Abstract
The velocity distribution between two boreholes is reconstructed by cross-well tomography, which is commonly used in geology. In this paper, iterative methods, Kaczmarz’s algorithm, algebraic reconstruction technique (ART), and simultaneous iterative reconstruction technique (SIRT), are implemented to a specific cross-well tomography problem. Convergence to the solution of these methods and their CPU time for the cross-well tomography problem are compared. Furthermore, these three methods for this problem are compared for different tolerance values.
Highlights
Cross-well seismic tomography, which is used often in geology, mainly deals with reconstructing the velocity structure between two boreholes by measuring travel time for ray paths between them [1]
Hydrologists should have information regarding the locations of hydraulically conductive fractures if they want to clean up contaminants which are in fractured bedrock as stated in [3]
Since the model and data are continuous functions’ variables, and we want to determine the model from the data in our cross-well tomography problem, this problem is defined as a continuous inverse problem
Summary
Cross-well seismic tomography, which is used often in geology, mainly deals with reconstructing the velocity structure between two boreholes by measuring travel time for ray paths between them [1]. After P-waves are used in the bedrock, obtained data are processed by using tomographic methods The result of this process is known as tomogram [3]; that is, the structure of P-wave velocity between two wells. Since P-wave velocity is reduced by fractures, the locations of fractures can be obtained from the low velocity anomalies in the tomogram. These fractures can be hydraulically conductive ones [3]
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