Nonlinear waveform tomography applied to crosshole seismic data

TitleNonlinear waveform tomography applied to crosshole seismic data
Publication TypeJournal Article
Year of Publication1996
AuthorsReiter, DThompson, Rodi, W
Pagination902 - 913
Date PublishedJan-05-1996

The acoustic inverse problem of crosshole seismology is nonlinear in the medium velocities and ill‐posed because of the lack of complete data 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 minimize the normed misfit between observed and modeled data subject to a constraint on the spatial roughness of the model. This type of regularization produces minimum structure velocity models which can vary in their degree of smoothness versus fit to the data. We solve the Tikhonov minimization condition numerically using a conjugate gradient algorithm. To accurately calculate the components of the forward problem, we use a frequency‐domain integral equation method with sinc basis functions. 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 medium using general matrix decomposition techniques. We successfully apply nonlinear waveform tomography to a scale‐model data set obtained from an ultrasonic modeling tank. This data set comes from a mostly plane‐layered, epoxy‐resin model, and the data exhibit elastic effects and other complicated wave phenomena. We invert this data set for the lateral variations in the model using a smoothed 1-D starting model to demonstrate the usefulness and efficacy of nonlinear waveform tomography. Read More: