NON‐NORMAL INCIDENCE INVERSION: EXISTENCE OF SOLUTION*

Publisher Website
Google Scholar
Abstract
An inverse problem is one in which the parameters of a model are determined from measured seismic data. Important to the solution of inverse problems is the issue of whether or not a solution exists. In this paper we show, in a constructive manner, that a solution does exist to the specific inverse problem of determining the parameters of a horizontally stratified, lossless, isotropic and homogeneous layered system that is excited by a non‐normal incidence (NNI) plane wave. Mode conversion between P‐ and S‐waves is included.We develop a seven‐step layer‐recursive procedure for determining all of the parameters for layer j. These parameters are P‐wave and S‐wave velocities and angles of incidence, density, thickness, traveltimes, and reflection‐ and transmission‐coefficient matrices. Downward continuation of data from the top of one layer to the top of the next lower layer is an important step in our procedure, just as it is in normal incidence (NI) inversion. We show that, in order to compute all parameters of layer j, we need to (and can) compute some parameters for layer j+ 1. This is a non‐causal phenomenon that seems to be necessary in NNI inversion but is not present in NI inversion.