Orthogonal Polynomials: Their Use in Estimating the Regional Effect

Abstract

The examination of experimental data for significant trends by orthogonal polynomials is well known in statistics. The method is adapted here to the estimation of regional trends in potential field observations, and two characteristically‐different gravity maps are analyzed. The method is found to agree closely with a graphical solution in an area of fairly smooth contours, and to give a reasonable solution in an area where the graphical method would be difficult to apply. It is proposed that the orthogonal polynomials could also be adapted to evaluating total mass and to interpreting second derivative maps.

Trend Surface Analysis of Aeolian Sand Movement on the Southwest African Coast

“…Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever Introduction Since its development as a quantitative research tool by different scientistS' (eg. Oldham and Sutherland, 1955;Whitten, 1961) trend surface analysis (TSA) has been applied to different problems in different fields of study. The technique will not be explained in detail here (for this, see the excellent account by Unwin, 1975) but it is a fact that modern high speed computer allow the researcher to easily apply, TSA to areas where traditional mapping techniques fail to explainareal variation and distribution of parameters.…”

Statistical Analysis of the Gravity Method of Calculating the Depth to the Pre‐cenozoic Surface in Yucca Flat, Nevada Test Site*

“…A corrected gravity station is set on outcropping pre-Cenozoic rocks, away from the influence of the Cenozoic rocks, and approximately measures the regional gravity field. The regional gravity field is further defined by fitting a calculated orthogonal polynomial surface to the contoured gravity map (Agocs 1951, Oldham and Sutherland 1955, Simpson 1954. The closeness of the fit depends on the degree of the polynomial.…”

A Numerical Approach to Depth Determination from Residual Gravity Anomaly Due to Two Structures

“…The filter operations include for example, the radial weights methods (GRIFFIN, 1949;ELKINS, 1951;ROSENBACH, 1953;RAO et al, 1970;ABDELRAHMAN et al, 1989), the fast Fourier transform methods (BHAT- TACHARYYA, 1965;CLARKE, 1969;BOTEZATU, 1970;MESKO, 1984), the rational approximation techniques (AGARWAL and LAL, 1971), recursion filters (BHAT- TACHARYYA, 1969;INOUE, 1986), and the least-squares method (OLDHAM and SUTHERLAND, 1955;GRANT, 1957;AGOCS, 1951;FAJKLEWICZ, 1959;ABDELRAH-MAN et al, 1985). The determined residual gravity anomalies are then geologically interpreted to derive depth estimates, often without properly accounting for the uncertainties introduced by the filtering process.…”