APPROXIMATION IN GRAVITY INTERPRETATION CALCULATIONS

Abstract

Rigorous calculation of gravity effects of geologic bodies for the interpretation of subsurface structure from exploration gravity surveys is time‐consuming and tedious. Resort to electronic computers is convenient but not always necessary. Simple hand calculations can be instructive and are often adequate and useful. This paper reports the errors involved and ranges of validity of various simplifying approximations for commonly used geometric body shapes: (a) equivalent sphere approximation for an infinitely long horizontal cylinder, (b) circular plate approximation for horizontal slabs of finite width, (c) vertical line element and thin horizontal plate approximations for vertical cylinders of variable radii and heights (dome, salt dome, or plug), and (d) thin‐plate approximations for vertical dikes and horizontal fault blocks. The results are evaluated in terms of dimensionless parametric ratios, usually a characteristic dimension of the body versus depth to center of mass. Errors in the approximate calculations are remarkably small for several of the cases considered and the simplified results are valid for given precision over a rather large range of dimensions. For example, the maximum error in the thin‐plate approximation for an horizontal fault plate is less than one percent for a thickness/depth ratio ranging up to 0.75 which represents a very substantial fault throw. This particular example is more than adequate for most practical applications in geologic interpretations of gravity. On the other hand, some examples are shown to be unsuitable for simple approximation calculations.