Acoustic and elastic diffraction tomography and its application to fracture detection

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. This method is preferable over existing linearized methods because it can account for the diffractions in the medium. The inversion is performed using two separate methods, the conventional backpropagation 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 inversion methods are applied to field data collected from a 10.0 by 21.5 m rectangular region where fractures were known to exist. This region was chosen from the Grimsel test site facility in Switzerland. A complete coverage of the rectangular area with 0.5 m spacing of three-component receivers and a piezoelectric source was carried out. A data processing scheme, necessary to bring the field data into a form that can be used in the inversion algorithms, is developed and applied to the crosshole field data. Results of backpropagation, quadratic programming and ray tomography crosshole inversions agree well and show possible fracture zones which are confirmed by core samples.; 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. This inverse problem is in general ill-conditioned. 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. Incorporation of elliptical anisotropy is seen to improve the isotropic inversion results of the field data previously obtained.