a homogeneous orthorhombic layer is controlled by the anellipticity parameters η(1), η(2), and η(3), which are responsible for time processing of P‐wave data. If the dip plane of the reflector coincides with the vertical symmetry plane [x1, x3], A4 on the dip line is proportional to the in‐plane anellipticity parameter η(2) and always changes sign for a dip of 30○. The quartic coefficient on the strike line is a function of all three η–parameters, but for mild dips it is mostly governed by η(1)—the parameter defined in the incidence plane [x2, x3]. Whereas the magnitude of the dip line A4 typically becomes small for dips exceeding 45○, the nonhyperbolic moveout on the strike line may remain significant even for subvertical reflectors. The character of the azimuthal variation of A4 depends on reflector dip and is quite sensitive to the signs and relative magnitudes of η(1), η(2), and η(3). The analytic results and numerical modeling show that the azimuthal pattern of the quartic coefficient can contain multiple lobes, with one or two azimuths of vanishing A4 between the dip and strike directions. The strong influence of the anellipticity parameters on the azimuthally varying coefficient A4 suggests that nonhyperbolic moveout recorded in wide‐azimuth surveys can help to constrain the anisotropic velocity field. Since for typical orthorhombic models that describe naturally fractured reservoirs the parameters η(1,2,3) are closely related to the fracture density and infill, the results of azimuthal nonhyperbolic moveout analysis can also be used in reservoir characterization.

scholarly journals Physical and numerical modeling of tuning and diffraction in azimuthally anisotropic media

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1613-1621 ◽  
Author(s):  
Richard L. Gibson ◽  
Stephen Theophanis ◽  
M. Nafi Toksöz
Keyword(s):  
Numerical Modeling ◽  
Fractured Reservoirs ◽  
Homogeneous Model ◽  
Azimuthal Anisotropy ◽  
P Wave ◽  
Orthorhombic Symmetry ◽  
Fractured Reservoir ◽  
Sh Wave ◽  
Wave Data ◽  
Ray Methods

Fractured reservoirs are an important target for exploration and production geophysics, and the azimuthal anisotropy often associated with these reservoirs can strongly influence seismic wave propagation. We created a physical model of a fractured reservoir to simulate some of these propagation effects. The reservoir is represented by a phenolite disk that is thin with respect to the elastic wavelengths in the experiment, creating model dimensions that are representative of realistic reservoirs. Phenolite is strongly anisotropic with orthorhombic symmetry, which suggests that azimuthal amplitude versus offset (AVO) effects should be obvious in data. We acquired both SH- and P-wave data in common‐offset gathers with a near offset and a far offset and found that although the SH-wave data show clear azimuthal variations in AVO, the P-wave signals show no apparent changes with azimuth. We then applied numerical modeling to analyze the data. Because ray methods cannot model diffractions from the disk edge, we first used a ray‐Born technique to simulate variations in waveforms associated with such scattering. The synthetic seismograms reproduced variations in the SH-wave waveforms accurately, though the amplitude contrast between acquisition azimuths was overestimated. Assuming a laterally homogeneous model, we then applied ray methods to simulate tuning effects in SH- and P-wave data and confirmed that in spite of the large contrasts in elastic properties, the tuning of the P-wave reflections from the thin disk changed so there was negligible contrast in AVO with azimuth. Models of field scale reservoirs showed that the same effects could be expected for field applications.

The impact of common‐offset migration on porosity estimation by AVO inversion

Geophysics ◽  
2001 ◽  
Vol 66 (3) ◽  
pp. 755-762 ◽  
Author(s):  
Arild Buland ◽  
Martin Landrø
Keyword(s):  
P Wave ◽  
High Porosity ◽  
S Wave ◽  
Seismic Line ◽  
Data Set ◽  
The North ◽  
Avo Inversion ◽  
Time Migration ◽  
The Impact ◽  
Porosity Estimation

The impact of prestack time migration on porosity estimation has been tested on a 2-D seismic line from the Valhall/Hod area in the North Sea. Porosity is estimated in the Cretaceous chalk section in a two‐step procedure. First, P-wave and S-wave velocity and density are estimated by amplitude variation with offset (AVO) inversion. These parameters are then linked to porosity through a petrophysical rock data base based on core plug analysis. The porosity is estimated both from unmigrated and prestack migrated seismic data. For the migrated data set, a standard prestack Kirchhoff time migration is used, followed by simple angle and amplitude corrections. Compared to modern high‐cost, true amplitude migration methods, this approach is faster and more practical. The test line is structurally fairly simple, with a maximum dip of 5°; but the results differ significantly, depending on whether migration is applied prior to the inversion. The maximum difference in estimated porosity is of the order of 10% (about 50% relative change). High‐porosity zones estimated from the unmigrated data were not present on the porosity section estimated from the migrated data.

Elastic impedance parameterization and inversion with Young’s modulus and Poisson’s ratio

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. N35-N42 ◽  
Author(s):  
Zhaoyun Zong ◽  
Xingyao Yin ◽  
Guochen Wu
Keyword(s):  
Parameter Estimation ◽  
Young’S Modulus ◽  
Seismic Data ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Incident Angle ◽  
P Wave ◽  
Poisson's Ratio ◽  
Data Set ◽  
Elastic Impedance

