Application of diffraction tomography to fracture detection

Abstract

Two diffraction tomography techniques are applied to crosshole field data to detect fractures in granitic rock. The techniques used are the conventional back‐propagation method and a new quadratic programming method incorporating constraints. In this formulation, the Born approximation is used for linearization of the inverse problem. Two dimensional (2-D) pseudo spectral finite‐difference synthetic data are generated to demonstrate the inversion methods and justify use of the Born approximation. Also, using 2-D Born synthetic data, the velocity sensitivity of the inversion algorithm and reduction of fracture generated tube waves and S‐waves are investigated. The inversion methods are applied to field data from the Grimsel test site in Switzerland. The data are collected from a [Formula: see text] rectangular area where fractures are known to exist. Data acquisition with 0.5 m spacing of three component receivers and a piezoelectric source is carried out so as to obtain a nearly complete coverage of the region. Crosshole inversions are performed on data from the receiver components in the plane of the rectangular region and normal to its boundary. As the result of a separate experiment conducted in a homogeneous region of the granitic rock, a cosine function was found to best fit the source radiation pattern. A background attenuation value is estimated for the region, using a simple statistical approach, and estimates of the wavelet are found by common source gathers, common receiver gathers, and averages of all traces. The preprocessing steps are: (1) source radiation correction, (2) attenuation correction, (3) removal of the incident wavefield, (4) muting beginning of the traces and windowing the ends, (5) wavelet deconvolution, and (6) two‐and‐a‐half dimensional (2.5-D) corrections. This preprocessing is designed to enhance scattered P‐waves that are used in the inversions. Images obtained from the application of back‐propagation and quadratic programming methods to the preprocessed data show possible fracture zones that agree well at the boundaries of the region with the fracture sets observed from core samples taken from the boreholes. Although the quadratic programming method is an order of magnitude slower than the back‐propagation method, as demonstrated by the synthetic examples, it proves useful by yielding high resolution images when constraints can be imposed. Transmission ray tomography is also applied to the crosshole data, and although the resolution is not as high, general agreement with the wave equation based methods is obtained.