INTRODUCTION

We can divide methods of interpretation into two categories. "Classical" methods date from the days of small surveys, often done using analog instruments. Emphasis was on interpretation of single anomalies and treatment was often semi-quantitative. "Modern" methods, in contrast, emphasize automatic interpretation of huge numbers of anomalies mapped using digital recording of large, detailed surveys.

CLASSICAL METHODS

The oldest classical method is simple empirical correlation of anomalies to known sources. For example a survey of a toxic waste site might reveal that certain anomalies correspond to buried steel drums. If the geology is simple enough, we can then pick out all the other drums based simply on the visual appearance of the anomalies. Another common example is interpretation of crystalline bedrock geology of Pre-Cambrian shields. After training on areas of known geology, the geophysicist can readily pick out felsic and mafic plutons, fold belts and faults based just on the visual attributes of the magnetic map.

"Rules of thumb" and "characteristic curves" can be used to get semi-quantitative interpretation of single anomalies. The rules use certain anomaly characteristics (half-widths, slopes, etc.), simple formula and graphs to estimate such source parameters as depth. These methods can give good results but are time consuming and don’t fully exploit the data.

In a gravity lab exercise we have seen how data can be interpreted using trial-and-error computer modeling. One advantage of this approach is that incorporation of geologic constraints is easy. Some disadvantages are that the interpretation is very time consuming and requires trained personnel with good local geologic knowledge.

As with other geophysical methods we can find models using automatic computer inversions to find best least-squares models, smoothest models and Monte Carlo bounds. These methods will be very slow for large data sets and it may be difficult to incorporate geological constraints.

MODERN METHODS

With the advent of rapid, digital data collection and huge detailed surveys the need has arisen for fast, automatic methods of interpretation. With such masses of data and large surveys we have to employ computer methods, at least in the initial stages of interpretation.

WERNER DECONVOLUTION

The goal of this method is to determine the depths of magnetic sources beneath sedimentary basins (Jain, 1976; Birch, 1983). In particular we seek the location, depth and intensity of thin vertical dikes. In class we’ll assume a vertical background field (Bo), a vertical component magnetometer, induced magnetization and a two-dimensional geometry.

Under these conditions we see that we can find the three unknown parameters by solving three simultaneous linear equations for the field at any three points on the profile. In practice we get separate trios of estimates using points #1-3, #2-4, #3-5, etc. along the profile from one end to the other. Our problem now is to decide which source estimates correspond to real sources and which are just junk. Many of the source estimates correspond to overlapping anomalies and thus are utterly invalid. Closely grouped clusters of estimates may come from a single real source.

EULER DECONVOLUTION

We have just learned that Werner deconvolution assumes a source geometry (thin vertical dike) and solves for source location, depth and strength. In Euler deconvolution we find source shape, location and depth but not strength (Thompson, 1982; Reid et al., 1990). The basic equation was found by Leonard Euler in the 1700’s, long before the days of modern magnetic exploration.

The equation contains three unknowns: source location, source depth and a "shape index" (N). We can solve for these using the field plus the horizontal and vertical field gradients at any three neighboring points on the profile. In practice we work from one end of the profile to the other in the same way as with Werner disconsolation. For each pass we specify a constant value for "N" (N=1 is a vertical dike; N=2 is a vertical cylinder, etc.). Output consists of a cross-section with sources plotted; often a different symbol is used for each N.

As with Werner disconsolation we need to separate the meaningful sources from the junk. We may get poor results from overlapping anomalies and from wide or extensive sources. The choice of regional field has a strong effect. And of course we need gradient data, not just the magnetic field values.

FOURIER SPECTRAL ANALYSIS

This method is used to get average source depths along a profile. We do not get individual source depths and the results are insensitive to the exact shape of the individual anomalies.

The basic idea of Fourier analysis is that any (normal) function can be expressed as the sum of simple sine and cosine functions ("harmonics"). The spectrum of a function or data series (that is, the magnetic profile) is just a plot of the amplitude of each harmonic versus the wavelength of each harmonic (cycles per kilometer).

For a vertical dike it turns out that the plot of the logarithm of the amplitude (of a harmonic) versus the corresponding wave number (radians per data interval) is a straight line. The (negative) slope of the line equals the source depth. Thus to get the source depth for a segment of a profile we simply calculate the Fourier series or transform and plot the spectrum on semi-log paper. The zero intercept gives the source strength (thickness times susceptibility). In calculating the spectrum we integrate over the x coordinate so source location within the window (segment) is lost. These results are true for the average depth of several sources within the window.

REFERENCES AND READINGS

Behrent and Klitgord, 1980, Geophysics

Birch, 1983, GroundWater, 22, 427-432.

Jain, 1976, Geophysics, 41, 531-.

Reid et al., 1990, Geophysics, 55, 80-.

Thompson, 1982, Geophysics, 47, 31-37.