INTRODUCTION

In gravity exploration and in many fields of geophysics and other sciences, it is necessary or convenient to separate a "background" field from a "local field" (Gupta and Romani, 1980). In gravity exploration the background or "regional" field is caused by deep and/or widespread density anomalies. The local or "residual" field is intended to be a result of only shallow density anomalies. (Some authors use the term "residual anomaly" to indicate the misfit between gravity of a model and the gravity data.)

There are two main reasons for making the separation. One is simply to locate or highlight anomalous areas. The other is to isolate just the local anomaly in a form suitable for quantitative modeling.

There are many ways to accomplish the separation. There is no best or unique procedure; only ones that are convenient and reasonable in a given context. Here are some common methods.

DO NOTHING METHOD

In some cases, making a regional-residual separation is not necessary. In the case of the Barracuda Fault Zone study, I simply modeled the Free Air anomaly in its entirety (Birch, 1970). Because of the great depth and essentially uniform density of the ocean water, there were no local density anomalies. In this case, a constant has to be added to the model gravity values in order to match the Free Air ones.

SMOOTH PROFILING

Figure 6-17 in your text illustrates this simple graphical methods. The regional is just sketched in by hand or with drafting tools. I guess you could do this by computer also. Although this method often gives excellent results, it is blatantly subjective. Different people will get different residual anomalies.

Smooth contouring is a similar process applied to gravity maps (Bothner, 1974).

SMOOTH PROFILING WITH GEOLOGICAL CONSTRAINTS

I picked this method for my Albuquerque Basin project (Birch, 1982). Basically I used a "physical spline" (i.e. flexible strip of plastic) to draw smooth regional curves between outcrops of Precambrian granite far from strong influence of the low density basin sediments. In other words, I was defining a world of uniform granite as background for anomalies caused by lower density sedimentary rock. Given enough control points this use of a specific geological hypothesis worked very well, but of course it is still subjective.

A benefit of such a scheme is that only non-anomalous points are used to define the regional field.

DIGITAL FILTERING

This method uses data evenly spaced on a profile or grid (Agocs, 1951; Fuller, 1966). The regional field is defined as some sort of weighted average of nearby gravity values. As with all methods, the residual is just the difference between the gravity value at a point and the regional field at the same point.

Digital filters can be designed to include or exclude any given range of wavelengths of gravity (or period of seismic waves for example). This method is objective in the sense that the procedure is cut-and-dried once the particular filter coefficients (weights) are chosen.

The basic limitation is that sources at any depth have spectra composed of all possible wavelengths. Thus, a perfect spectral separation is not possible.

As we saw in class, digital filtering tends to produce equal positive and negative anomalies. That could be geologically unreasonable in many situations. Filtering can also produce spurious anomalies of no geological significance.

From another point of view, we see that the residual is not entirely "pure" because anomalous local points are used in determination of the regional.

LEAST-SQUARES POLYNOMIALS

You are all familiar with the concept of the mean of some data points and of a least-squares regression line. These can be considered zero-degree and first-degree polynomials. The slopes and intercepts can readily be found using common computer programs such as "Excel". In the same was we can find the second, third, fourth degree polynomials, etc., to use as regional profiles. An analogous set of polynomial surfaces can be used as map data.

The great advantage of polynomials is that the procedure is entirely objective once the degree of polynomial is selected (a very subjective step!). If the degree is too low, the regional will be too simple and will not describe a reasonable regional trend. If the degree is too high, the residual will mainly be random noise and the significant anomaly values taken away as part of the regional.

As with polynomials, the least squares regional values are contaminated by local anomalous points.

Another problem with a very complex regional is it can not correspond to a uniform background density against which to define density contrasts in a model: quantitative modeling becomes impossible.

SUMMARY AND CONCLUSIONS

Regional-residual separation is inherently subjective. There is no mathematical trick or procedure to avoid this fact of life. Choice of method should be based on convenience and geological common sense.

REFERENCES AND READINGS

Agocs, 1951, Geophysics, 16, 686-.

Birch, 1970, Deep Sea Research, 17, 847-.

Birch, 1982, Geophysics, 47, 1185-.

Bothner, 1974, Geological Society of America Bulletin, 85, 51-.

Fuller, 1966, in "Mining Geophysics II", Society of Exploration Geophysicists, Tulsa

Gupta and Romani, 1980, Geophysics, 45, 1412-.