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High resolution conductivity-depth transformation of TEM data

Summary Conductivity depth transformation of TEM data remains an important tool for preliminary interpretation, despite the increasing speed of 1D inversion. Conductivity-depth imaging (CDI) is very fast, does not require a starting model, and is an effective means for data quality assessment. Moreover, CDI sections can serve as starting models for inversion. This paper describes a high resolution enhancement of an existing CDI algorithm for TEM data. Conductivitydepth transformation is accomplished in two steps. Measured voltages or B-field at a given delay time are first transformed to apparent conductivity. For dB/dt data, the assigned depth, z(t), at each time is the depth of the electric field or current maximum (Emax depth) in a half-space with conductivity equal to the apparent conductivity. For B-field data, the depth to the halfspace B-field maximum (Bmax depth) is employed. CDI sections based on apparent conductivity provide a vertically smoothed representation of the true conductivity profile. The apparent conductivity at any time can be represented as an inner product of the true conductivity with the Frechet kernel. The Frechet kernel at time t can be approximated as a linear function, decreasing from its maximum value at the surface to zero at a depth d(t). Therefore, given apparent conductivities from the CDI algorithm, a sharper estimate of the true conductivity can be generated via solution of a simple integral equation. We solve the integral equation for a “minimum structure” model using linear programming. The implementation of this high resolution CDI algorithm is illustrated on selected examples of synthetic and real airborne TEM data.