Interval inversion approach for an improved interpretation of well logs

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.

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Uncertainty reduction of interval inversion estimation results using a factor analysis approach

GEM - International Journal on Geomathematics ◽

10.1007/s13137-020-0144-4 ◽

2020 ◽

Vol 11 (1) ◽

Author(s):

Armand Abordán ◽

Norbert Péter Szabó

Keyword(s):

Inverse Problem ◽

Factor Analysis ◽

Water Saturation ◽

Inversion Method ◽

Model Parameters ◽

Depth Range ◽

Petrophysical Parameters ◽

Shale Volume ◽

Interval Inversion ◽

The Impact

AbstractThis paper aims to investigate the impact of the overdetermination (data-to-unknowns) ratio on the global inversion of wireline logging data. In the course of the so-called interval inversion method, geophysical data measured in a borehole over a longer depth range is jointly inverted and the depth variation of the investigated petrophysical parameters are expanded into series using Legendre polynomials as basis functions resulting in a highly overdetermined inverse problem. A metaheuristic Particle Swarm Optimization (PSO) approach is applied as a first phase of inversion for decreasing the starting model dependence of the interval inversion procedure. In the subsequent linear inversion steps, by using the measurement error of logging tools and the covariance matrix of the estimated petrophysical parameters, we can quantify the accuracy of the model parameters. The dataset used in this study consists of nuclear, resistivity and sonic logs which are inverted to compute porosity, shale volume and water saturation along the investigated interval. For increasing the data-to-unknowns ratio of the inverse problem, shale volume is estimated separately by a PSO-based factor analysis and fixed as known parameter for the interval inversion process. Since the shale volume has been described as high degree Legendre polynomial, a significant increase of the overdetermination ratio considerably decreases the uncertainty of the remaining model parameters allowing for a more reliable calculation of hydrocarbon content.

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Joint seismic and petrophysical nonlinear inversion with Gaussian mixture-based adaptive regularization

Geophysics ◽

10.1190/geo2021-0017.1 ◽

2021 ◽

pp. 1-57

Author(s):

Qiang Guo ◽

Jing Ba ◽

Li-Yun Fu ◽

Cong Luo

Keyword(s):

Inverse Problem ◽

Seismic Data ◽

Simulated Annealing Algorithm ◽

Gaussian Mixture ◽

Forward Model ◽

Inversion Method ◽

Model Parameters ◽

Adaptive Regularization ◽

Petrophysical Parameters ◽

Highly Nonlinear

The estimation of reservoir parameters from seismic observations is one of the main objectives in reservoir characterization. However, the forward model relating petrophysical properties of rocks to observed seismic data is highly nonlinear, and solving the relevant inverse problem is a challenging task. We present a novel inversion method for jointly estimating elastic and petrophysical parameters of rocks from prestack seismic data. We combine a full rock-physics model and the exact Zoeppritz equation as the forward model. To overcome the ill-conditioning of the inverse problem and address the complex prior distribution of model parameters given lithofacies variations, we introduce a regularization term based on the prior Gaussian mixture model under Bayesian framework. The objective function is optimized by the fast simulated annealing algorithm, during which the Gaussian mixture-based regularization terms are adaptively and iteratively adjusted by the maximum likelihood estimator, allowing the posterior distribution to be more consistent with the observed seismic data. The adaptive regularization method improves the accuracy of petrophysical parameters compared to the sequential inversion and non-adaptive regularization methods, and the inversion result can be used for indicating gas-saturated areas when applied to field data.

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Velocity model estimation with data‐derived wavefront attributes

Geophysics ◽

10.1190/1.1649394 ◽

2004 ◽

Vol 69 (1) ◽

pp. 265-274 ◽

Cited By ~ 113

Author(s):

Eric Duveneck

Keyword(s):

Velocity Model ◽

Inversion Method ◽

Data Set ◽

Velocity Models ◽

Common Reflection Surface ◽

Data Points ◽

Inversion Procedure ◽

Optimum Model ◽

Zero Offset ◽

Kinematic Information

Kinematic information for constructing velocity models can be extracted in a robust way from seismic prestack data with the common‐reflection‐surface (CRS) stack. This data‐driven process results, in addition to a simulated zero‐offset section, in a number of wavefront attributes—wavefront curvatures and normal ray emergence angles—associated with each simulated zero‐offset sample. A tomographic inversion method is presented that uses this kinematic information to determine smooth, laterally heterogeneous, isotropic subsurface velocity models for depth imaging. The input for the inversion consists of wavefront attributes picked at a number of locations in the simulated zero‐offset section. The smooth velocity model is described by B‐splines. An optimum model is found iteratively by minimizing the misfit between the picked data and the corresponding modeled values. The required forward‐modeled quantities are obtained during each iteration by dynamic ray tracing along normal rays pertaining to the input data points. Fréchet derivatives for the tomographic matrix are calculated by ray perturbation theory. The inversion procedure is demonstrated on a 2D synthetic prestack data set.

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Evaluation of induced polarization measurements using a new inversion method

Acta Geodaetica et Geophysica ◽

10.1007/s40328-021-00355-3 ◽

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.

