A Weighting Function-Based Method for Resistivity Inversion in Subsurface Investigations

2020 ◽  
Vol 25 (1) ◽  
pp. 129-138
Author(s):  
Lichao Nie ◽  
Zhao Ma ◽  
Bin Liu ◽  
Zhenhao Xu ◽  
Wei Zhou ◽  
...  
Keyword(s):  
Objective Function ◽  
Weighting Function ◽  
Real Data ◽  
Weighting Factor ◽  
Inversion Method ◽  
Depth Information ◽  
Detection Accuracy ◽  
Resistivity Inversion ◽  
Inversion Procedure ◽  
Anomalous Bodies

There is a high demand for high detection accuracy and resolution with respect to anomalous bodies due to the increased development of underground spaces. This study focused on the weighted inversion of observed data from individual array type electrical resistivity tomography (ERT), and developed an improved method of applying a data weighing function to the geoelectrical inversion procedure. In this method, the weighting factor as an observed data weighting term was introduced into the objective function. For individual arrays, the sensitivity decreases with increasing electrode interval. Therefore, the Jacobian matrices were computed for the observed data of individual arrays to determine the value of the weighting factor, and the weighting factor was calculated automatically during inversion. In this work, 2D combined inversion of ERT data from four-electrode Alfa-type arrays is examined. The effectiveness of the weighted inversion method was demonstrated using various synthetic and real data examples. The results indicated that the inversion method based on observed data weighted function could improve the contribution of observed data with depth information to the objective function. It has been proven that the combined weighted inversion method could be a feasible tool for improving the accuracies of positioning and resolution while imaging deep anomalous bodies in the subsurface.

scholarly journals Evaluation of induced polarization measurements using a new inversion method

2021 ◽  
Author(s):  
Tamás Fancsik ◽  
Endre Turai ◽  
Norbert Péter Szabó ◽  
Judit Somogyiné Molnár ◽  
Tünde Edit Dobróka ◽  
...  
Keyword(s):  
Objective Function ◽  
Series Expansion ◽  
Least Squares Method ◽  
Delta Function ◽  
Induced Polarization ◽  
General Definition ◽  
Inversion Method ◽  
Model Parameters ◽  
Ore Minerals ◽  
Inversion Procedure

AbstractIn this paper, a new inversion method is proposed to process laboratory-measured induced polarization (IP) data. In the new procedure, the concept of the series expansion-based inversion is combined with a more general definition of the objective function. The time constant spectrum of the IP effect is assumed a line spectrum approximated by a series of Dirac’s delta function resulting in a square-integrable forward problem formula. This gives the applicability of the generalized objective function. The expansion coefficients as unknowns represent the model parameters of the inversion procedure. We use the new inversion procedure on an apparent polarizability dataset measured on a rock sample originated from the Recsk ore complex, northeast Hungary. The inversion results was compared to those of three additional laboratory datasets, which were measured on samples rich in ore minerals collected from the same area. The results are compared to those given by the traditional series expansion-based least squares method. It is shown that the newly proposed method gives more accurate and stable parameter estimation.

Seismic inversion based on proximal objective function optimization algorithm

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. R237-R246 ◽  
Author(s):  
Ronghuo Dai ◽  
Fanchang Zhang ◽  
Hanqing Liu
Keyword(s):  
Objective Function ◽  
Optimization Algorithm ◽  
Computational Efficiency ◽  
Real Data ◽  
Cauchy Distribution ◽  
Critical Issue ◽  
Seismic Inversion ◽  
Function Optimization ◽  
Inversion Method ◽  
Reservoir Prediction

Seismic impedance inversion has become a common approach in reservoir prediction. At present, the critical issue in the application of seismic inversion is its low computational efficiency, especially in 3D. To improve the computational efficiency, we have developed an inversion method derived from the proximal objective function optimization algorithm. Our inversion method calculates each unknown parameter in the model vector, one by one during iteration. Compared with routine gradient-dependent inversion algorithms, such as the iteratively reweighted least-squares (IRLS) algorithm, our inversion method has lower computational complexity as well as higher efficiency. In addition, to obtain a sparse reflectivity series, a long-tailed Cauchy distribution is used as the a priori constraint. The weak nonlinear problem owing to the introduction of Cauchy sparse constraint is addressed by taking advantage of reweighting strategy. Results of synthetic and real data tests illustrate that the proposed inversion method has higher computational efficiency than IRLS algorithm, and its inversion accuracy remains the same.

