Diffraction tomography and multisource holography applied to seismic imaging

Abstract Seismic tomography is emerging as an imaging method for determining subsurface structure. When the view-angle coverage is limited and the scale of the medium inhomogeneities is comparable with the wavelength, as is often true in geophysical applications, the performance of ordinary ray tomography becomes poor. Other tomographic methods are needed to improve the imaging process. Here we study diffraction tomography and multisource holography and evaluate their performances for surface reflection profiling (SRP), vertical seismic profiling (VSP), and cross-hole measurements. Theoretical formulations are derived for two-dimensional geometry in terms of line sources along a source line and line receivers along a receiver line. The theory for diffraction tomography is based on the Born or Rytov approximation.The performances of diffraction tomography and multisource holography are evaluated by examining the information coverage in the spatial frequency domain and by numerical examples. Multisource holography, which is similar to Kirchhoff-type migration, often gives distorted images of the object. This distortion causes long tails of the image in the case of SRP and a strong noise belt in the case of VSP and is due to incomplete and nonuniform coverage of the object spectrum. The filtering operation of diffraction tomography helps in correcting the nonuniform coverage (including duplication) of the object spectrum in the reconstruction process and therefore reduces the distortions. On the other hand, multisource holography is better suited for imaging sharp boundaries with large acoustic impedance contrasts since diffraction tomography is restricted, as presently formulated, to weak inhomogeneities. In addition, multisource holography has the flexibility to be used with an arbitrary number of sources (including a single source). Its sampling interval is not restricted by the Nyquist frequency.Numerical examples show that combined data sets (such as surface reflection data combined with VSP data, or cross-hole data combined with surface data, etc.) improve the image quality.