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Geothermal Resources Recognition and Characterization on the Basis of Well Logging and Petrophysical Laboratory Data, Polish Case Studies

Energies ◽

10.3390/en14040850 ◽

2021 ◽

Vol 14 (4) ◽

pp. 850

Author(s):

Jadwiga A. Jarzyna ◽

Stanisław Baudzis ◽

Mirosław Janowski ◽

Edyta Puskarczyk

Keyword(s):

Gamma Ray ◽

Laboratory Data ◽

Well Logging ◽

Well Logs ◽

Geothermal Resources ◽

Radiogenic Heat ◽

Petrophysical Parameters ◽

Heat Calculation

Examples from the Polish clastic and carbonate reservoirs from the Central Polish Anticlinorium, Carpathians and Carpathian Foredeep are presented to illustrate possibilities of using well logging to geothermal resources recognition and characterization. Firstly, there was presented a short description of selected well logs and methodology of determination of petrophysical parameters useful in geothermal investigations: porosity, permeability, fracturing, mineral composition, elasticity of orogeny and mineralization of formation water from well logs. Special attention was allotted to spectral gamma-ray and temperature logs to show their usefulness to radiogenic heat calculation and heat flux modelling. Electric imaging and advanced acoustic logs provided with continuous information on natural and induced fracturing of formation and improved lithology recognition. Wireline and production logging were discussed to present the wealth of methods that could be used. A separate matter was thermal conductivity provided from the laboratory experiments or calculated from the results of the comprehensive interpretation of well logs, i.e., volume or mass of minerals composing the rocks. It was proven that, in geothermal investigations and hydrocarbon prospection, the same petrophysical parameters are considered, and well-logging acquisition equipment and advanced methods of processing and interpretation, developed and improved for almost one hundred years, can be successfully used in the detection and characterization of the potential geothermal reservoirs. It was shown that the newest (current investment)—as well as the old type (archive)—logs provide useful information.

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Some practical aspects of prestack waveform inversion using a genetic algorithm: An example from the east Texas Woodbine gas sand

Geophysics ◽

10.1190/1.1444538 ◽

1999 ◽

Vol 64 (2) ◽

pp. 326-336 ◽

Cited By ~ 100

Author(s):

Subhashis Mallick

Keyword(s):

Genetic Algorithm ◽

Biological Evolution ◽

Synthetic Data ◽

Posteriori Probability ◽

Inversion Method ◽

Model Parameters ◽

East Texas ◽

Data Set ◽

A Posteriori Probability ◽

Prestack Inversion

In this paper, a prestack inversion method using a genetic algorithm (GA) is presented, and issues relating to the implementation of prestack GA inversion in practice are discussed. GA is a Monte‐Carlo type inversion, using a natural analogy to the biological evolution process. When GA is cast into a Bayesian framework, a priori information of the model parameters and the physics of the forward problem are used to compute synthetic data. These synthetic data can then be matched with observations to obtain approximate estimates of the marginal a posteriori probability density (PPD) functions in the model space. Plots of these PPD functions allow an interpreter to choose models which best describe the specific geologic setting and lead to an accurate prediction of seismic lithology. Poststack inversion and prestack GA inversion were applied to a Woodbine gas sand data set from East Texas. A comparison of prestack inversion with poststack inversion demonstrates that prestack inversion shows detailed stratigraphic features of the subsurface which are not visible on the poststack inversion.

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Fast probabilistic petrophysical mapping of reservoirs from 3D seismic data

Geophysics ◽

10.1190/geo2011-0340.1 ◽

2012 ◽

Vol 77 (3) ◽

pp. O1-O19 ◽

Cited By ~ 21

Author(s):

Mohammad S. Shahraeeni ◽

Andrew Curtis ◽

Gabriel Chao

Keyword(s):

Seismic Data ◽

Water Saturation ◽

Random Noise ◽

Clay Content ◽

Inversion Method ◽

Model Parameters ◽

Nonlinear Inversion ◽

Desktop Computer ◽

Data Set ◽

Mixture Density

A fast probabilistic inversion method for 3D petrophysical property prediction from inverted prestack seismic data has been developed and tested on a real data set. The inversion objective is to estimate the joint probability density function (PDF) of model vectors consisting of porosity, clay content, and water saturation components at each point in the reservoir, from data vectors with compressional- and shear-wave-impedance components that are obtained from the inversion of seismic data. The proposed inversion method is based on mixture density network (MDN), which is trained by a given set of training samples, and provides an estimate of the joint posterior PDF’s of the model parameters for any given data point. This method is much more time and memory efficient than conventional nonlinear inversion methods. The training data set is constructed using nonlinear petrophysical forward relations and includes different sources of uncertainty in the inverse problem such as variations in effective pressure, bulk modulus and density of hydrocarbon, and random noise in recorded data. Results showed that the standard deviations of all model parameters were reduced after inversion, which shows that the inversion process provides information about all parameters. The reduction of uncertainty in water saturation was smaller than that for porosity or clay content; nevertheless the maximum of the a posteriori (MAP) of model PDF clearly showed the boundary between brine saturated and oil saturated rocks at wellbores. The MAP estimates of different model parameters show the lateral and vertical continuity of these boundaries. Errors in the MAP estimate of different model parameters can be reduced using more accurate petrophysical forward relations. This fast, probabilistic, nonlinear inversion method can be applied to invert large seismic cubes for petrophysical parameters on a standard desktop computer.

