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.

scholarly journals Determination of synchronous generator nonlinear model parameters based on power rejection tests using a gradient optimization algorithm

2017 ◽  
Vol 65 (4) ◽  
pp. 479-488 ◽  
Author(s):  
A. Boboń ◽  
A. Nocoń ◽  
S. Paszek ◽  
P. Pruski
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Least Squares Method ◽  
Synchronous Generator ◽  
Operating Conditions ◽  
Model Parameters ◽  
State Variables ◽  
Starting Point ◽  
Gradient Optimization

AbstractThe paper presents a method for determining electromagnetic parameters of different synchronous generator models based on dynamic waveforms measured at power rejection. Such a test can be performed safely under normal operating conditions of a generator working in a power plant. A generator model was investigated, expressed by reactances and time constants of steady, transient, and subtransient state in the d and q axes, as well as the circuit models (type (3,3) and (2,2)) expressed by resistances and inductances of stator, excitation, and equivalent rotor damping circuits windings. All these models approximately take into account the influence of magnetic core saturation. The least squares method was used for parameter estimation. There was minimized the objective function defined as the mean square error between the measured waveforms and the waveforms calculated based on the mathematical models. A method of determining the initial values of those state variables which also depend on the searched parameters is presented. To minimize the objective function, a gradient optimization algorithm finding local minima for a selected starting point was used. To get closer to the global minimum, calculations were repeated many times, taking into account the inequality constraints for the searched parameters. The paper presents the parameter estimation results and a comparison of the waveforms measured and calculated based on the final parameters for 200 MW and 50 MW turbogenerators.

Resolution of well-known resistivity equivalences by inclusion of time-domain induced polarization data

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. E47-E54 ◽  
Author(s):  
Line Meldgaard Madsen ◽  
Gianluca Fiandaca ◽  
Anders Vest Christiansen ◽  
Esben Auken
Keyword(s):  
Time Domain ◽  
Equivalence Problem ◽  
Induced Polarization ◽  
Monte Carlo Algorithm ◽  
High Resistivity ◽  
Inversion Method ◽  
Model Parameters ◽  
Clay Layer ◽  
Equivalent Models ◽  
Equivalence Problems

The principle of equivalence is known to cause nonuniqueness in interpretations of direct current (DC) resistivity data. Low- or high-resistivity equivalences arise when a thin geologic layer with a low/high resistivity is embedded in a relative high-/low-resistivity background formation causing strong resistivity-thickness correlations. The equivalences often make it impossible to resolve embedded layers. We found that the equivalence problem could be significantly reduced by combining the DC data with full-decay time-domain induced polarization (IP) measurements. We applied a 1D Markov chain Monte Carlo algorithm to invert synthetic DC data of models with low- and high-resistivity equivalences. By applying this inversion method, it is possible to study the space of equivalent models that have an acceptable fit to the observed data, and to make a full sensitivity analysis of the model parameters. Then, we include a contrast in chargeability into the model, modeled in terms of spectral Cole-Cole IP parameters, and invert the DC and IP data in combination. The results show that the addition of IP data largely resolves the DC equivalences. Furthermore, we present a field example in which DC and IP data were measured on a sand formation with an embedded clay layer known from a borehole drilling. Inversion results show that the DC data alone do not resolve the clay layer due to equivalence problems, but by adding the IP data to the inversion, the layer is resolved.

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 3D Gravity Inversion on Unstructured Grids

2021 ◽  
Vol 11 (2) ◽  
pp. 722
Author(s):  
Siyuan Sun ◽  
Changchun Yin ◽  
Xiuhe Gao
Keyword(s):  
Objective Function ◽  
Unstructured Grids ◽  
Gravity Data ◽  
Depth Resolution ◽  
Continuous Model ◽  
Gravity Inversion ◽  
Inversion Method ◽  
Model Parameters ◽  
Fuzzy C Means ◽  
Fuzzy C Means Clustering

Compared with structured grids, unstructured grids are more flexible to model arbitrarily shaped structures. However, based on unstructured grids, gravity inversion results would be discontinuous and hollow because of cell volume and depth variations. To solve this problem, we first analyzed the gradient of objective function in gradient-based inversion methods, and a new gradient scheme of objective function is developed, which is a derivative with respect to weighted model parameters. The new gradient scheme can more effectively solve the problem with lacking depth resolution than the traditional inversions, and the improvement is not affected by the regularization parameters. Besides, an improved fuzzy c-means clustering combined with spatial constraints is developed to measure property distribution of inverted models in both spatial domain and parameter domain simultaneously. The new inversion method can yield a more internal continuous model, as it encourages cells and their adjacent cells to tend to the same property value. At last, the smooth constraint inversion, the focusing inversion, and the improved fuzzy c-means clustering inversion on unstructured grids are tested on synthetic and measured gravity data to compare and demonstrate the algorithms proposed in this paper.

