Two-dimensional inversion of direct current resistivity data incorporating topography by using finite difference techniques with triangle cells: Investigation of Kera fault zone in western Crete

Abstract

In this study, we suggest the use of a finite difference (FD) forward solution with triangular grid to incorporate topography into the inverse solution of direct current resistivity data. A new inversion algorithm was developed that takes topography into account with finite difference and finite element forward solution by using triangular grids. Using the developed algorithm, surface topography could also be incorporated by using triangular cells in a finite difference forward solution. Initially, the inversion algorithm was tested for two synthetic data sets. Inversion of synthetic data with the finite difference forward solution gives accurate results as well as inversion with finite element forward solution and requires less CPU time. The algorithm was also tested with a field data set acquired across the Kera fault located in western Crete, Greece. The fault location and basement depth of sedimentary units were resolved by the developed algorithm. These inversion results showed that if underground structure boundaries are not shaped according to surface topography, inversion using our finite difference forward solution with triangular cells is superior to inversion using our finite element forward solution in terms of CPU time and estimated models.

Research on Inversion Resolution for ERT Data and Applications for Mineral Exploration

“…ERT surveys have been used in resource exploration (Tang et al 2007;Yi et al 2011;Fikos et al 2012;Hermans et al 2012b), hydrogeology surveys (Lee et al 2008;Hermans et al 2012a;Maiti et al 2012;Muchingami et al 2012), engineering geology surveys (Chang et al 2012;Lehmann et al 2013;Springman et al 2013;Perrone et al 2014) and environmental geology surveys (Martínez-Pagán et al 2010;Metwaly et al 2013;Sirhan and Hamidi 2013;Sonkamble 2014). Numerous approaches have been developed by geophysicists including the finite-difference (FD) method (Dey and Morrison 1979a;Mizunaga and Ushijima 1991;Mizunaga et al 2003;Zhang et al 2011;Demirci et al 2012), the finite-element (FE) method (Bing and Greenhalgh 2001;Zhou and Greenhalgh 2002;Zhou et al 2009;Vachiratienchai et al 2010;Vachiratienchai and Siripunvaraporn 2013) and the boundary-integral (BI) method (Schulz 1983(Schulz , 1985Hvoždara 2012). The electric potential (difference) in twodimensional (2-D) and three-dimensional (3-D) conductivity structures can be obtained using the linear system of equations solution arising from partial differential equation discretization using these numerical approaches.…”

3D assessment of an underground mine pillar by combination of photogrammetric and geoelectric methods

“…This research follows the works of Sasaki (1994) and more recently the papers of Demirci et al (2012) and Erdoğan et al, 2008 introducing the problem of topography in the inversion process. The latter present five different solutions based on finite-difference or finite-element modeling and with a half or full representation of the air volume.…”

“…However, conventional 2D and 3D imaging techniques are mainly applied to flat surface surveys (Dahlin, 1996) or to surfaces with moderate topography (Fox et al, 1980;Günther et al, 2006;Erdoğan et al, 2008;Demirci et al, 2012;Fargier et al, 2014). Interesting results can be obtained using a 3D forward model (using a complex geometry) and performing a 2D inversion (Lesparre et al, 2014).…”

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

“…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.…”