Estimating the elastic parameters of anisotropic media using a joint inversion of P‐wave and SV‐wave traveltime error

Abstract

A B S T R A C TA method is presented to estimate the elastic parameters and thickness of media that are locally laterally homogeneous using P-wave and vertically polarized shearwave (SV-wave) data. This method is a 'layer-stripping' technique, and it uses many aspects of common focal point (CFP) technology. For each layer, a focusing operator is computed using a model of the elastic parameters with which a CFP gather can be constructed using the seismic data. Assuming local homogeneity, the resulting differential time shifts (DTSs) represent error in the model due to anisotropy and error in thickness. In the (τ − p) domain, DTSs are traveltimes τ that connect error in layer thickness z, vertical slowness q, and ray parameter p. Series expansion is used to linearize τ with respect to error in the elastic parameters and thickness, and least-squares inversion is used to update the model.For stability, joint inversion of P and SV data is employed and, as pure SV data are relatively rare, the use of mode-converted (PSV) data to represent SV in the joint inversion is proposed. Analytic and synthetic examples are used to demonstrate the utility and practicality of this inversion. I N T R O D U C T I O NCommon focal point (CFP) technology (Berkhout 1997; Berkhout and Verschuur 2001) is a useful tool in exploration seismology. CFPs are selected for reflectors of interest, and operators are used to back-propagate the reflection data to the CFPs. The resulting CFP gathers are then cross-correlated in time (i.e. moveout-corrected) with their corresponding focusing operators (computed by forward-propagating models of the seismic sources). For operators that exactly mimic wave propagation from the source and receiver locations to the CFP, energy corresponding to specular reflection aligns at zero-lag on the moveout-corrected CFP gather. The amplitude of this energy is a measure of the reflectivity at the CFP location, and it can be analysed as such or summed into an average reflectivity for imaging (de Bruin, Wapenaar and Berkhout 1990). Misalignment, or differential time shift (DTS), is the result of error in estimating the heterogeneity and anisotropy of the medium above. In strict adherence to the CFP method, DTSs are used in imaging to update the one-way traveltime operators (focusing operators) instead of the underlying velocity model (Berkhout and Verschuur 2001).Apart from the CFP method, other methods have been used in attempts to estimate velocity heterogeneity for isotropic media. Cox and Verschuur (2001) use tomographic inversion to extract a velocity model from the updated operators, and Kabir

Azimuthal τ-panalysis in anisotropic media

“…Unlike , makes no approximation. Thus, it is more suitable for determining accurate interval velocity (Sen & Mukherjee, 2003; Ferguson & Sen, 2004).…”

Depth migration anisotropy analysis in the time domain

“…To estimate velocity heterogeneity in isotropic media, Kabir (1997) implements the CFP method in the space‐time domain. For homogeneous anisotropic media, Ferguson and Sen (2004) propose plane‐wave domain implementation of this technique for anisotropic parameter estimation when both P and Sv‐wave data are available. Velocity analysis in the plane‐wave domain is advantageous, as it avoids the problem of multipathing and triplication, and the measured differential time shifts directly relate ray parameters to errors in both vertical slowness and layer thickness (Ferguson and Sen 2004).…”