Maximum Entropy Inversion of data sets from Subsurface Resistivity Surveying

Szymanski, J.E., Tsourlos, P. and Dittmer, J.K.
Department of Electronics
University of York, Heslington
York, YO1 5DD


The non-destructive exploration of the top few meters of the subsurface is a major challenge from both the technological and data-processing viewpoints, with application areas including archaeology, environmental assessment and shallow civil engineering. Resistivity surveying is an established, non-invasive and indirect method of probing below the ground surface: a series of probes at the ground surface are used to inject low-frequency currents into the ground and to measure local variations in surface potential differences. These represent isolated single-boundary measurements of quite large equipotential surfaces which are hemispherical for a homogeneous soil, but which will be distorted considerably by the presence of buried objects or regions of variable electrical conductivity. By using different potential probe spacings the equipotentials tend to be more sensitive to varying depths, and the established technique of constructing a resistivity pseudosection involves systematically increasing the probe spacings and assigning the experimental results to steadily deeper positions, hence building an approximate representation of the electrical properties of a vertical section of soil beneath a line of electrodes.

Pseudosection approaches have severe limitations in that they represent a very poor approximate and linearised inversion of the true problem --- they are known to be sensitive to noise and to produce major spurious artefacts. Further, they demand a simple and rigidly defined data set: they cannot readily cope with missing data values or with the large and complex oversampled data sets capable of being provided by the new multiprobe resistive tomography systems.

The inversion of the data sets arising from resistivity surveying is a difficult problem which offers a number of unusual challenges to the Maximum Entropy method in that each data value is, in theory, influenced by changes in any region of the subsurface: a decentralised `geophysical blur' is involved, but the point-spread function of this blur is not constant over the data set --- it depends radically not only on the particular configuration of the probes and the distances between them, but also on the (unknown) nature of the subsurface. The single-boundary nature of the problem also means that the quality of the reconstruction must decrease rapidly with depth and, in combination with the limited sample size, means that instrumental noise will impact on different regions of the parameterised subsurface to different degrees.

In most applications a high resolution is required and the inversion should be robust to noise and easy to interpret: in this paper a number of comparative studies using a nonlinear finite-element forward model show that the Maximum Entropy approach offers significant advantages over not only the established, pragmatic, methods but also other inversion routines.

MaxEnt 94 Abstracts /