On the least‐squares residual anomaly determination

Abstract

This paper discusses an approach to determine the least‐squares optimum order of the regional surface which, when subtracted from the Bouguer gravity anomaly data, minimizes distortion of the residual component of the field. The least‐squares method was applied to theoretical composite gravity fields each consisting of a constant residual component (sphere or vertical cylinder) and a regional component of different order using successively increasing orders of polynomial regionals for residual determination. The overall similarity between each two successive residual maps was determined by computing the correlation factor between the mapped variables. Similarity between residual maps of the lowest orders, verified by good correlation, may generally be considered a criterion for determining the optimum order of the regional surface and consequently the least distorted residual component. The residual map of the lower order in this well‐correlated doublet is considered the most plausible one and may be used for gravity interpretation. This approach was successfully applied to the Bouguer gravity of Abu Roash dome, located west of Cairo in the Western Desert of Egypt.

Estimation of 2½ Dimensional Surface Structure in Kelud Volcano Region Based on Gravity Survey

“…Penurunan matematisnya dilakukan oleh Abdelrahman [6] dimana metode ini telah berhasil diujikan pada data anomali Bouguer lengkap kubah garam Abu Roash yang terletak di sebelah Barat Kairo, Mesir [7].…”

“…Dalam kesimpulannya Dampney [9] menyatakan bahwa kedalaman optimum dari massa ekivalen harus memenuhi persamaan (6).…”

A New Algorithm for Depth Determination from Total Magnetic Anomalies due to Spheres

“…Under these circumstances, the interpretation of magnetic data must involve removing unwanted field components to isolate the desired total field magnetic anomaly, as, for example, regionalresidual separation. This operation includes graphical methods (NETTLETON, 1976), leastsquares filtering techniques (ABDELRAHMAN et al, 1985), Fourier transformation methods (SYBERG, 1972), and regional susceptibility modeling methods (LI and OLDENBERG, 1998). The derived local and regional magnetic anomalies are then geologically interpreted to estimate the depth often without properly accounting for uncertainties introduced by the filtering process.…”

An Iterative Approach to Depth Determination from Second Moving Average Residual Magnetic Anomalies

“…regional-residual separation). The initial filtering operation include, for example, least-squares filtering techniques (Abdelrahman et al 1985), Fourier transform methods (Syberg, 1972), regional susceptibility modeling methods (Li and Oldenberg, 1998), and two-coaxial structures analysis method (Abdelrahman et al 2002). The derived local magnetic anomaly is then geologically interpreted to estimate the depth, often without properly accounting for uncertainties introduced by the filtering process.…”