1968
DOI: 10.1111/j.1365-2478.1968.tb01961.x
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Analysis of Gravity Anomalies of Two‐dimensional Faults Using Fourier Transforms*

Abstract: The Fourier transform formula for a two‐dimensional fault truncating a horizontal bed at an arbitrary angle of inclination is derived. The amplitude spectrum of the Fourier transform is found to give information about the depth to the top of the upper part of the faulted bed and the inclination of the fault‐plane. Under suitable conditions the thickness and the displacement of the bed involved can be obtained. With actual field data, these transforms can be obtained at discrete points by a Fourier analysis of … Show more

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Cited by 53 publications
(15 citation statements)
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“…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...…”
Section: Introductionmentioning
confidence: 99%
“…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...…”
Section: Introductionmentioning
confidence: 99%
“…Several numerical techniques have been presented and reported for interpreting gravity and magnetic anomalies and estimating depths and amplitude coefficients of geological structures, assuming fixed simple source geometry as a sphere, a horizontal cylinder, or a vertical cylinder. These techniques include, for example, graphical methods (NETTLETON, 1962(NETTLETON, , 1976, ratio methods (BOWIN et al, 1986;ABDELRAHMAN et al, 1989), Fourier transform (ODEGARD and BERG, 1965;SHARMA and GELDART, 1968), Euler deconvolution (THOMPSON, 1982), neural network (ELAWADI et al, 2001), Mellin transform (MOHAN et al, 1986), leastsquares minimization approaches (GUPTA, 1983;LINES AND TREITEL, 1984;ABDELRAHMAN, 1990;ABDELRAH-MAN et al, 1991;ABDELRAHMAN and EL-ARABY, 1993;ABDELRAHMAN and SHARAFELDIN, 1995a), Werner deconvolution (HARTMANN et al, 1971;JAIN, 1976). KILTY (1983) extended the Werner deconvolution technique to the analysis of gravity data using both the residual anomaly and its first and second horizontal derivatives; KU and SHARP (1983) further refined the method by using iteration for reducing and eliminating the interference field and then applied Marquardt's non linear least squares method to further refine automatically the first approximation provided by deconvolution.…”
Section: Introductionmentioning
confidence: 99%
“…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.…”
Section: Introductionmentioning
confidence: 99%