Modelling and compact inversion of magnetic data: A Matlab code

Stocco, Stefano; Godio, Alberto; Sambuelli, Luigi

doi:10.1016/j.cageo.2009.04.002

Cited by 48 publications

(34 citation statements)

References 14 publications

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“…A N-S profile is extracted from the vertical gradient field of the vertical component map of the area and subjected to inversion using PTRS technique. Although no constraints are added except the method's powerful dynamic trust region estimation, the results show a remarkable compatibility to previous results (Stocco et al, 2009). Fig.…”

Section: Field Examplesupporting

confidence: 78%

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Solving ill-posed magnetic inverse problem using a Parameterized Trust-Region Sub-problem

Abdelazeem

2013

Contributions to Geophysics and Geodesy

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Abstract:The aim of this paper is to find a plausible and stable solution for the inverse geophysical magnetic problem. Most of the inverse problems in geophysics are considered as ill-posed ones. This is not necessarily due to complex geological situations, but it may arise because of ill-conditioned kernel matrix. To deal with such ill-conditioned matrix, one may truncate the most ill part as in truncated singular value decomposition method (TSVD). In such a method, the question will be where to truncate? In this paper, for comparison, we first try the adaptive pruning algorithm for the discrete L-curve criterion to estimate the regularization parameter for TSVD method. Linear constraints have been added to the ill-conditioned matrix. The same problem is then solved using a global optimizing and regularizing technique based on Parameterized Trust Region Sub-problem (PTRS). The criteria of such technique are to choose a trusted region of the solutions and then to find the satisfying minimum to the objective function. The ambiguity is controlled mainly by proper choosing the trust region. To overcome the natural decay in kernel with depth, a specific depth weighting function is used. A Matlab-based inversion code is implemented and tested on two synthetic total magnetic fields contaminated with different levels of noise to simulate natural fields. The results of PTRS are compared with those of TSVD with adaptive pruning L-curve. Such a comparison proves the high stability of the PTRS method in dealing with potential field problems. The capability of such technique has been further tested by applying it to real data from Saudi Arabia and Italy.

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Section: Field Examplesupporting

confidence: 78%

“…The PTRS has also been applied to magnetic data in a well-studied area of the Sabine Necropolis at Motelibretti, Rome, Italy (Stocco et al, 2009). This archeological site is characterized by chamber tombs, and we have to find its position and size.…”

Section: Field Examplementioning

confidence: 99%

Solving ill-posed magnetic inverse problem using a Parameterized Trust-Region Sub-problem

Abdelazeem

2013

Contributions to Geophysics and Geodesy

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“…where F is the local Earth magnetic field intensity and K i;j represents a known geometrical function relating the size and the distance of the prism j from the measurement point i (details in Stocco et al, 2009). Equation 1, neglecting F, can also be written in matrix form as…”

Section: Magnetic Surveymentioning

confidence: 99%

“…The principle of the compact inversion used (Last and Kubik, 1983) involves minimizing the area of the source body (maximize its compactness). The problem is slightly underdetermined and it can be profitably solved using the weighted -damped least-squares inversion (Stocco et al, 2009).…”

Section: Magnetic Surveymentioning

confidence: 99%

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Magnetic, electrical, and GPR waterborne surveys of moraine deposits beneath a lake: A case history from Turin, Italy

et al. 2011

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Bathymetry and bottom sediment types of inland water basins provide meaningful information to estimate water reserves and possible connections between surface and groundwater. Waterborne geophysical surveys can be used to obtain several independent physical parameters to study the sediments. We explored the possibilities of retrieving information on both shallow and deep geological structures beneath a morainic lake by means of waterborne nonseismic methods. In this respect, we discuss simultaneous magnetic, electrical, and groundpenetrating radar (GPR) waterborne surveys on the Candia morainic lake in northerly Turin (Italy). We used waterborne GPR to obtain information on the bottom sediment and the bathymetry needed to constrain the magnetic and electrical inversions. We obtained a map of the total magnetic field (TMF) over the lake from which we computed a 2D constrained compact magnetic inversion for selected profiles, along with a laterally constrained inversion for one electrical profile. The magnetic survey detected some deep anomalous bodies within the subbottom moraine. The electrical profiles gave information on the more superficial layer of bottom sediments. We identify where the coarse morainic material outcrops from the bottom finer sediments from a correspondence between high GPR reflectivity, resistivity, and magnetic anomalies.

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Edge detection for the buried archaeological structures with the geophysical image processing method in the Alabanda Ancient Cistern in Turkey

Karaaslan

2020

Archaeological Prospection

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Edge detection techniques are some of the most useful techniques to determine the lineaments of buried structures from magnetic data. In this context, many techniques have been designed by using the magnetic gradient tensor (MGT). In this work, eigenvalue analysis of the full MGT and a new normalized approach [normalized edge detector (NK)], which balances strong and weak amplitude anomalies simultaneously, was utilized to outline lineaments of the buried archaeological structures. Satisfactory results were obtained from noisy and noise free synthetic data which were generated from prism models. The techniques were implemented on the archaeological magnetic data acquired from a buried ancient cistern. In addition, three‐dimensional (3D) electrical resistivity tomography (ERT) inversion sections and two‐dimensional (2D) magnetic inversion section and tilt angle methods were used to compare them against the results of edge detection analysis. The results of the normalized eigenvalue analysis agreed closely with all techniques in detecting the lineaments of the buried archaeological structure. NK detected the lineaments of the buried structure more clearly than the tilt angle and had better resolution. All of the results have shown that eigenvalue analysis of the full MGT and especially the newly introduced approach NK can provide important information for archaeological studies.

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Modelling and compact inversion of magnetic data: A Matlab code

Cited by 48 publications

References 14 publications

Solving ill-posed magnetic inverse problem using a Parameterized Trust-Region Sub-problem

Solving ill-posed magnetic inverse problem using a Parameterized Trust-Region Sub-problem

Magnetic, electrical, and GPR waterborne surveys of moraine deposits beneath a lake: A case history from Turin, Italy

Edge detection for the buried archaeological structures with the geophysical image processing method in the Alabanda Ancient Cistern in Turkey

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