Relaxation mechanisms for 3-D seismic and 2.5-D GPR data with applications to full-wavefield simulation and inversion

In this dissertation, attenuation present in seismic and GPR data is investigated by newly developed 3-D and 2.5-D modeling algorithms. A state-of-the-art 3-D inversion method which directly images earth properties from prestack seismic data is proposed and successfully tested on synthetic data.;An efficient 3-D viscoelastic modeling algorithm which introduces composite memory variables and relaxation frequencies has made it feasible to analyze 3-D seismic exploration data at a reasonable cost with current computer capability. A constant quality factor (Q) model is used in the modeling to describe the attenuation behavior. The algorithm is used to verify a strongly heterogeneous distribution of near surface velocities and attenuation associated with local geology in surface seismic data from a 3-D survey in southeast Oklahoma. Good agreement between field and viscoelastic modeling results are obtained.;A 2.5-D ground penetrating radar modeling algorithm which uses the superposition of Debye functions to phenomenologically represent the electric and magnetic relaxation mechanisms is able to simulate EM wave propagations in a lossy and dispersive soil environment. The algorithm assumes the medium is homogeneous in one spatial direction and takes a Fourier transform of Maxwell's equation in that direction. The measured electric and magnetic properties of soil samples are incorporated into Maxwell's equations. This modeling technique is used with lab measurements of soil samples to understand the traveltime and amplitude features in zero-offset radargrams acquired over a buried pipe near Yuma, Arizona. Heterogeneous distributions of the dielectric, conductive, and magnetic properties are inferred through comparison between the simulated and real data.;3-D prestack full wavefield inversion of scalar seismic data involves two steps, the first is extrapolating backward in time, of the residual wavefield (the difference between the observed data and the wavefield generated by the current estimates of the model). The second is the correlation, at each time step, of this propagating residual with the forward propagating wavefield. This directly images the P-wave velocity distribution of the earth. To avoid convergence to a local minimum, a wavenumber filter is applied during inversion. A new 3-D data acquisition design, which requires fewer sources but more receivers than the currently prevailing 3-D acquisition geometry, is proposed and illustrated by application to synthetic data from a monocline and fault/dome model. The inversion converges in several iterations.