Practical techniques for 3D resistivity surveys and data inversion1

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Abstract
Techniques to reduce the time needed to carry out 3D resistivity surveys with a moderate number (25 to 100) of electrodes and the computing time required to interpret the data have been developed. The electrodes in a 3D survey are normally arranged in a square grid and the pole‐pole array is used to make the potential measurements. The number of measurements required can be reduced to about one‐third of the maximum possible number without seriously degrading the resolution of the resulting inversion model by making measurements along the horizontal, vertical and 45° diagonal rows of electrodes passing through the current electrode. The smoothness‐constrained least‐squares inversion method is used for the data interpretation. The computing time required by this technique can be greatly reduced by using a homogeneous half‐space as the starting model so that the Jacobian matrix of partial derivatives can be calculated analytically. A quasi‐Newton updating method is then used to estimate the partial derivatives for subsequent iterations. This inversion technique has been tested on synthetic and field data where a satisfactory model is obtained using a modest amount of computer time. On an 80486DX2/66 microcomputer, it takes about 20 minutes to invert the data from a 7 by 7 electrode survey grid. using the techniques described below, 3D resistivity surveys and data inversion can be carried out using commercially available field equipment and an inexpensive microcomputer.