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Joint inversion of Rayleigh-wave dispersion and P-wave refraction data for laterally varying layered models

Geophysics ◽

10.1190/geo2013-0212.1 ◽

2014 ◽

Vol 79 (4) ◽

pp. EN49-EN59 ◽

Cited By ~ 14

Author(s):

Daniele Boiero ◽

Laura Valentina Socco

Keyword(s):

Rayleigh Wave ◽

Joint Inversion ◽

A Priori ◽

P Wave ◽

Inversion Method ◽

Model Parameters ◽

Data Set ◽

Wave Refraction ◽

Velocity Models ◽

Refraction Data

We implemented a joint inversion method to build P- and S-wave velocity models from Rayleigh-wave and P-wave refraction data, specifically designed to deal with laterally varying layered environments. A priori information available over the site and any physical law to link model parameters can be also incorporated. We tested and applied the algorithm behind the method. The results from a field data set revealed advantages with respect to individual surface-wave analysis (SWA) and body wave tomography (BWT). The algorithm imposed internal consistency for all the model parameters relaxing the required a priori assumptions (i.e., Poisson’s ratio level of confidence in SWA) and the inherent limitations of the two methods (i.e., velocity decreases for BWT).

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Seismic data interpolation by greedy local Radon transform

Geophysics ◽

10.1190/1.3484195 ◽

2010 ◽

Vol 75 (6) ◽

pp. WB225-WB234 ◽

Cited By ~ 58

Author(s):

Juefu Wang ◽

Mark Ng ◽

Mike Perz

Keyword(s):

Radon Transform ◽

Interpolation Method ◽

Synthetic Data ◽

Inversion Method ◽

Model Parameters ◽

Weighted Norm ◽

Data Interpolation ◽

Data Set ◽

Time Space ◽

Model Spaces

We propose a greedy inversion method for a spatially localized, high-resolution Radon transform. The kernel of the method is based on a conventional iterative algorithm, conjugate gradient (CG), but is utilized adaptively in amplitude-prioritized local model spaces. The adaptive inversion introduces a coherence-oriented mechanism to enhance focusing of significant model parameters, and hence increases the model resolution and convergence rate. We adopt the idea in a time-space domain local linear Radon transform for data interpolation. We find that the local Radon transform involves iteratively applying spatially localized forward and adjoint Radon operators to fit the input data. Optimal local Radon panels can be found via a subspace algorithm which promotes sparsity in the model, and the missing data can be predicted using the resulting local Radon panels. The subspacing strategy greatly reduces the cost of computing local Radon coefficients, thereby reducing the total cost for inversion. The method can handle irregular and regular geometries and significant spatial aliasing. We compare the performance of our method using three simple synthetic data sets with a popular interpolation method known as minimum weighted norm Fourier interpolation, and show the advantage of the new algorithm in interpolating spatially aliased data. We also test the algorithm on the 2D synthetic data and a field data set. Both tests show that the algorithm is a robust antialiasing tool, although it cannot completely recover missing strongly curved events.

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Exploiting surface consistency for surface-wave characterization and mitigation — Part 2: Application to 3D data

Geophysics ◽

10.1190/geo2016-0020.1 ◽

2017 ◽

Vol 82 (1) ◽

pp. V39-V50 ◽

Cited By ~ 5

Author(s):

Christine E. Krohn ◽

Partha S. Routh

Keyword(s):

Surface Wave ◽

Low Frequency ◽

Single Mode ◽

Complex Surface ◽

Surface Elevation ◽

Inversion Method ◽

Model Parameters ◽

Nonlinear Inversion ◽

Data Set ◽

Near Surface

We present a case history demonstrating the 3D implementation of the surface-wave impulse estimation and removal (SWIPER) method. SWIPER is a tomographic inversion method that is able to predict and remove complex surface waves, which are multimodal and heterogeneous. The inversion generates surface-consistent model parameters, which correlate with near-surface elevation. These parameters include a surface map of the propagation velocity and attenuation values for each surface-wave mode as a function of frequency. The method also determines variations in source coupling as a function of frequency, which also correlate with the near-surface elevation changes. We show that the method works equally well with a fully sampled and decimated 3D dynamite-sourced data set. We start with a linear single-mode inversion and use the results to generate the starting model for a subsequent three-mode nonlinear inversion. The resulting velocity-dispersion grid has greater lateral resolution and extends to higher frequencies than that generated by a conventional array beam forming method. The propagation and source coupling parameters can be used together to predict the surface-wave waveforms, which are then adaptively subtracted from the data on a trace-to-trace basis. We demonstrate with decimated data that low-frequency reflections can be preserved, even when the data are highly aliased and would be removed by traditional multichannel filters.

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