Technical Notes - Helicopter Electromagnetics

Short Note on Inversion of Fugro Data

Introduction

From the user's point of view, an inversion is a process to convert EM data to geology. Some do it better, some do it worse. The most useful inversion is one which can do this conversion reliably and accurately, producing the correct geological model with minimal input or control from the user. Since we often do not know what is the "correct geological model", a geologically reasonable model within some range of known geological and data parameters is generally accepted.

Without going into the mathematical description, inversions are processes in which data are created by forward modeling from a resistivity distribution, and compared to some input data presumably collected over some real, geology. The quality of the fit between the real and modeled data is measured, and the model is adjusted to improve the fit until some user-defined limit on accuracy or time is reached.

Inversions can be made to work well on theoretical data, but the real test comes in applying them to field data, with its noise, and limitations on signal and resolution of the resistivity variations. The process requires a plethora of inputs and controls, and cross-matches these to a basketful of geological parameters. Along the way, there are many opportunities for the process to proceed along a divergent path from that deemed reasonable, and it is the task of the applications geophysicist to control this divergence.

Types Of Sections And Inversions

There are four types of sections commonly in use for Fugro data (Figure 1). The Sengpiel section (1b) is a transform which creates a section by plotting the halfspace apparent resistivity at a depth which is a function of the skin-depth - in turn a function of resistivity and frequency (Sengpiel, 1988). A Differential section (1c)is a modification of the Sengpiel section, which uses the resistivity and depths calculated for higher (shallow-penetrating) frequencies to modify the measured halfspace apparent resistivity of the lower frequencies to try to determine a more accurate measure of the resistivity at depth (Huang and Fraser, 1996). Being transforms, these are very fast and robust techniques for producing resistivity sections and 3D blocks.

The multi-layer inversion (1d) uses Singular Value Decomposition (SVD) to match the model results from a fixed number of layers with varying thickness and resistivity to the data (Huang and Palacky, 1991).

The Occam inversion (1e) models the conductivity distribution with a fixed number of thin layers of fixed thickness, varying the resistivity to match the data (Constable et al, 1987).

The multi-layer inversion provides the most accurate match of model to geology in areas with discrete layers of different resistivity. It also provides the most definitive measure of the depth or thickness of a discrete layer. Bathymetry is an application where the multi-layer inversion is the best style. Multi-layer inversions are much slower than the transforms, and much more affected by noise and errors.

The Occam inversion produces a section in which the resistivities tend to vary more gradually, and is more applicable to geology in which there are not discrete layers. Because the inversion does not match specific model layers to geological layers, reasonable results are less dependent on getting an accurate definition of the correct number of layers. Occam inversions are slower than the multi-layer, but are more robust when applied to changing geology.

Figure 2 shows the two types of inversions on some field data, calculated over a dipping layer. In this case, the Occam inversion works best - meaning that it produces the result most similar to a normal geological section. Note that the top of the dipping layer is reflected by an offset in the topography, adding confirmation to the interpretation.

• Constable, S.C., Parker, R.L., And Constable, C.G., 1987, Occam's inversion: a practical algorithm for generating smooth models from electromagnetic sounding data: Geophysics, 52, 289-300
• Huang, H. and Fraser, D.C., 1996, The differential parameter method for multi-frequency airborne resistivity mapping, Geophysics, v.61 100-109
• Huang, H. and Palacky, G.J., 1991, Damped least-squares inversion of time-domain airborne EM data based on singular value decomposition: Geophysical Prospecting, v.39, 827-844
• Sengpiel, K.P., 1988, Approximate inversion of airborne EM data from a multi-layered ground. Geophysical Prospecting, v.36, 446-459
• Vrbancich, J., Hallett, M., Hodges, G, 2000, Airborne electromagnetic bathymetry of Sydney Harbour. Exploration Geophysics, in press.

Greg Hodges, Chief Geophysicist, 2001