Joint inversion using the convolutional model
Winslow, Nathan Warren
Symes, William W.
Master of Arts
A detailed imaging of an acoustic medium via a seismic experiment requires an accurate representation of the source. A joint source and reflectivity inversion may provide the means to obtain the desired detail. Joint inversion using the acoustic wave equation is computationally expensive. The convolutional model of the seismogram in the offset-time domain provides a computationally cheaper means of approximating the wave equation. We rigorously derive the convolutional model of the seismogram as an approximation to the linearized acoustic wave equation where the medium to be imaged is layered and has a constant density. Using the Hilbert Class Library (a mathematical C++ library that among other things provides access to optimization algorithms), we implement the convolutional model and its inverse. Using linear and non-linear optimization methods applied to a least squares data residual objective function we test the robustness of inversion results from the convolutional model in the offset-time domain. (Abstract shortened by UMI.)
Geophysics; Mathematics; Computer science