NONLINEAR WAVE-FORM TOMOGRAPHY APPLIED TO CROSSHOLE SEISMIC DATA

The acoustic inverse problem of crosshold seismology is nonlinear in t he medium velocities and ill-posed because of the lack of complete dat a coverage surrounding the area of interest. In light of these facts, this paper develops a new nonlinear waveform tomography technique for imaging acoustic velocities from crosshole seismic data. The technique , based on Tikhonov regularization, defines solution models that minim ize the normed misfit between observed and modeled data subject to a c onstraint on the spatial roughness of the model. This type of regulari zation produces minimum structure velocity models which can vary in th eir degree of smoothness versus fit to the data. We solve the Tikhonov minimization condition numerically using a conjugate gradient algorit hm. To accurately calculate the components of the forward problem, we use a frequency-domain integral equation method with sinc basis functi ons. The integral equation method discretizes the integral form of the acoustic wave equation over a 2-D area and produces a two-part matrix problem that we solve for Green's functions and total fields in the m edium using general matrix decomposition techniques. We successfully a pply nonlinear waveform tomography to a scale-model data set obtained from an ultrasonic modeling tank. This data set comes from a mostly pl ane-layered, epoxy-resin model, and the data exhibit elastic effects a nd other complicated wave phenomena. We invert this data set for the l ateral variations in the model using a smoothed 1-D starting model to demonstrate the usefulness and efficacy of nonlinear waveform tomograp hy.