Joint non-linear inversion of amplitudes and travel times in a vertical transversely isotropic medium using compressional and converted shear waves

Abstract

Massive shales and fractures are the main cause of seismic anisotropy in the upper-most part of the crust, caused either by sedimentary or tectonic processes. Neglecting the effect of seismic anisotropy in seismic processing algorithms may incorrectly image the seismic reflectors. This will also influence the quantitative amplitude analysis such as the acoustic or elastic impedance inversion and amplitude versus offsets analysis. Therefore it is important to obtain anisotropy parameters from seismic data. Conventional layer stripping inversion schemes and reflector based reflectivity inversion methods are solely dependent upon a specific reflector, without considering the effect of the other layers. This, on one hand, does not take the effect of transmission in reflectivity inversion into the account, and on the other hand, ignores the information from the waves travelling toward the lower layers. I provide a framework to integrate the information for each specific layer from all the rays which have travelled across this layer. To estimate anisotropy parameters I have implemented unconstrained minimization algorithms such as nonlinear conjugate gradients and variable metric methods, I also provide a nonlinear least square method, based on the Levenberg-Marquardt algorithm. In a stack of horizontal transversely isotropic layers with vertical axis of symmetry, where the layer properties are laterally invariant, we provide two different inversion schemes; traveltime and waveform inversion.Both inversion schemes utilize compressional and joint compressional and converted shear waves. A new exact traveltime equation has been formulated for a dipping transversely isotropic system of layers. These traveltimes are also parametrized by the ray parameters for each ray element. I use the Newton method of minimization to estimate the ray parameter using a random prior model from a uniform distribution. Numerical results show that with the assumption of weak anisotropy, Thomsen’s anisotropy parameters can be estimated with a high accuracy. The inversion algorithms have been implemented as a software package in a C++ object oriented environment.