On the use of super-resolution algorithms in seismics : applications within diffraction separation and imaging

Abstract

It is both an experimental and theoretical fact that imaging of scatterers using bandlimited signals results in what is known as a diffraction-limited image. As a consequence, the best possible resolution obtained from a diffraction-limited system is about half a wavelength of the illuminating wavefield. In the near-field imaging systems used in optics this problem has been overcome by measuring the contribution of evanescent wavefields. However, in case of seismics, the sources and receivers are placed more than three times the wavelength away from the target and the evanescent wavefields are highly attenuated and thus fall below the noise level. Nevertheless, super-resolution imaging (i.e. imaging beyond the diffraction-limit) is possible by utilizing the time-reversal MUltiple SIgnal Classification (MUSIC) algorithm. The main idea is then to perform a Singular Value Decomposition (SVD) of the Multistatic Response (MSR) matrix to obtain the source and receiver side singular vectors which transforms the active experiment into a purely passive one. These singular vectors contain interaction information about the different scatterers, which is the key to obtain super-resolution. Though this algorithm can provide a super-resolved localization of point targets, it is also highly noise sensitive. In this thesis, we propose a phase-coherent time-reversal MUSIC (PC-MUSIC) algorithm, which utilizes the band of frequencies present in the measured data and exhibits a phase-coherent nature of the time-reversal operator. The noise present in the resulting monochromatic time-reversal MUSIC image can now be minimized by averaging over a smaller band of frequencies. The robustness and super-resolution ability of PC-MUSIC has been demonstrated employing both experimental ultrasonic data and numerical simulations based on the Foldy-Lax interaction model.

Both time-reversal MUSIC and its phase-coherent version, PC-MUSIC, are originally designed to localize point like targets. In seismic or Ground Penetrating Radar (GPR) signals, the contributions from point like targets are carried by the diffracted wavefield. However, diffracted signals both in seismic and GPR are often much weaker than the specular reflections making it difficult to utilize them for super-resolution imaging. In this thesis, we propose to separate the diffracted signals from the reflected ones using two parameterized diffraction traveltime approximations. The first technique is based on a modified version of the Common Reflection Surface (CRS) technique. The second diffraction traveltime approximation is based on the REplacement Medium (REM) approach derived in this thesis for applications in a laterally smooth velocity field. The actual diffraction enhancement (or separation) is then carried out by stacking the data along the two approximate diffraction traveltime surfaces with optimal parameters determined using a coherency measure. As possible coherency measure candidates we tested both conventional Semblance and higher-resolution coherency measures like MUSIC, Eigen Vector (EV) and Minimum Variance (MV). The higher-resolution coherency measures, originally developed for narrowband Direction Of Arrival (DOA) estimation, were extended to handle the highly correlated and wideband seismic and GPR signals. From this extensive testing, employing both controlled data (Marmousi) as well as field data (both GPR and seismic), we concluded that the MUSIC coherency measure provides the most optimal diffraction traveltime parameters. After separating the diffractions from the reflections by stacking along the optimized diffraction traveltime surfaces, we performed diffraction imaging using both conventional Kirchhoff migration and a new high-resolution MUSIC like imaging algorithm known as Semblance balanced MUSIC (SB-MUSIC). This new algorithm outperformed classical migration when applied to various controlled and field data.