Shallow Applications of Geophysical Diffraction Tomography

Diffraction tomography is the generalization of conventional (X-ray) tomography to applications employing diffracting wave fields such as ultrasound, seismic, and low-frequency electromagnetic waves. One approach to diffraction tomography is the filtered back-back-propagation algorithm that has been suggested as a means for subsurface exploration in the oil industry. In this paper we investigate the influence of a number of factors on the quality of tomographic reconstructions obtained via the filtered backpropagation algorithm. These include the presence of strong scatterers, the approximate generation of plane waves, the attenuation of high-frequency components, the density of receivers, and the quality of the received signal. The objective of this study is the acquisition of information to serve as a basis for the design of field instrumentation and implementation of geophysical diffraction tomography. It is found that the density of receivers limits the size of the smallest features that can be imaged, while the loss of high-frequency components limits the image sharpness. The filtered backpropagation algorithm can yield adequate images with at least moderate noise added to the signal. Errors that can occur as a result of the approximate generation of plane waves can be overcome by an appropriate slant stack procedure. Isolated strong scatterers will be difficult to distinguish from weak scatterers in the reconstruction, and the presence of a strong scatterer could obscure nearby features.