FAST ACCURATE COMMUNITY DETECTION BASED ON DYNAMICS PROCESS AND STABILITY OPTIMIZATION

2012 ◽  
Vol 26 (31) ◽  
pp. 1250189 ◽  
Author(s):  
YUE ZHAO ◽  
JIE-LIANG MA ◽  
HUI-JIA LI
Keyword(s):  
Em Algorithm ◽  
Objective Function ◽  
Potts Model ◽  
Weighting Function ◽  
Real Data ◽  
Well Performance ◽  
Resolution Limit ◽  
Optimal Value ◽  
Important Means ◽  
Novel Method

Utilizing dynamics system to identify community structure has become an important means of research. In this paper, inspired by the relationship between topology structures of networks and the dynamic Potts model, we present a novel method that describes the conditional inequality forming simple community can be transformed into the objective function F which is analogous to the Hamilton function of Potts model. Likewise, to detect the well performance of partitioning we develop improved-EM algorithm to search the optimal value of the objective function F by successively updating the dynamic process of the membership vector of nodes which is also commonly influenced by the weighting function W and the tightness expression T. Via adjusting relevant parameters properly, our method can effectively detect the community structures. Furthermore, stability as the new measure quality method is applied for refining the partitions the improved-EM algorithm detects and mitigating resolution limit brought by modularity. Simulation experiments on benchmark and real-data network all give excellent results.

scholarly journals Implementation of a Modified Faster R-CNN for Target Detection Technology of Coastal Defense Radar

2021 ◽  
Vol 13 (9) ◽  
pp. 1703
Author(s):  
He Yan ◽  
Chao Chen ◽  
Guodong Jin ◽  
Jindong Zhang ◽  
Xudong Wang ◽  
...  
Keyword(s):  
False Alarm ◽  
False Alarm Rate ◽  
Target Detection ◽  
Real Data ◽  
Detection Performance ◽  
Detection Accuracy ◽  
Constant False Alarm Rate ◽  
Data Set ◽  
Detection Technology ◽  
Coastal Defense

The traditional method of constant false-alarm rate detection is based on the assumption of an echo statistical model. The target recognition accuracy rate and the high false-alarm rate under the background of sea clutter and other interferences are very low. Therefore, computer vision technology is widely discussed to improve the detection performance. However, the majority of studies have focused on the synthetic aperture radar because of its high resolution. For the defense radar, the detection performance is not satisfactory because of its low resolution. To this end, we herein propose a novel target detection method for the coastal defense radar based on faster region-based convolutional neural network (Faster R-CNN). The main processing steps are as follows: (1) the Faster R-CNN is selected as the sea-surface target detector because of its high target detection accuracy; (2) a modified Faster R-CNN based on the characteristics of sparsity and small target size in the data set is employed; and (3) soft non-maximum suppression is exploited to eliminate the possible overlapped detection boxes. Furthermore, detailed comparative experiments based on a real data set of coastal defense radar are performed. The mean average precision of the proposed method is improved by 10.86% compared with that of the original Faster R-CNN.

PREDICTION OF THE TRANSPORT PROPERTIES OF SF6 WITH O2, CO2, CF4, N2 AND CH4 MIXTURES AT LOW DENSITY BY THE INVERSION METHOD (PART II)

2004 ◽  
Vol 03 (01) ◽  
pp. 69-90 ◽  
Author(s):  
BEHZAD HAGHIGHI ◽  
ALIREZA HASSANI DJAVANMARDI ◽  
MOHAMAD MEHDI PAPARI ◽  
MOHSEN NAJAFI
Keyword(s):  
Potential Energy ◽  
Diffusion Coefficients ◽  
Potential Energy Function ◽  
Model Potential ◽  
Inversion Method ◽  
Low Density ◽  
Initial Model ◽  
Lennard Jones ◽  
Inversion Procedure ◽  
And Diffusion

Viscosity and diffusion coefficients for five equimolar binary gas mixtures of SF 6 with O 2, CO 2, CF 4, N 2 and CH 4 gases are determined from the extended principle of corresponding states of viscosity by the inversion technique. The Lennard–Jones 12-6 (LJ 12-6) potential energy function is used as the initial model potential required by the technique. The obtained interaction potential energies from the inversion procedure reproduce viscosity within 1% and diffusion coefficients within 5%.

