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.

scholarly journals Pixels and their neighbors: Finite volume

2016 ◽  
Vol 35 (8) ◽  
pp. 703-706 ◽  
Author(s):  
Rowan Cockett ◽  
Lindsey J. Heagy ◽  
Douglas W. Oldenburg
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Direct Current ◽  
Numerical Results ◽  
Dc Resistivity ◽  
Matrix Representations ◽  
Volume Method

We take you on the journey from continuous equations to their discrete matrix representations using the finite-volume method for the direct current (DC) resistivity problem. These techniques are widely applicable across geophysical simulation types and have their parallels in finite element and finite difference. We show derivations visually, as you would on a whiteboard, and have provided an accompanying notebook at http://github.com/seg to explore the numerical results using SimPEG ( Cockett et al., 2015 ).

scholarly journals Multidimensional scaling for the evaluation of a geostatistical seismic elastic inversion methodology

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. M1-M10 ◽  
Author(s):  
Leonardo Azevedo ◽  
Ruben Nunes ◽  
Pedro Correia ◽  
Amílcar Soares ◽  
Luis Guerreiro ◽  
...  
Keyword(s):  
Multidimensional Scaling ◽  
Metric Space ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Inversion ◽  
Inversion Algorithm ◽  
Data Set ◽  
The Real ◽  
Geostatistical Inversion ◽  
Impedance Models

Due to the nature of seismic inversion problems, there are multiple possible solutions that can equally fit the observed seismic data while diverging from the real subsurface model. Consequently, it is important to assess how inverse-impedance models are converging toward the real subsurface model. For this purpose, we evaluated a new methodology to combine the multidimensional scaling (MDS) technique with an iterative geostatistical elastic seismic inversion algorithm. The geostatistical inversion algorithm inverted partial angle stacks directly for acoustic and elastic impedance (AI and EI) models. It was based on a genetic algorithm in which the model perturbation at each iteration was performed recurring to stochastic sequential simulation. To assess the reliability and convergence of the inverted models at each step, the simulated models can be projected in a metric space computed by MDS. This projection allowed distinguishing similar from variable models and assessing the convergence of inverted models toward the real impedance ones. The geostatistical inversion results of a synthetic data set, in which the real AI and EI models are known, were plotted in this metric space along with the known impedance models. We applied the same principle to a real data set using a cross-validation technique. These examples revealed that the MDS is a valuable tool to evaluate the convergence of the inverse methodology and the impedance model variability among each iteration of the inversion process. Particularly for the geostatistical inversion algorithm we evaluated, it retrieves reliable impedance models while still producing a set of simulated models with considerable variability.

2.5‐D inversion of frequency‐domain electromagnetic data generated by a grounded‐wire source

Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1753-1768 ◽  
Author(s):  
Yuji Mitsuhata ◽  
Toshihiro Uchida ◽  
Hiroshi Amano
Keyword(s):  
Frequency Domain ◽  
Regularization Parameter ◽  
Synthetic Data ◽  
Magnetic Data ◽  
Statistical Criterion ◽  
Model Parameters ◽  
Inversion Algorithm ◽  
Gas Field ◽  
Data Set ◽  
Transient Electromagnetic

Interpretation of controlled‐source electromagnetic (CSEM) data is usually based on 1‐D inversions, whereas data of direct current (dc) resistivity and magnetotelluric (MT) measurements are commonly interpreted by 2‐D inversions. We have developed an algorithm to invert frequency‐Domain vertical magnetic data generated by a grounded‐wire source for a 2‐D model of the earth—a so‐called 2.5‐D inversion. To stabilize the inversion, we adopt a smoothness constraint for the model parameters and adjust the regularization parameter objectively using a statistical criterion. A test using synthetic data from a realistic model reveals the insufficiency of only one source to recover an acceptable result. In contrast, the joint use of data generated by a left‐side source and a right‐side source dramatically improves the inversion result. We applied our inversion algorithm to a field data set, which was transformed from long‐offset transient electromagnetic (LOTEM) data acquired in a Japanese oil and gas field. As demonstrated by the synthetic data set, the inversion of the joint data set automatically converged and provided a better resultant model than that of the data generated by each source. In addition, our 2.5‐D inversion accounted for the reversals in the LOTEM measurements, which is impossible using 1‐D inversions. The shallow parts (above about 1 km depth) of the final model obtained by our 2.5‐D inversion agree well with those of a 2‐D inversion of MT data.

