A least‐squares minimization approach to invert gravity data

Abstract

The interpretation of gravity data often involves initial steps to eliminate or attenuate unwanted field components in order to isolate the desired anomaly (e.g., residual‐regional separations). These initial filtering operations include, for example, the radial weights methods (Griffin, 1949; Elkins, 1951; Abdelrahman et al., 1990), the fast Fourier transform methods (Bhattacharyya, 1965; Clarke, 1969; Meskó, 1969, 1984, Botezatu, 1970), the rational approximation techniques (Agarwal and Lal, 1971) and recursion filters (Bhattacharyya, 1976), and the bicubic spline approximation techniques (Bhattacharyya, 1969; Inoue, 1986). The derived local gravity anomalies are then geologically interpreted to derive depth estimates, often without properly accounting for the uncertainties introduced by the filtering process. When filters are applied to observed data, the filters often cause serious distortions in the shape of the gravity anomalies (Hammer, 1977). Thus the filtered gravity anomalies generally yield unreliable geologic interpretations (Rao and Radhakrishnamurthy, 1965; Hammer, 1977; Abdelrahman et al., 1985, 1989.

A Versatile Nonlinear Inversion to Interpret Gravity Anomaly Caused by a Simple Geometrical Structure

“…In most cases, these methods consider the geometrical shape factor of the buried body being a priori assumed, and the depth variable may thereafter be obtained by graphical methods applied on the residualized anomaly (NETTLETON, 1962(NETTLETON, , 1976, ratio techniques (BOWIN et al, 1986;ABDELRAHMAN et al, 1989), Fourier transform (ODEGARD and BERG, 1965), Mellin transform (MOHAN et al, 1986), least-squares minimization approaches (GUPTA, 1983;LINES and TREITEL, 1984;ABDELRAHMAN, 1990;ABDELRAHMAN et al, 1991;ABDELRAHMAN and EL-ARABY, 1993;ABDELRAHMAN and SHARAFELDIN, 1995a). However, only a few methods have been developed to determine the shape of the buried structure from the residualized gravity anomaly.…”

Depth Estimation of Simple Causative Sources from Gravity Gradient Tensor Invariants and Vertical Component

“…6) over a salt dome, offshore Luisiana, USA (NETTLETON, 1976) has been used. Several authors have analyzed this anomaly using a spherical target as is commonly assumed for salt-dome geometry (NETTLETON, 1976;MOHAN et al, 1986;ABDELRAHMAN et al, 1991;SHAW and AGARWAL, 1997;SALEM et al, 2004;ESSA, 2007). The GGT components from residual gravity map have been calculated using the method based on the FFT by MICKUS and HINOJOSA (2001).…”

“…In general, geologic structures in mineral and petroleum exploration can be classified as spheres, infinite horizontal cylinders and semi-infinite vertical cylinders. Several methods have been presented for interpreting gravity anomalies and estimating depths of geologic structures, assuming these simply shaped bodies (NETTLETON, 1962;ODEGARD and BERG, 1965;SHARMA and GELDART, 1968;GUPTA, 1983;BOWIN et al, 1986;MOHAN et al, 1986;ABDELRAHMAN et al, 1989;SHAW and AGARWAL, 1990;ABDELRAHMAN, 1990;ABDELRAHMAN et al, 1991;ABDELRAHMAN and EL-ARABY, 1993). Recently, ABDELRAHMAN et al (2001), SALEM et al (2003 and ASFAHANI and TLAS (2008) have developed least-squares minimization approaches which are derived to estimate the depths from residual gravity anomaly profile.…”

Global nonlinear optimization for the interpretation of source parameters from total gradient of gravity and magnetic anomalies caused by thin dyke

“…2001], Fourier transform [Odegard and Berg 1965, Bhattacharyya 1965, Sharma and Geldart 1968, Euler deconvolution [Thompson 1982], Mellin transform [Mohan et al 1986], Hilbert transforms [Mohan et al 1982], least squares minimization approaches [Gupta 1983, Silva 1989, McGrath and Hood 1973, Lines and Treitel 1984, Abdelrahman 1990, Abdelrahman et al 1991, Abdelrahman and El-Araby 1993, Abdelrahman and Sharafeldin 1995a, Werner deconvolution [Hartmann et al 1971, Jain 1976, Kilty 1983; Walsh Transformation [Shaw and Agarwal 1990], Continual least-squares methods [Abdelrahman and Sharafeldin 1995b, Abdelrahman et al 2001a, b, Essa 2012, Euler deconvolution method [Salem and Ravat 2003], Fair function minimization procedure andAsfahani 2011a, Asfahani andTlas 2012], DEXP method [Fedi 2007], deconvolution technique [Tlas and Asfahani 2011b]; Regularised inversion [Mehanee 2014, Mehanee andEssa 2015]; Simplex algorithm [Tlas and Asfahani 2015], simulated annealing methods [Gokturkler and Balkaya 2012], Very fast simulated annealing Acharya 2016, Biswas andSharma 2016a, b;Biswas 2015, b, Sharma and Biswas 2013a, particle swarm optimization [Singh and Biswas 2016] and Differential Evolution ] have been used to solve similar kind of no...…”