Hydraulic Tomography Study Involving the Singular Value Decomposition Method

An oscillatory pressure signal has been generated in the field; and, the amplitude decay and phase shift have been monitored between source and receiver wells in a hydraulic tomography study. Hydraulic tomography studies traditionally require great amounts of time and computing power to process the large amount of data. Modeling of theoretical data indicates that the hydraulic conductivity values can be represented by spatially averaged straight ray paths. This is a good approximation except near the upper and lower boundaries, since the straight ray path method assumes an infinite aquifer. The assumption of a straight ray path greatly reduces the time and computing power needed for data processing, as no nonlinear iterative methods are necessary. The area between wells is divided into rectangular elements. The equations describing the ray paths are solved using Singular Value Decomposition (SVD) for the hydraulic conductivity distribution. The SVD method can resolve differing hydraulic conductivity values for elements of about one meter square or larger. Instability problems arise at the top and bottom of the area because there are fewer ray paths through these regions than through the center. The instability problem is avoided by collapsing the top row of elements into a single element and the bottom row into a single element. After collapsing the rows, the center values are still resolvable into one meter square blocks. Data collected in the field have been processed using the SVD method. The hydraulic conductivity values obtained from the SVD program are within the range of values typically obtained by other methods at the site. The SVD method shows promising results for a relatively simple analysis of oscillatory hydraulic tomography data. This work is funded by the Strategic Environmental Research and Development Program (SERDP) as project ER-1367.