A hybrid finite difference–finite element method to incorporate topography for 2D direct current (DC) resistivity modeling

Vachiratienchai, Chatchai; Boonchaisuk, Songkhun; Siripunvaraporn, Weerachai

doi:10.1016/j.pepi.2010.09.008

Cited by 29 publications

(18 citation statements)

References 20 publications

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“…Such outliers accounted for less than 7% of the total data acquired in the area. Many researchers have discussed the influence of topography on measured resistivity data and the steps that can be used to filter out their effects (Erdogan et al, 2008;Mendoza and Dahlin, 2008;Vachiratienchai et al, 2010;Arango-Galván et al, 2011). In this study, influence of topography on the measured data was checked in situ by carefully orienting the profile parallel to the Calabar-Itu Road across the debris flow direction where elevation difference at all points along the profile was below 60 cm.…”

Section: Electrical Resistivity Studiesmentioning

confidence: 99%

Geophysical investigation of Obot Ekpo Landslide site, Cross River State, Nigeria

Akpan

Ilori

Essien

2015

Journal of African Earth Sciences

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Section: Electrical Resistivity Studiesmentioning

confidence: 99%

Geophysical investigation of Obot Ekpo Landslide site, Cross River State, Nigeria

Akpan

Ilori

Essien

2015

Journal of African Earth Sciences

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“…However, topography inclusion can be difficult. In contrast, FE is difficult to apply and slow to converge but topography inclusion is more natural (Vachiratienchai et al 2010). In addition to FD or FE, another technique is the integral equation (IE) formulation (Weidelt 1975;Hohmann 1975;Wannamaker 1991;Zhdanov 2002Zhdanov , 2009).…”

Section: Magnetotelluric Forward Modelingmentioning

confidence: 99%

“…This would again lead to a larger system of equations and require much more CPU time to obtain the same accuracy as with FE. An efficient hybrid FE-FD method has been successfully used to incorporate the topography for 2-D direct current (DC) resistivity codes (Vachiratienchai et al 2010). It has been shown to be as accurate as the FE method but requires less CPU time than the FD method for the same grid discretization size.…”

Section: Dos and Don'ts When Performing 3-d Inversionmentioning

confidence: 99%

Three-Dimensional Magnetotelluric Inversion: An Introductory Guide for Developers and Users

Siripunvaraporn

2011

Surv Geophys

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116

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In the last few decades, the demand for three-dimensional (3-D) inversions for magnetotelluric data has significantly driven the progress of 3-D codes. There are currently a lot of new 3-D inversion and forward modeling codes. Some, such as the WSINV3DMT code of the author, are available to the academic community. The goal of this paper is to summarize all the important issues involving 3-D inversions. It aims to show how inversion works and how to use it properly. In this paper, I start by describing several good reasons for doing 3-D inversion instead of 2-D inversion. The main algorithms for 3-D inversion are reviewed along with some comparisons of their advantages and disadvantages. These algorithms are the classical Occam's inversion, the data space Occam's inversion, the Gauss-Newton method, the Gauss-Newton with the conjugate gradient method, the non-linear conjugate gradient method, and the quasi-Newton method. Other variants are based on these main algorithms. Forward modeling, sensitivity calculations, model covariance and its parallel implementation are all necessary components of inversions and are reviewed here. Rules of thumb for performing 3-D inversion are proposed for the benefit of the 3-D inversion novice. Problems regarding 3-D inversions are discussed along with suggested topics for future research for the developers of the next decades.

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“…Numerical techniques have been applied to solve the forward problem of the geoelectric field, including the finite‐difference (FD) method (Mufti ; Dey and Morrison , b; Spitzer ; Zhang, Sun and Sun ; Demirci, Erdogan and Candansayar ), the finite‐element (FE) method (Coggon ; Bing and Greenhalgh ; Vachiratienchai, Boonchaisuk and Siripunvaraporn ; Vachiratienchai and Siripunvaraporn ), and the boundary integral method (Schulz ; Schulz ; Hvoždara ). Generally, the FD methods are numerical methods for differential equations using FD equations to mathematically approximate derivatives.…”

Section: Introductionmentioning

confidence: 99%

Out‐of‐plane effects in 2D borehole‐to‐surface resistivity tomography and applications in mineral exploration

Zhang

et al. 2016

Geophysical Prospecting

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In this paper, we discuss the effects of anomalous out‐of‐plane bodies in two‐dimensional (2D) borehole‐to‐surface electrical resistivity tomography with numerical resistivity modelling and synthetic inversion tests. The results of the two groups of synthetic resistivity model tests illustrate that anomalous bodies out of the plane of interest have an effect on two‐dimensional inversion and that the degree of influence of out‐of‐plane body on inverted images varies. The different influences are derived from two cases. One case is different resistivity models with the same electrode array, and the other case is the same resistivity model with different electrode arrays. Qualitative interpretation based on the inversion tests shows that we cannot find a reasonable electrode array to determine the best inverse solution and reveal the subsurface resistivity distribution for all types of geoelectrical models. Because of the three‐dimensional effect arising from neighbouring anomalous bodies, the qualitative interpretation of inverted images from the two‐dimensional inversion of electrical resistivity tomography data without prior information can be misleading. Two‐dimensional inversion with drilling data can decrease the three‐dimensional effect. We employed two‐ and three‐dimensional borehole‐to‐surface electrical resistivity tomography methods with a pole–pole array and a bipole–bipole array for mineral exploration at Abag Banner and Hexigten Banner in Inner Mongolia, China. Different inverse schemes were carried out for different cases. The subsurface resistivity distribution obtained from the two‐dimensional inversion of the field electrical resistivity tomography data with sufficient prior information, such as drilling data and other non‐electrical data, can better describe the actual geological situation. When there is not enough prior information to carry out constrained two‐dimensional inversion, the three‐dimensional electrical resistivity tomography survey is the better choice.

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A hybrid finite difference–finite element method to incorporate topography for 2D direct current (DC) resistivity modeling

Cited by 29 publications

References 20 publications

Geophysical investigation of Obot Ekpo Landslide site, Cross River State, Nigeria

Geophysical investigation of Obot Ekpo Landslide site, Cross River State, Nigeria

Three-Dimensional Magnetotelluric Inversion: An Introductory Guide for Developers and Users

Out‐of‐plane effects in 2D borehole‐to‐surface resistivity tomography and applications in mineral exploration

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