Seismic waveform inversion in the frequency domain; Part 2; Fault delineation in sediments using crosshole data

A crosshole experiment was carried out in a layered sedimentary environment in which a normal fault is known to cut through the section. Initial traveltime inversions produced stable but low-resolution images from which the fault could be only vaguely inferred. To image the fault, wavefield inversion was used to produce a velocity model consistent with the detailed phase and amplitude of the data at a number of frequencies. Our wavefield inversion scheme uses a classical, descent-type algorithm for decreasing the data misfit by iteratively computing the gradient of this misfit by repeated forward and backward propagations. Our propagator is a full-wave equation, frequency-domain, acoustic, finite-difference method. The use of the frequency-space domain yields computational advantages for multisource data and allows an easy incorporation of viscous effects. By running wavefield inversion on the field data, a quantitative velocity image was produced that yielded a significantly improved image of the fault (when compared with the original traveltime inversions). Because the original field data were noisy and contained a high degree of multiple scattering (from the layering of the sediments), the transmitted arrivals were selectively windowed to enhance the image. The sediments at the site were strongly attenuating; we therefore used a viscoacoustic model during the modeling and the inversion that correctly simulated the observed decrease in amplitude with increasing frequency and source-receiver offset. Furthermore, since the traveltime inversion indicated a high degree of anisotropy at the site, a fixed, homogeneous level of anisotropy was used during the inversion. Tests at varying levels of anisotropy confirmed the improvement in image quality and in data fit when anisotropy was incorporated. The final image was verified by examining the distribution of the residuals in the frequency domain, by comparing time-domain modeled wavefields with the observed data, and by direct comparison with borehole logs.