Application of Filter Theory and Information Theory to the Interpretation of Gravity Measurements

Abstract

A wavenumber filter can be used in conjunction with the Hartley‐Tuller‐Shannon formula to bring about some reduction in the number of ambiguous contours on a gravity map. The filter focuses the interpreter’s attention on the maximum response to density changes within a given layer. At the same time, characteristics of the filter design, such as bandwidth and power of the desired output relative to other interfering outputs, can be used in the H‐T‐S formula to determine a minimum contouring threshold, such that the relative number of false anomalies and missed true anomalies is minimized. In addition, it is also possible to estimate a lower limit on the probability that an anomaly observed on a map originates in a target layer.

Ambiguity assessment of gravity interpretation for an inhomogeneous multilayered sedimentary basin

“…This method can easily be extended to an n-layered model on lines similar to those worked out by Sax [1966]. The computation of channel capacity by either the ItTS formula or Gabor's formula is no longer feasible, owing to the phenomenon of cross talk, which occurs because the layers have been considered as transmitters.…”

“…The lower limit of this ambiguity range is fixed by using Gaboffs modified formula, the beats produced between signal and noise being taken into account. The upper limit is obtained by the Hartley-Tuller-Shannon formula after Sax (1966). Wider effective applications of this combined approach to various problems of interpretation have been indicated by the illustration of the controversial gravity interpretations of Mono basin in California.…”

“…The ambiguity in the interpretation of a gravity field over stratified earth increases with the number of layers. Sax [1966] has worked out an elegant technique to measure the uncertainty by selecting an optimum contour interval for a good resolution of a gravity map with minimum error. Sax used the Hartley-Tuller-Shannon (HTS) formula to find the channel capacity of the target layer, treating it as a transmitter in a noisy communication system that does not involve the phenomenon of beats between signal and noise.…”

“…The technique is applied to the Mono basin in California to assess the ambiguity in its interpretation by Pakiser [1968Pakiser [ , 1970 and Christenser• et al [1969]. distance received at the surface with minimum uncertainty and is given by [Sax, 1966] NEGI ET AL. : AMBIGUITY ASSESSMENT OF GRAVITY INTERPRETATION C --A__•_K log2 [1 q-(S/N)] (6) 2•r bits per unit distance, where SIN is the signalto-noise power ratio and AK is the bandwidth.…”

“…The computation of channel capacity requires the signal-to-noise ratio and is given by Sax [ 1966] $[d(x, y) proper values of A, B, a, d•, and d= from Sierra and hence is of major importance. A number of geoscientists [e.g., Russell, 1889; Putnam, 1938Putnam, , 1949Putnam, , 1950Mayo et al, !936;Gilbert, 1938Gilbert, , 1941Gilbert, , 1968Pakiser, 1968Pakiser, , 1970Pakiser et al, 1960Pakiser et al, , 1964Christensen et al, 1969;Christensen and Gilbert, 1970] Table 2.…”