Highly efficient density inversion of gravity data using nonlinear density polynomial fitting

Geophysics ◽  
2021 ◽  
pp. 1-34
Author(s):  
Guoqing Ma ◽  
Zongrui Li ◽  
Lili Li ◽  
Taihan Wang
Keyword(s):  
Weighting Function ◽  
Gravity Data ◽  
Real Life ◽  
Density Variation ◽  
Density Change ◽  
Inversion Method ◽  
Density Inversion ◽  
Perspective View ◽  
Polynomial Fitting ◽  
Polynomial Coefficients

The density inversion of gravity data is commonly achieved by discretizing the subsurface into prismatic cells and calculating the density of each cell. During this process, a weighting function is introduced to the iterative computation to reduce the skin effect during the inversion. Thus, the computation process requires a significant number of matrix operations, which results in low computational efficiency. We have adopted a density inversion method with nonlinear polynomial fitting (NPF) that uses a polynomial to represent the density variation of prismatic cells in a certain space. The computation of each cell is substituted by the computation of the nonlinear polynomial coefficients. Consequently, the efficiency of the inversion is significantly improved because the number of nonlinear polynomial coefficients is less than the number of cells used. Moreover, because representing the density change of all of the cells poses a significant challenge when the cell number is large, we adopt the use of a polynomial to represent the density change of a subregion with fewer cells and multiple nonlinear polynomials to represent the density changes of all prism cells. Using theoretical model tests, we determine that the NPF method more efficiently recovers the density distribution of gravity data compared with conventional density inversion methods. In addition, the density variation of a subregion with 8 × 8 × 8 prismatic cells can be accurately and efficiently obtained using our cubic NPF method, which can also be used for noisy data. Finally, the NPF method was applied to real gravity data in an iron mining area in Shandong Province, China. Convergent results of a 3D perspective view and the distribution of the iron ore bodies were acquired using this method, demonstrating the real-life applicability of this method.

Velocity inversion by global optimization using finite-offset common-reflection-surface stacking applied to synthetic and Tacutu Basin seismic data

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R165-R174 ◽  
Author(s):  
Marcelo Jorge Luz Mesquita ◽  
João Carlos Ribeiro Cruz ◽  
German Garabito Callapino
Keyword(s):  
Objective Function ◽  
Real Data ◽  
Velocity Model ◽  
Data Sets ◽  
Layer By Layer ◽  
Velocity Inversion ◽  
Very Fast Simulated Annealing ◽  
Target Layer ◽  
Common Reflection Surface ◽  
The Mean

Estimation of an accurate velocity macromodel is an important step in seismic imaging. We have developed an approach based on coherence measurements and finite-offset (FO) beam stacking. The algorithm is an FO common-reflection-surface tomography, which aims to determine the best layered depth-velocity model by finding the model that maximizes a semblance objective function calculated from the amplitudes in common-midpoint (CMP) gathers stacked over a predetermined aperture. We develop the subsurface velocity model with a stack of layers separated by smooth interfaces. The algorithm is applied layer by layer from the top downward in four steps per layer. First, by automatic or manual picking, we estimate the reflection times of events that describe the interfaces in a time-migrated section. Second, we convert these times to depth using the velocity model via application of Dix’s formula and the image rays to the events. Third, by using ray tracing, we calculate kinematic parameters along the central ray and build a paraxial FO traveltime approximation for the FO common-reflection-surface method. Finally, starting from CMP gathers, we calculate the semblance of the selected events using this paraxial traveltime approximation. After repeating this algorithm for all selected CMP gathers, we use the mean semblance values as an objective function for the target layer. When this coherence measure is maximized, the model is accepted and the process is completed. Otherwise, the process restarts from step two with the updated velocity model. Because the inverse problem we are solving is nonlinear, we use very fast simulated annealing to search the velocity parameters in the target layers. We test the method on synthetic and real data sets to study its use and advantages.

