Acoustic and elastic diffraction tomography and its application to fracture detection.

摘要

The inverse problem of fracture detection is approached using a waveform imaging method. The Born approximation is utilized for the linearization of the nonlinear inverse scattering problem. The inversion is performed using two separate methods, the conventional back propagation method and a quadratic programming method with constraints. Initially, the two-dimensional acoustic problem is discussed and the following developments are treated: estimation of a background velocity to be used in the inversion, sensitivity of the inversion algorithm to velocity and how this can be utilized to reduce unwanted wave modes, effect of the total field on the inversion, incorporation of free-surfaces, inversion with slanted boreholes, and two-and-a-half-dimensional corrections. The theory for the elastic case is developed next. The operators acting on the elastic parameters are discussed and their properties used for the inversion of individual elastic parameters. A method that stabilizes the inverse problem using multi-frequencies and constrained angles is introduced and tested on synthetic data. A fractured medium will in general be transversely isotropic. Therefore, the theory is extended to the transverse isotropy case for SH-waves and elliptical anisotropy for quasi-P waves. Reconstruction of multi-parameters in a transversely isotropic medium is also discussed. 65 refs. (ERA citation 15:033262)