Young’s modulus and Poisson’s ratio are related to quantitative reservoir properties such as porosity, rock strength, mineral and total organic carbon content, and they can be used to infer preferential drilling locations or sweet spots. Conventionally, they are computed and estimated with a rock physics law in terms of P-wave, S-wave impedances/velocities, and density which may be directly inverted with prestack seismic data. However, the density term imbedded in Young’s modulus is difficult to estimate because it is less sensitive to seismic-amplitude variations, and the indirect way can create more uncertainty for the estimation of Young’s modulus and Poisson’s ratio. This study combines the elastic impedance equation in terms of Young’s modulus and Poisson’s ratio and elastic impedance variation with incident angle inversion to produce a stable and direct way to estimate the Young’s modulus and Poisson’s ratio, with no need for density information from prestack seismic data. We initially derive a novel elastic impedance equation in terms of Young’s modulus and Poisson’s ratio. And then, to enhance the estimation stability, we develop the elastic impedance varying with incident angle inversion with damping singular value decomposition (EVA-DSVD) method to estimate the Young’s modulus and Poisson’s ratio. This method is implemented in a two-step inversion: Elastic impedance inversion and parameter estimation. The introduction of a model constraint and DSVD algorithm in parameter estimation renders the EVA-DSVD inversion more stable. Tests on synthetic data show that the Young’s modulus and Poisson’s ratio are still estimated reasonable with moderate noise. A test on a real data set shows that the estimated results are in good agreement with the results of well interpretation.

Joint inversion of P- and PS-waves in orthorhombic media: Theory and a physical modeling study

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 146-161 ◽  
Author(s):  
Vladimir Grechka ◽  
Stephen Theophanis ◽  
Ilya Tsvankin
Keyword(s):  
Shear Wave ◽  
Physical Modeling ◽  
Horizontal Plane ◽  
Joint Inversion ◽  
Symmetry Plane ◽  
P Wave ◽  
Simple Relationship ◽  
Converted Wave ◽  
Data Set ◽  
Converted Waves

Reflection traveltimes recorded over azimuthally anisotropic fractured media can provide valuable information for reservoir characterization. As recently shown by Grechka and Tsvankin, normal moveout (NMO) velocity of any pure (unconverted) mode depends on only three medium parameters and usually has an elliptical shape in the horizontal plane. Because of the limited information contained in the NMO ellipse of P-waves, it is advantageous to use moveout velocities of shear or converted modes in attempts to resolve the coefficients of realistic orthorhombic or lower‐symmetry fractured models. Joint inversion of P and PS traveltimes is especially attractive because it does not require shear‐wave excitation. Here, we show that for models composed of horizontal layers with a horizontal symmetry plane, the traveltime of converted waves is reciprocal with respect to the source and receiver positions (i.e., it remains the same if we interchange the source and receiver) and can be adequately described by NMO velocity on conventional‐length spreads. The azimuthal dependence of converted‐wave NMO velocity has the same form as for pure modes but requires the spatial derivatives of two-way traveltime for its determination. Using the generalized Dix equation of Grechka, Tsvankin, and Cohen, we derive a simple relationship between the NMO ellipses of pure and converted waves that provides a basis for obtaining shear‐wave information from P and PS data. For orthorhombic models, the combination of the reflection traveltimes of the P-wave and two split PS-waves makes it possible to reconstruct the azimuthally dependent NMO velocities of the pure shear modes and to find the anisotropic parameters that cannot be determined from P-wave data alone. The method is applied to a physical modeling data set acquired over a block of orthorhombic material—Phenolite XX-324. The inversion of conventional‐spread P and PS moveout data allowed us to obtain the orientation of the vertical symmetry planes and eight (out of nine) elastic parameters of the medium (the reflector depth was known). The remaining coefficient (c12 or δ(3) in Tsvankin’s notation) is found from the direct P-wave arrival in the horizontal plane. The inversion results accurately predict moveout curves of the pure S-waves and are in excellent agreement with direct measurements of the horizontal velocities.

scholarly journals Probabilistic moveout analysis by time warping

Geophysics ◽  
2020 ◽  
Vol 85 (1) ◽  
pp. U1-U20
Author(s):  
Yanadet Sripanich ◽  
Sergey Fomel ◽  
Jeannot Trampert ◽  
William Burnett ◽  
Thomas Hess
Keyword(s):  
Parameter Estimation ◽  
Posterior Probability ◽  
Model Building ◽  
Probability Distributions ◽  
Real Data ◽  
Inversion Method ◽  
Time Warping ◽  
Anisotropic Models ◽  
Trade Offs ◽  
Set Up

Parameter estimation from reflection moveout analysis represents one of the most fundamental problems in subsurface model building. We have developed an efficient moveout inversion method based on the process of automatic flattening of common-midpoint (CMP) gathers using local slopes. We find that as a by-product of this flattening process, we can also estimate reflection traveltimes corresponding to the flattened CMP gathers. This traveltime information allows us to construct a highly overdetermined system and subsequently invert for moveout parameters including normal-moveout velocities and quartic coefficients related to anisotropy. We use the 3D generalized moveout approximation (GMA), which can accurately capture the effects of complex anisotropy on reflection traveltimes as the basis for our moveout inversion. Due to the cheap forward traveltime computations by GMA, we use a Monte Carlo inversion scheme for improved handling of the nonlinearity between the reflection traveltimes and moveout parameters. This choice also allows us to set up a probabilistic inversion workflow within a Bayesian framework, in which we can obtain the posterior probability distributions that contain valuable statistical information on estimated parameters such as uncertainty and correlations. We use synthetic and real data examples including the data from the SEAM Phase II unconventional reservoir model to demonstrate the performance of our method and discuss insights into the problem of moveout inversion gained from analyzing the posterior probability distributions. Our results suggest that the solutions to the problem of traveltime-only moveout inversion from 2D CMP gathers are relatively well constrained by the data. However, parameter estimation from 3D CMP gathers associated with more moveout parameters and complex anisotropic models are generally nonunique, and there are trade-offs among inverted parameters, especially the quartic coefficients.

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