Velocity analysis in transversely isotropic media

Geophysics ◽  
1980 ◽  
Vol 45 (6) ◽  
pp. 1094-1095 ◽  
Author(s):  
A. L. Lucas ◽  
P. N. S. O’Brien ◽  
J. H. Thomas
Keyword(s):  
Transversely Isotropic ◽  
Vertical Axis ◽  
Two Dimensions ◽  
P Wave ◽  
Velocity Analysis ◽  
Wave Surface ◽  
Common Depth Point ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Ellipsoid Of Revolution

In transversely isotropic media, the moveout velocity obtained from common‐depth‐point (CDP) analysis may be significantly different from the horizontal velocity of the pseudo‐P wave. In Levin’s (1978) paper, he discusses, among other things, the problem of velocity determination in a medium in which the pseudo‐P wave surface produced by a point source is an ellipsoid of revolution. He points out that one would expect many sedimentary rocks to be transversely isotropic with a vertical axis of symmetry. In his Appendix he proves that an ellipse (using two dimensions for convenience) is one possible shape for the wave surface in such a medium. He also shows, as have others, that in this case CDP velocity analysis measures the velocity of horizontal propagation.

Anisotropic velocity analysis for lithology discrimination

Geophysics ◽  
1989 ◽  
Vol 54 (12) ◽  
pp. 1564-1574 ◽  
Author(s):  
B. S. Byun ◽  
D. Corrigan ◽  
J. E. Gaiser
Keyword(s):  
Vertical Velocity ◽  
Transversely Isotropic ◽  
Wave Model ◽  
P Wave ◽  
Velocity Analysis ◽  
Velocity Anisotropy ◽  
Transversely Isotropic Media ◽  
Wide Range ◽  
Isotropic Media ◽  
Vsp Data

A new velocity analysis technique is presented for analyzing moveout of signals on multichannel surface seismic or VSP data. An approximate, skewed hyperbolic moveout formula is derived for horizontally layered, transversely isotropic media. This formula involves three measurement parameters: the average vertical velocity and horizontal and skew moveout velocities. By extending Dix‐type hyperbolic moveout analysis, we obtain improved coherence over large source‐geophone offsets for more accurate moveout correction. Compared with the stacking velocity obtained by simple hyperbolic analysis methods, the three velocity parameters estimated by this technique contain more physically meaningful geologic information regarding the anisotropy and/or velocity heterogeneity of the subsurface. Synthetic P‐wave model experiments demonstrate that the skewed hyperbolic moveout formula yields an excellent fit to time‐distance curves over a wide range of ray angles. Consequently, the measurement parameters are shown to reflect adequately the characteristics of velocity dependence on ray angle, i.e., velocity anisotropy. The technique is then applied to two field offset VSP data sets to measure and analyze the velocity parameters. The results show that the apparent anisotropy, defined as the ratio between the horizontal moveout velocity and average vertical velocity, correlates reasonably well with lithology. Highly anisotropic shale and chalk exhibit higher horizontal‐to‐vertical velocity ratios and sandstones show lower ratios.

Ray-based gridded tomography for tilted transversely isotropic media

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. C11-C23 ◽  
Author(s):  
Xiaoxiang Wang ◽  
Ilya Tsvankin
Keyword(s):  
Symmetry Axis ◽  
A Priori ◽  
Transversely Isotropic ◽  
P Wave ◽  
Model Parameters ◽  
Velocity Analysis ◽  
Symmetry Direction ◽  
Reflection Data ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Reflection tomography in the migrated domain can help reconstruct heterogeneous, anisotropic velocity fields needed for accurate depth imaging of complex geologic structures. The presence of anisotropy, however, increases the uncertainty in velocity analysis and typically requires a priori constraints on the model parameters. Here, we develop a 2D P-wave tomographic algorithm for heterogeneous transversely isotropic media with a tilted symmetry axis (TTI) and investigate the conditions necessary for stable estimation of the symmetry-direction velocity [Formula: see text] and the anisotropy parameters [Formula: see text] and [Formula: see text]. The model is divided into rectangular cells, and the parameters [Formula: see text], [Formula: see text], [Formula: see text], and the tilt [Formula: see text] of the symmetry axis are defined at the grid points. To increase the stability of the inversion, the symmetry axis is set orthogonal to the imaged reflectors, with the tilt interpolated inside each layer. The iterative migration velocity analysis involves efficient linearized parameter updating designed to minimize the residual moveout in image gathers for all available reflection events. The moveout equation in the depth-migrated domain includes a nonhyperbolic term that describes long-offset data, which are particularly sensitive to [Formula: see text]. Synthetic tests for models with a “quasi-factorized” TTI syncline (i.e., [Formula: see text] and [Formula: see text] are constant inside the anisotropic layer) and a TTI thrust sheet demonstrate that stable parameter estimation requires either strong smoothness constraints or additional information from walkaway VSP (vertical seismic profiling) traveltimes. If the model is quasi-factorized with a linear spatial variation of [Formula: see text], it may be possible to obtain the interval TTI parameters just from long-spread reflection data.