Fast 2-D ray+Born migration/inversion in complex media

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 162-181 ◽  
Author(s):  
Philippe Thierry ◽  
Stéphane Operto ◽  
Gilles Lambaré
Keyword(s):  
Numerical Approximation ◽  
Reference Model ◽  
Real Data ◽  
Model Parameters ◽  
Complex Media ◽  
Inversion Algorithm ◽  
Numerical Approximations ◽  
Data Set ◽  
Cpu Time ◽  
Computational Evaluation

In this paper, we evaluate the capacity of a fast 2-D ray+Born migration/inversion algorithm to recover the true amplitude of the model parameters in 2-D complex media. The method is based on a quasi‐Newtonian linearized inversion of the scattered wavefield. Asymptotic Green’s functions are computed in a smooth reference model with a dynamic ray tracing based on the wavefront construction method. The model is described by velocity perturbations associated with diffractor points. Both the first traveltime and the strongest arrivals can be inverted. The algorithm is implemented with several numerical approximations such as interpolations and aperture limitation around common midpoints to speed the algorithm. Both theoritical and numerical aspects of the algorithm are assessed with three synthetic and real data examples including the 2-D Marmousi example. Comparison between logs extracted from the exact Marmousi perturbation model and the computed images shows that the amplitude of the velocity perturbations are recovered accurately in the regions of the model where the ray field is single valued. In the presence of caustics, neither the first traveltime nor the most energetic arrival inversion allow for a full recovery of the amplitudes although the latter improves the results. We conclude that all the arrivals associated with multipathing through transmission caustics must be taken into account if the true amplitude of the perturbations is to be found. Only 22 minutes of CPU time is required to migrate the full 2-D Marmousi data set on a Sun SPARC 20 workstation. The amplitude loss induced by the numerical approximations on the first traveltime and the most energetic migrated images are evaluated quantitatively and do not exceed 8% of the energy of the image computed without numerical approximation. Computational evaluation shows that extension to a 3-D ray+Born migration/inversion algorithm is realistic.

Two-dimensional inversion of magnetotelluric/radiomagnetotelluric data by using unstructured mesh

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. E197-E210 ◽  
Author(s):  
Özcan Özyıldırım ◽  
Mehmet Emin Candansayar ◽  
İsmail Demirci ◽  
Bülent Tezkan
Keyword(s):  
Surface Topography ◽  
Unstructured Grid ◽  
Unstructured Mesh ◽  
Synthetic Data ◽  
Solution Technique ◽  
Inversion Algorithm ◽  
2D Inversion ◽  
Two Samples ◽  
Speed And Accuracy ◽  
Grid Based

We have compared structured and unstructured grid-based 2D inversion algorithms for magnetotelluric (MT) and radiomagnetotelluric (RMT) data in terms of speed and accuracy. We have developed a new 2D inversion algorithm for MT and RMT data by using a finite-element (FE) method that uses unstructured triangle grids. We compare the inversion results of our unstructured grid-based algorithm with those of the conventional algorithm, which uses either a structured FE or structured finite-difference (FD) numerical solution technique. The imaging of the surface topography and the underground resistivity structures by the new algorithm requires fewer elements than those that use FE and FD structured grids. We also find that when unstructured grids are used, the quality of the mesh is increased and the numerical errors are significantly reduced. Thus, the program runs faster and can simulate the complex surface topography in a more stable setting than the classic inversion algorithms. Furthermore, we implement a new smoothing matrix format for the unstructured triangle grids for the inversion procedure. We use two samples of synthetic data for the MT and RMT frequencies as well as a sample of field RMT data collected across a fault zone for comparison. In our synthetic data experiment, we find that the resistivity values and the boundaries obtained from the inversion of the unstructured mesh are closer to those of the true a priori synthetic model. Results of the synthetic and field data verify the computational advantages (speed and accuracy) of our inversion algorithm with respect to the conventional structured grid-based inversion algorithms.

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.

scholarly journals Waveform inversion using a logarithmic wavefield

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. R31-R42 ◽  
Author(s):  
Changsoo Shin ◽  
Dong-Joo Min
Keyword(s):  
Objective Function ◽  
Field Data ◽  
Velocity Structure ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Velocity Model ◽  
Matrix Formalism ◽  
Inversion Algorithm ◽  
Data Set ◽  
Short Period

Although waveform inversion has been studied extensively since its beginning [Formula: see text] ago, applications to seismic field data have been limited, and most of those applications have been for global-seismology- or engineering-seismology-scale problems, not for exploration-scale data. As an alternative to classical waveform inversion, we propose the use of a new, objective function constructed by taking the logarithm of wavefields, allowing consideration of three types of objective function, namely, amplitude only, phase only, or both. In our wave form inversion, we estimate the source signature as well as the velocity structure by including functions of amplitudes and phases of the source signature in the objective function. We compute the steepest-descent directions by using a matrix formalism derived from a frequency-domain, finite-element/finite-difference modeling technique. Our numerical algorithms are similar to those of reverse-time migration and waveform inversion based on the adjoint state of the wave equation. In order to demonstrate the practical applicability of our algorithm, we use a synthetic data set from the Marmousi model and seismic data collected from the Korean continental shelf. For noise-free synthetic data, the velocity structure produced by our inversion algorithm is closer to the true velocity structure than that obtained with conventional waveform inversion. When random noise is added, the inverted velocity model is also close to the true Marmousi model, but when frequencies below [Formula: see text] are removed from the data, the velocity structure is not as good as those for the noise-free and noisy data. For field data, we compare the time-domain synthetic seismograms generated for the velocity model inverted by our algorithm with real seismograms and find that the results show that our inversion algorithm reveals short-period features of the subsurface. Although we use wrapped phases in our examples, we still obtain reasonable results. We expect that if we were to use correctly unwrapped phases in the inversion algorithm, we would obtain better results.

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