Sundararajan transform—an application to geophysical data analysis

Al‐Garni, Mansour A.; Srinivas, Y.; Natarajan, Sundararajan

doi:10.1007/s12517-009-0037-1

Cited by 4 publications

(3 citation statements)

References 11 publications

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“…The results show that the thickness of the fault is about 1,015 m and extends from 285.81 m ( z 1) below the surface to 1299.84 m ( z 2) depth. The results of some previous researchers through a Sundararajan integral transformation (Al‐Garni et al., 2010), an artificial neural network application (ANN) (Al‐Garni, 2016), a DE optimization (Ekinci et al., 2020), and an MRFO application (Ben, Ekwok, et al., 2022; Ben et al., 2021) can also be seen in the table. Although all of the above approaches resulted in different parameter estimates when evaluating the Lachlan Fold Belt aeromagnetic anomaly, on average, they yield a thickness of about 1050 m for the fault.…”

Section: Resultsmentioning

confidence: 99%

Fault Structure Reconstruction From Magnetic Anomalies Using an Improved Backtracking Search Optimization Algorithm

Balkaya,

Ekinci,

et al. 2024

Earth and Space Science

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Fault structure reconstruction is an important aspect of magnetic prospecting as it contributes to understanding tectonic history, hazard assessment, and infrastructure planning. Metaheuristics have proven useful in estimating fault structure parameters from geophysical anomalies. Recently, a modified version of the Backtracking Search Optimization Algorithm (BSA), named mBSA, has been proposed that combines mutation steps of BSA and Differential Evolution (DE) algorithms to achieve a better balance between exploration and exploitation. Here, we present imBSA as an efficient approach that builds on the improvements of mBSA. It uses an adaptive amplitude control factor in the mutation step derived from a normally distributed random number obtained via an exponential function. The performances of these approaches were tested on some widely used benchmark functions such as Rosenbrock, Rastrigin, Griewank, and Himmelblau. Synthetic magnetic fault anomalies were evaluated with and without noise, as well as three real anomalies from the Dehri (India), Perth Basin, and Lachlan Fold Belt (Australia). Prior to the optimizations, the solvability of the model parameters was examined using some error topography images. The obtained solutions in the synthetic cases were evaluated using principal component analysis. In addition, a novel visualization option for high‐dimensional optimization problems was introduced. The experiments showed that imBSA has a faster convergence rate and better optimization statistics compared to BSA and mBSA. Therefore, it is believed to be an efficient and good alternative tool to widely used metaheuristics such as Particle Swarm Optimization and DE in explaining geophysical anomalies and optimization problems in other geoscientific disciplines.

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Section: Resultsmentioning

confidence: 99%

Fault Structure Reconstruction From Magnetic Anomalies Using an Improved Backtracking Search Optimization Algorithm

Balkaya,

Ekinci,

et al. 2024

Earth and Space Science

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“…2D Fault. The magnetic effect for a 2D fault (Figure 1(a)) is given by the following equation [36,93]:…”

Section: Methodsmentioning

confidence: 99%

Interpretation of Magnetic Anomalies over 2D Fault and Sheet-Type Mineralized Structures Using Very Fast Simulated Annealing Global Optimization: An Understanding of Uncertainty and Geological Implications

Biswas

Rao

2021

Lithosphere

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Identification of intraterrane dislocation zones and associated mineralized bodies is of immense importance in exploration geophysics. Understanding such structures from geophysical anomalies is challenging and cumbersome. In the present study, we present a fast and competent algorithm for interpreting magnetic anomalies from such dislocation and mineralized zones. Such dislocation and mineralized zones are well explained from 2D fault and sheet-type structures. The different parameters from 2D fault and sheet-type structures such as the intensity of magnetization (k), depth to the top (z1), depth to the bottom (z2), origin location (x0), and dip angle (θ) of the fault and sheet from magnetic anomalies are interpreted. The interpretation suggests that there is uncertainty in defining the model parameters z1 and z2 for the 2D inclined fault; k, z1, and z2 for the 2D vertical fault and finite sheet-type structure; and k and z for the infinite sheet-type structure. Here, it shows a wide range of solutions depicting an equivalent model with smaller misfits. However, the final interpreted mean model is close to the actual model with the least uncertainty. Histograms and crossplots for 2D fault and sheet-type structures also reveal the same. The present algorithm is demonstrated with four theoretical models, including the effect of noises. Furthermore, the investigation of magnetic data was also applied from three field examples from intraterrane dislocation zones (Australia), deep-seated dislocation zones (India) as a 2D fault plane, and mineralized zones (Canada) as sheet-type structures. The final estimated model parameters are in good agreement with the earlier methods applied for these field examples with a priori information wherever available in the literature. However, the present method can simultaneously interpret all model parameters without a priori information.

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“…It has been demonstrated that the Hilbert transform is not always respondent especially when the given function is odd (Mohan et al,1982 ;Sundararajan, 1982). To overcome this, modified Hilbert transform is defined (Sundararajan 1996;Al-Garni, 2009). In this paper, interpretation of gravity anomalies due to spherical and cylindrical models is studied using modified Hilbert transform.…”

Section: Introductionmentioning

confidence: 99%

Depth estimation of gravity anomalies using modified Hilbert transform

Ashena

Ardestani

2012

International Geophysical Conference and Oil &Amp; Gas Exhibition, Istanbul, Turkey, 17-19 September 2012

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Depth estimation of gravity anomalies can be determined using modified Hilbert transform. Modified Hilbert transform is identical in amplitude with conventional Hilbert transform but differs in phase as it yields a phase shift of 270°, whereas Hilbert transform is a 90° phase shifter. It has been shown mathematically that abscissa of the intersection point of the gravity field and the modified Hilbert transform is equal to the depth of the structure. The procedure is applied to spherical and cylindrical models at different depths and radiuses, then the effect of random noise is examined on the models that shown satisfactory results. To see the applicability of the method, the practical application of real data is also illustrated. The results from interpretation of real data are compared to the ones obtained from Euler deconvolution method, where an acceptable agreement is noticed.

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Sundararajan transform—an application to geophysical data analysis

Cited by 4 publications

References 11 publications

Fault Structure Reconstruction From Magnetic Anomalies Using an Improved Backtracking Search Optimization Algorithm

Fault Structure Reconstruction From Magnetic Anomalies Using an Improved Backtracking Search Optimization Algorithm

Interpretation of Magnetic Anomalies over 2D Fault and Sheet-Type Mineralized Structures Using Very Fast Simulated Annealing Global Optimization: An Understanding of Uncertainty and Geological Implications

Depth estimation of gravity anomalies using modified Hilbert transform

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