scholarly journals The offset-midpoint traveltime pyramid in 3D transversely isotropic media with a horizontal symmetry axis

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. T51-T62 ◽  
Author(s):  
Qi Hao ◽  
Alexey Stovas ◽  
Tariq Alkhalifah
Keyword(s):  
Symmetry Axis ◽  
Transversely Isotropic ◽  
P Wave ◽  
Analytic Representation ◽  
Velocity Inversion ◽  
Transversely Isotropic Media ◽  
Horizontal Symmetry ◽  
Time Domains ◽  
Isotropic Media ◽  
Hti Media

Analytic representation of the offset-midpoint traveltime equation for anisotropy is very important for prestack Kirchhoff migration and velocity inversion in anisotropic media. For transversely isotropic media with a vertical symmetry axis, the offset-midpoint traveltime resembles the shape of a Cheops’ pyramid. This is also valid for homogeneous 3D transversely isotropic media with a horizontal symmetry axis (HTI). We extended the offset-midpoint traveltime pyramid to the case of homogeneous 3D HTI. Under the assumption of weak anellipticity of HTI media, we derived an analytic representation of the P-wave traveltime equation and used Shanks transformation to improve the accuracy of horizontal and vertical slownesses. The traveltime pyramid was derived in the depth and time domains. Numerical examples confirmed the accuracy of the proposed approximation for the traveltime function in 3D HTI media.

scholarly journals An efficient wavefield inversion for transversely isotropic media with a vertical axis of symmetry

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. R195-R206 ◽  
Author(s):  
Chao Song ◽  
Tariq Alkhalifah
Keyword(s):  
High Resolution ◽  
Optimization Problem ◽  
Source Function ◽  
Transversely Isotropic ◽  
Vertical Axis ◽  
Trade Off ◽  
Transversely Isotropic Media ◽  
Highly Nonlinear ◽  
Isotropic Media ◽  
Axis Of Symmetry

Conventional full-waveform inversion (FWI) aims at retrieving a high-resolution velocity model directly from the wavefields measured at the sensor locations resulting in a highly nonlinear optimization problem. Due to the high nonlinearity of FWI (manifested in one form in the cycle-skipping problem), it is easy to fall into local minima. Considering that the earth is truly anisotropic, a multiparameter inversion imposes additional challenges in exacerbating the null-space problem and the parameter trade-off issue. We have formulated an optimization problem to reconstruct the wavefield in an efficient matter with background models by using an enhanced source function (which includes secondary sources) in combination with fitting the data. In this two-term optimization problem to fit the wavefield to the data and to the background wave equation, the inversion for the wavefield is linear. Because we keep the modeling operator stationary within each frequency, we only need one matrix inversion per frequency. The inversion for the anisotropic parameters is handled in a separate optimization using the wavefield and the enhanced source function. Because the velocity is the dominant parameter controlling the wave propagation, it is updated first. Thus, this reduces undesired updates for anisotropic parameters due to the velocity update leakage. We find the effectiveness of this approach in reducing parameter trade-off with a distinct Gaussian anomaly model. We find that in using the parameterization [Formula: see text], and [Formula: see text] to describe the transversely isotropic media with a vertical axis of symmetry model in the inversion, we end up with high resolution and minimal trade-off compared to conventional parameterizations for the anisotropic Marmousi model. Application on 2D real data also indicates the validity of our method.

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