Inversion for the Elastic Parameters of Layered Transversely Isotropic Media

Abstract

In most cases of seismic processing and interpretation, elastic isotropy is assumed. However, velocity anisotropy is found to exist in most subsurface media. Hence, there exists a fundamental inconsistency between theory on the one hand, and practice on the other. If not recognised, this can invalidate interpretation of seismic data. In this thesis, inversion methods for elastic parameters are developed to quantify the degree of velocity anisotropy of multi-layered transversely isotropic media. This primarily involves examining the velocity fields of layered media using anisotropic elastic wave propagation theory, and developing inversion programs to recover elastic parameters from those velocity fields. The resolved elastic parameter information is used in carrying out further studies on the effects of seismic anisotropy on normal moveout (NMO). Mathematical analyses, numerical simulations, and physical modelling experiments are used in this research for verification purposes before application to field survey data. Numerical studies show the transmission velocity field through layered media appears to be equivalent to that through a single-layered medium, within the practical offset limits in field surveys. The elastic parameters, which describe the property of such equivalent single-layered media, can be used as apparent elastic parameters to describe the collective mechanical property of the layered media. During this research, Snell's law was used in ray tracing to determine ray paths through the interface between any two component layers. By analyzing the signals recorded by any receiver in a walkaway VSP survey, the apparent transmission velocity field for the layered media above this receiver depth was inverted.Software was developed to recover the apparent elastic parameters for the layered media above this receiver depth using the transmission velocity field as input. Based on a two-layered model, another method was developed to recover the interval elastic parameters for an individual layer of interest, using the signals recorded by receivers on the upper and lower surfaces of this layer. The recovered elastic parameters may be considerably different from the real values if a transversely isotropic medium with a tilted symmetry axis (TTI) is treated as a transversely isotropic medium with a vertical symmetry axis (VTI). A large angle of tilt of the symmetry axis significantly influences the recorded velocity field through the medium. An inversion program was written to recover the value of the tilt angle of a TTI medium, and the elastic parameters of the medium. Programs were also developed to combine information from P, SV, and SH-waves in an inversion procedure. This capability in inversion programs enables us to use the additional information provided by a multi-component VSP survey to obtain accurate estimates of the elastic parameters of geological formations. Software testing and development was carried out on numerically generated input data. Up to 10 milliseconds of random noise in travel time was added to the input to confirm the stability of the inversion software. Further testing was carried out on physical model data where the parameters of the model were known from direct measurements. Finally the inversion software was applied to actual field data and found to give plausible results.In software testing in the physical modelling laboratory, other practical problems were encountered. System errors caused by the disproportionately large size of the transducers used affected the accuracy of the inversion results obtained. Transducer performance was studied, and it was found that reducing the size of transducers or making offset corrections would decrease the errors caused by the disproportionately large transducer dimensions. In using the elastic parameters recovered, it was found that the elastic parameter δ significantly influences the seismic records from a horizontal reflector. The normal moveout velocity was found to show variations from the zero-offset normal moveout velocity depending on the value and sign of elastic parameter δ. New approximate expressions for anisotropic normal moveout, phase and ray velocity functions at short offsets were developed. The value of anisotropic parameter δ was found to be the major factor controlling these relations. If the recovered parameter δ has a large negative value, analytical and numerical studies demonstrated that the new expression for moveout velocity developed herein should be used instead of Thomsen's normal moveout equation.