Wave equation inversion of skeletalized geophysical data

Abstract

SUMMARY Inversion methods based on gradient optimization techniques require the directional derivative of the data with respect to the model parameters. Unfortunately, the data (e.g., pressure seismograms) are usually restricted to that explicitly given in the fundamental governing equation (e.g., wave equation). This limited choice of data type may lead to misfit functions that are pathologically non-linear with respect to the model parameters. We present a methodology which allows for the calculation of directional derivatives for skeletalized data sets, yet still uses the fundamental governing equations without the need for approximations. Skeletalized data are defined as a reduced data set derived from the original data which retains the important information about the model parameter of interest. The motivation for working with skeletalized data rather than raw data is that the skeleton data may be strongly influenced by only one type of model parameter and lead to a quasi-linear misfit function. Examples of skeletalized data sets include first arrival traveltimes picked from CDP seismograms for velocity inversion, amplitudes of transmitted earthquake SH-waves for earthquake moment inversion, or pulse width measured from first arrivals for attenuation inversion. As an example we devise a traveltime inversion method based on the wave equation and free of any high-frquency approximations. Results show that wave equation traveltime (WT) inversion is superior to ray traced traveltime inversion for complicated velocity models. It is also shown that WT inversion converges quickly for starting velocity models that are far from the actual model.