Comparison of Waveform Inversion Schemes for Horizontally Stratified Media

Abstract

Five different methods for inversion of seismic reflection data are considered for a model with vertically travelling waves in a medium with homogeneous, isotropic and lossless horizontal layers. The first three of these methods involve application of a detection scheme, that is, having removed the effect of, say the first k layers, either on the surface seismogram or by downward continuation, the reflection coefficient and travel time for layer k+1 is found by detecting the primary reflection from this layer and estimating its amplitude and time of arrival. These three methods are:

• A) Downward continuation in the time domain (1). The method implies that the wavefield is split into up- and down- going waves which are both estimated.

• B) Layer removal in the frequency domain. This implies that the effect of a known layer may be removed by applying a nonlinear formula in the frequency domain, whereupon the next layer may be estimated.

• C) Surface calculations in the time domain. Given that the k first layers are known, the effect of these are removed from the registered seismogram by calculating a synthetic seismogram. From the residual seismogram the parameters of layer k+1 are then estimated.