The 4-D microgravity method for waterflood surveillance: A model study for the Prudhoe Bay reservoir, Alaska

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 78-87 ◽  
Author(s):  
Jennifer L. Hare ◽  
John F. Ferguson ◽  
Carlos L. V. Aiken ◽  
Jerry L. Brady
Keyword(s):  
Total Mass ◽  
Least Squares Method ◽  
Gravity Data ◽  
Water Injection ◽  
Gravity Modeling ◽  
Inversion Method ◽  
Model Parameters ◽  
Worst Case ◽  
Inverse Models ◽  
Prudhoe Bay

Forward and inverse gravity modeling is carried out on a suite of reservoir simulations of a proposed water injection in the Prudhoe Bay reservoir, Alaska. A novel surveillance technique is developed in which surface gravity observations are used to monitor the progress of a gas cap waterflood in the reservoir at 8200-ft (2500-m) depth. This cost‐effective method requires that high‐precision gravity surveys be repeated over periods of years. Differences in the gravity field with time reflect changes in the reservoir fluid densities. Preliminary field tests at Prudhoe Bay indicates survey accuracy of 5–10 μGal can be achieved for gravity data using a modified Lacoste & Romberg “G” type meter or Scintrex CG-3M combined with the NAVSTAR Global Positioning System (GPS). Forward gravity modeling predicts variations in surface measurements of 100 μGal after 5 years of water injection, and 180–250 μGal after 15 years. We use a constrained least‐squares method to invert synthetic gravity data for subsurface density distributions. The modeling procedure has been formulated and coded to allow testing of the models for sensitivity to gravity sampling patterns, noise types, and various constraints on model parameters such as density, total mass, and moment of inertia. Horizontal‐feature resolution of the waterflood is about 5000 ft (1520 m) for constrained inverse models from synthetic gravity with 5 μGal standard deviation (SD) noise. The inversion method can account for total mass of injected water to within a few percent. Worst‐case scenarios result from inversion of gravity data which are contaminated by high levels (greater than 10–15 μGal SD) of spatially correlated noise, in which case the total mass estimate from inverse models may over or underestimate the mass by 10–20%. The results of the modeling indicate that inversion of time‐lapse gravity data is a viable technique for the monitoring of reservoir gas cap waterfloods.

scholarly journals Interval inversion approach for an improved interpretation of well logs

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. D155-D167 ◽  
Author(s):  
Mihály Dobróka ◽  
Norbert Péter Szabó ◽  
József Tóth ◽  
Péter Vass
Keyword(s):  
Inverse Problem ◽  
Well Logging ◽  
Well Logs ◽  
Depth Interval ◽  
Inversion Method ◽  
Model Parameters ◽  
Data Set ◽  
Petrophysical Parameters ◽  
Inversion Procedure ◽  
Interval Inversion

The quality analysis of well-logging inversion results has always been an important part of formation evaluation. The precise calculation of hydrocarbon reserves requires the most accurate possible estimation of porosity, water saturation, and shale and rock-matrix volumes. The local inversion method conventionally used to predict the above model parameters depth by depth represents a marginally overdetermined inverse problem, which is rather sensitive to the uncertainty of observed data and limited in estimation accuracy. To reduce the harmful effect of data noise on the estimated model, we have suggested the interval inversion method, in which an increase of the overdetermination ratio allows a more accurate solution of the well-logging inverse problem. The interval inversion method inverts the data set of a longer depth interval to predict the vertical distributions of petrophysical parameters in a joint inversion procedure. In formulating the forward problem, we have extended the validity of probe response functions to a greater depth interval assuming the petrophysical parameters are depth dependent, and then we expanded the model parameters into a series using the Legendre polynomials as basis functions for modeling inhomogeneous formations. We solved the inverse problem for a much smaller number of expansion coefficients than data to derive the petrophysical parameters in a stable overdetermined inversion procedure. The added advantage of the interval inversion method is that the layer thicknesses and suitably chosen zone parameters can be estimated automatically by the inversion procedure to refine the results of inverse and forward modeling. We have defined depth-dependent model covariance and correlation matrices to compare the quality of the local and interval inversion results. A detailed study using well logs measured from a Hungarian gas-bearing unconsolidated formation revealed that the greatly overdetermined interval inversion procedure can be effectively used in reducing the estimation errors in shaly sand formations, which may refine significantly the results of reserve calculation.

Constructing and model-fitting receiver operator characteristics using continuous data.

2018 ◽  
Author(s):  
Josephine Ann Urquhart ◽  
Akira O'Connor
Keyword(s):  
Signal Detection ◽  
Least Squares Method ◽  
Model Fitting ◽  
Simulated Data ◽  
Continuous Variable ◽  
Continuous Data ◽  
Model Parameters ◽  
Operating Characteristics ◽  
Unequal Variance ◽  
Discrete Discrimination

