Incorporating topography into 2D resistivity modeling using finite-element and finite-difference approaches

Geophysics ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. F135-F142 ◽  
Author(s):  
Erhan Erdoğan ◽  
Ismail Demirci ◽  
Mehmet Emin Candansayar
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
High Resistivity ◽  
Topographic Effects ◽  
Surface Geometry ◽  
Forward Solution ◽  
Numerical Solution Methods ◽  
Solution Methods ◽  
2D Resistivity ◽  
Resistivity Modeling

We incorporate topography into the 2D resistivity forward solution by using the finite-difference (FD) and finite-element (FE) numerical-solution methods. To achieve this, we develop a new algorithm that solves Poisson’s equation using the FE and FD approaches. We simulate topographic effects in the modeling algorithm using three FE approaches and two alternative FD approaches in which the air portion of the mesh is represented by very resistive cells. In both methods, we use rectangular and triangular discretization. Furthermore, we account for topographic effects by distorting the FE mesh with respect to the topography. We compare all methods for accuracy and calculation time on models with varying surface geometry and resistivity distributions. Comparisons show that model responses are similar when high-resistivity values are assigned to the top half of the rectangular cells at the air/earth boundary with the FE and FD methods and when the FE mesh is distorted. This result supports the idea that topographic effects can be incorporated into the forward solution by using the FD method; in some cases, this method also shortens calculation times. Additionally, this study shows that an FD solution with triangular discretization can be used successfully to calculate 2D DC-resistivity forward solutions.

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

Geophysics ◽  
2012 ◽  
Vol 77 (1) ◽  
pp. E67-E75 ◽  
Author(s):  
Ismail Demirci ◽  
Erhan Erdoğan ◽  
M. Emin Candansayar
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Surface Topography ◽  
Direct Current ◽  
Synthetic Data ◽  
Inversion Algorithm ◽  
Forward Solution ◽  
Data Set ◽  
Cpu Time ◽  
Resistivity Data

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.

Micromechanics as a Basis of Stochastic Finite Elements and Differences: An Overview

1993 ◽  
Vol 46 (11S) ◽  
pp. S136-S147 ◽  
Author(s):  
M. Ostoja-Starzewski
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Classical Method ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Solution Methods ◽  
Stochastic Solution ◽  
Stochastic Finite Elements

A generalization of conventional deterministic finite element and difference methods to deal with spatial material fluctuations hinges on the problem of determination of stochastic constitutive laws. This problem is analyzed here through a paradigm of micromechanics of elastic polycrystals and matrix-inclusion composites. Passage to a sought-for random meso-continuum is based on a scale dependent window playing the role of a Representative Volume Element (RVE). It turns out that the microstructure cannot be uniquely approximated by a random field of stiffness with continuous realizations, but, rather, two random continuum fields may be introduced to bound the material response from above and from below. Since the RVE corresponds to a single finite element, or finite difference cell, not infinitely larger than the crystal size, these two random fields are to be used to bound the solution of a given boundary value problem at a given scale of resolution. The window-based random continuum formulation is also employed in analysis of rigid perfectly-plastic materials, whereby the classical method of slip-lines is generalized to a stochastic finite difference scheme. The present paper is complemented by a comparison of this methodology to other existing stochastic solution methods.

Topographic responses in magnetometric resistivity modeling

Geophysics ◽  
1992 ◽  
Vol 57 (11) ◽  
pp. 1409-1418 ◽  
Author(s):  
Chieh‐Hou Yang ◽  
Hung‐Wen Tseng
Keyword(s):  
Finite Element ◽  
Effective Means ◽  
Ground Surface ◽  
Fault Model ◽  
Topographic Effects ◽  
Surface Form ◽  
Terrain Effects ◽  
Contact Models ◽  
Relief Area ◽  
Resistivity Modeling

The magnetometric resistivity (MMR) topographic responses due to earth topography were simulated using a finite‐element method. An algorithm was developed and the computer program was verified by comparison with analytic responses for half‐space and contact models. The topographic responses for different rugged surfaces were computed, and the model results indicate topographic effects can affect MMR sounding interpretation. In general, MMR topographic responses do depend on surface form; the more rugged the ground surface is, the larger the MMR topographic anomaly will be. These topographic effects will decrease as the distance between the source (and/or receiver) position and the high relief area is increased. We only address the problem of determining MMR anomalies over a two‐dimensional (2-D) topography. A numerical example illustrates an effective means of reducing the terrain effects for a 45‐degree dipping fault model incorporating a 45‐degree ramp surface, suggesting that the finite‐element modeling technique does provide a means of determining topographic correction for MMR sounding data.

An Investigation Into the Compliance of SCARA Robots. Part II: Experimental and Numerical Validation

1988 ◽  
Vol 110 (1) ◽  
pp. 23-30 ◽  
Author(s):  
H. A. ElMaraghy ◽  
B. Johns
Keyword(s):  
Elastic Compliance ◽  
Servo Control ◽  
Compliance Matrix ◽  
End Effector ◽  
Prismatic Parts ◽  
Numerical Solution Methods ◽  
Solution Methods ◽  
Using Data ◽  
Assembly Performance ◽  
Robot Configurations

A model of inherent elastic compliance was developed for general position-controlled SCARA, with conventional joint feedback control, for both rotational and prismatic part insertion (Part I). The developed model was applied to the SKILAM and ADEPT I robots for validation. Experimental procedures and numerical solution methods are described. It was found that the ADEPT I robot employs a coupled control strategy between joints one and two which produces a constant, decoupled end effector compliance. The applicable compliance matrix, in this case, is presented and the experimental results are discussed. The model may be used to develop compliance maps that define the amount of end effector compliance, as a function of the joints compliance, as well as its variation for different robot configurations. This is illustrated using data for the SKILAM SCARA robot. Results are plotted and discussed. The most appropriate robot postures for assembly were found for both rotational and prismatic parts. The conditions necessary to achieve compliance or semicompliance centers with the SKILAM robot were examined. The results and methods demonstrated in these examples may be used to select appropriate robots for given applications. They can also guide robot designers in selecting joint servo-control gains to obtain the desired joints compliance ratio and improve assembly performance.

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