Spatial resolution of diffraction tomography

Diffraction tomography is an imaging technique applicable to crosshole seismic data and aimed at achieving optimal spatial resolution away from the borehole. In principle the method can form acoustic images equivalent to extending acoustic well logs away from the wellbore and into the formation with a spatial resolution less than one wavelength of the radiation employed to gather the crosshole data. This paper reports on the capability of diffraction tomography to produce high-resolution reconstructions of simple targets from limited-view-angle data. The goal is to quantify the resolution and velocity-reconstruction capability of diffraction tomography with realistic source–receiver geometries. Simple targets (disks and low-contrast sequences of layers) are used for this study. The scattering from these targets can be calculated without approximation, making them ideal test cases for the algorithm. The resolution capability of diffraction tomography is determined to be on the order of one wavelength for several experimental geometries. It is shown that the image-formation characteristics of diffraction tomography, in terms of its ability to determine object boundaries and velocities, are closely related to the experimental geometry. Reflection and vertical seismic profiling (VSP) experiments tend to reproduce boundaries well, while crosshole experiments give the best overall reconstruction of both target boundaries and velocity. The quantitative accuracy of the velocity reconstruction depends upon the match between the spatial-frequency content of the object and the spatial-frequency response of the algorithm. For some targets, the velocity cannot be correctly reproduced from limited-view-angle data.