Receiver operating characteristics (ROCs) are plots which provide a visual summary of a classifier’s decision response accuracy at varying discrimination thresholds. Typical practice, particularly within psychological studies, involves plotting an ROC from a limited number of discrete thresholds before fitting signal detection parameters to the plot. We propose that additional insight into decision-making could be gained through increasing ROC resolution, using trial-by-trial measurements derived from a continuous variable, in place of discrete discrimination thresholds. Such continuous ROCs are not yet routinely used in behavioural research, which we attribute to issues of practicality (i.e. the difficulty of applying standard ROC model-fitting methodologies to continuous data). Consequently, the purpose of the current article is to provide a documented method of fitting signal detection parameters to continuous ROCs. This method reliably produces model fits equivalent to the unequal variance least squares method of model-fitting (Yonelinas et al., 1998), irrespective of the number of data points used in ROC construction. We present the suggested method in three main stages: I) building continuous ROCs, II) model-fitting to continuous ROCs and III) extracting model parameters from continuous ROCs. Throughout the article, procedures are demonstrated in Microsoft Excel, using an example continuous variable: reaction time, taken from a single-item recognition memory. Supplementary MATLAB code used for automating our procedures is also presented in Appendix B, with a validation of the procedure using simulated data shown in Appendix C.

EXPRESS: Baseline Correction Based on a Search Algorithm from Artificial Intelligence

2020 ◽  
pp. 000370282097751
Author(s):  
Xin Wang ◽  
Xia Chen
Keyword(s):  
Artificial Intelligence ◽  
Objective Function ◽  
Least Squares ◽  
Least Squares Method ◽  
Search Algorithm ◽  
Absolute Error ◽  
Search Problem ◽  
Baseline Correction ◽  
Current Spectrum ◽  
Data Points

Many spectra have a polynomial-like baseline. Iterative polynomial fitting (IPF) is one of the most popular methods for baseline correction of these spectra. However, the baseline estimated by IPF may have substantially error when the spectrum contains significantly strong peaks or have strong peaks located at the endpoints. First, IPF uses temporary baseline estimated from the current spectrum to identify peak data points. If the current spectrum contains strong peaks, then the temporary baseline substantially deviates from the true baseline. Some good baseline data points of the spectrum might be mistakenly identified as peak data points and are artificially re-assigned with a low value. Second, if a strong peak is located at the endpoint of the spectrum, then the endpoint region of the estimated baseline might have significant error due to overfitting. This study proposes a search algorithm-based baseline correction method (SA) that aims to compress sample the raw spectrum to a dataset with small number of data points and then convert the peak removal process into solving a search problem in artificial intelligence (AI) to minimize an objective function by deleting peak data points. First, the raw spectrum is smoothened out by the moving average method to reduce noise and then divided into dozens of unequally spaced sections on the basis of Chebyshev nodes. Finally, the minimal points of each section are collected to form a dataset for peak removal through search algorithm. SA selects the mean absolute error (MAE) as the objective function because of its sensitivity to overfitting and rapid calculation. The baseline correction performance of SA is compared with those of three baseline correction methods: Lieber and Mahadevan–Jansen method, adaptive iteratively reweighted penalized least squares method, and improved asymmetric least squares method. Simulated and real FTIR and Raman spectra with polynomial-like baselines are employed in the experiments. Results show that for these spectra, the baseline estimated by SA has fewer error than those by the three other methods.

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%.

Inversion of induced polarization data

Geophysics ◽  
1994 ◽  
Vol 59 (9) ◽  
pp. 1327-1341 ◽  
Author(s):  
Douglas W. Oldenburg ◽  
Yaoguo Li
Keyword(s):  
Inverse Problem ◽  
Objective Function ◽  
Effective Conductivity ◽  
Optimization Theory ◽  
Induced Polarization ◽  
Dc Resistivity ◽  
Earth Structure ◽  
Nonlinear Inverse Problem ◽  
Polarization Data ◽  
The Earth

We develop three methods to invert induced polarization (IP) data. The foundation for our algorithms is an assumption that the ultimate effect of chargeability is to alter the effective conductivity when current is applied. This assumption, which was first put forth by Siegel and has been routinely adopted in the literature, permits the IP responses to be numerically modeled by carrying out two forward modelings using a DC resistivity algorithm. The intimate connection between DC and IP data means that inversion of IP data is a two‐step process. First, the DC potentials are inverted to recover a background conductivity. The distribution of chargeability can then be found by using any one of the three following techniques: (1) linearizing the IP data equation and solving a linear inverse problem, (2) manipulating the conductivities obtained after performing two DC resistivity inversions, and (3) solving a nonlinear inverse problem. Our procedure for performing the inversion is to divide the earth into rectangular prisms and to assume that the conductivity σ and chargeability η are constant in each cell. To emulate complicated earth structure we allow many cells, usually far more than there are data. The inverse problem, which has many solutions, is then solved as a problem in optimization theory. A model objective function is designed, and a “model” (either the distribution of σ or η)is sought that minimizes the objective function subject to adequately fitting the data. Generalized subspace methodologies are used to solve both inverse problems, and positivity constraints are included. The IP inversion procedures we design are generic and can be applied to 1-D, 2-D, or 3-D earth models and with any configuration of current and potential electrodes. We illustrate our methods by inverting synthetic DC/IP data taken over a 2-D earth structure and by inverting dipole‐dipole data taken in Quebec.

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