scholarly journals Nonnegative Signal Decomposition with Supervision

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Teng Li ◽  
Huan Chang ◽  
Jun Wu
Keyword(s):  
Objective Function ◽  
Image Classification ◽  
Pattern Classification ◽  
Optimization Problem ◽  
Real Data ◽  
Classification Performance ◽  
Signal Decomposition ◽  
Weak Supervision ◽  
Training Samples ◽  
Novel Algorithm

This paper presents a novel algorithm to numerically decompose mixed signals in a collaborative way, given supervision of the labels that each signal contains. The decomposition is formulated as an optimization problem incorporating nonnegative constraint. A nonnegative data factorization solution is presented to yield the decomposed results. It is shown that the optimization is efficient and decreases the objective function monotonically. Such a decomposition algorithm can be applied on multilabel training samples for pattern classification. The real-data experimental results show that the proposed algorithm can significantly facilitate the multilabel image classification performance with weak supervision.

Back Analysis of Material Parameters of Concrete Dam Using Genetic Algorithm

2012 ◽  
Vol 562-564 ◽  
pp. 1955-1958
Author(s):  
Jin Bao Liu ◽  
Shou Ju Li ◽  
Wei Zhu
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Optimization Problem ◽  
Back Analysis ◽  
Water Level Change ◽  
Concrete Dam ◽  
Material Parameters ◽  
Level Change ◽  
Inversion Procedure ◽  
The Difference

The inverse problem of parameter identification is deal with by minimizing an objective function that contains the difference between observed and calculated dam displacements. The optimization problem of minimizing objective function is solved with genetic algorithm. The calculated dam displacements are simulated by using finite element method according to water level change acting on dam upstream. The practical dam displacements are observed on the dam crest. The investigation shows that the forecasted dam displacements agree well with observed ones. The effectiveness of proposed inversion procedure is validated.

Frequency‐domain acoustic‐wave modeling and inversion of crosshole data: Part II—Inversion method, synthetic experiments and real‐data results

Geophysics ◽  
1995 ◽  
Vol 60 (3) ◽  
pp. 796-809 ◽  
Author(s):  
Zhong‐Min Song ◽  
Paul R. Williamson ◽  
R. Gerhard Pratt
Keyword(s):  
Frequency Domain ◽  
Real Data ◽  
Forward Modeling ◽  
Two Dimensions ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Data Set ◽  
Wave Inversion ◽  
Full Wave ◽  
And Inversion

In full‐wave inversion of seismic data in complex media it is desirable to use finite differences or finite elements for the forward modeling, but such methods are still prohibitively expensive when implemented in 3-D. Full‐wave 2-D inversion schemes are of limited utility even in 2-D media because they do not model 3-D dynamics correctly. Many seismic experiments effectively assume that the geology varies in two dimensions only but generate 3-D (point source) wavefields; that is, they are “two‐and‐one‐half‐dimensional” (2.5-D), and this configuration can be exploited to model 3-D propagation efficiently in such media. We propose a frequency domain full‐wave inversion algorithm which uses a 2.5-D finite difference forward modeling method. The calculated seismogram can be compared directly with real data, which allows the inversion to be iterated. We use a descents‐related method to minimize a least‐squares measure of the wavefield mismatch at the receivers. The acute nonlinearity caused by phase‐wrapping, which corresponds to time‐domain cycle‐skipping, is avoided by the strategy of either starting the inversion using a low frequency component of the data or constructing a starting model using traveltime tomography. The inversion proceeds by stages at successively higher frequencies across the observed bandwidth. The frequency domain is particularly efficient for crosshole configurations and also allows easy incorporation of attenuation, via complex velocities, in both forward modeling and inversion. This also requires the introduction of complex source amplitudes into the inversion as additional unknowns. Synthetic studies show that the iterative scheme enables us to achieve the theoretical maximum resolution for the velocity reconstruction and that strongly attenuative zones can be recovered with reasonable accuracy. Preliminary results from the application of the method to a real data set are also encouraging.

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