ABSTRACT
This chapter discusses some of the problems associated with obtaining an image of the elastic parameters of the earth between two boreholes, from seismic data generated and recorded in the holes. All wave theoretical imaging procedures perform optimally if they are essentially refining a well constrained starting model. A monofrequency image of the object function can be formed using this equation, a procedure which is normally referred to as acoustic holography. An algebraic relationship is obtained between the spatial Fourier transform of the scattered field and the spatial Fourier transform of the object function. The essential difference between holography and diffraction tomography is that the latter includes a filtering operation that corrects for the non-uniform coverage of the spectrum of the object function in the reconstruction process and therefore reduces image distortion. Migration algorithms, such as holography and diffraction stack methods, are usually formulated to yield images of reflection coefficient.
