scholarly journals Seismic AVO statistical inversion incorporating poroelasticity

2020 ◽  
Vol 17 (5) ◽  
pp. 1237-1258
Author(s):  
Kun Li ◽  
Xing-Yao Yin ◽  
Zhao-Yun Zong ◽  
Hai-Kun Lin
Keyword(s):  
Monte Carlo Algorithm ◽  
Inversion Method ◽  
Probability Density Distribution ◽  
Simultaneous Estimation ◽  
Model Parameters ◽  
Reflection Coefficients ◽  
Rock Matrix ◽  
Critical Porosity ◽  
Avo Inversion ◽  
Rock Porosity

Abstract Seismic amplitude variation with offset (AVO) inversion is an important approach for quantitative prediction of rock elasticity, lithology and fluid properties. With Biot–Gassmann’s poroelasticity, an improved statistical AVO inversion approach is proposed. To distinguish the influence of rock porosity and pore fluid modulus on AVO reflection coefficients, the AVO equation of reflection coefficients parameterized by porosity, rock-matrix moduli, density and fluid modulus is initially derived from Gassmann equation and critical porosity model. From the analysis of the influences of model parameters on the proposed AVO equation, rock porosity has the greatest influences, followed by rock-matrix moduli and density, and fluid modulus has the least influences among these model parameters. Furthermore, a statistical AVO stepwise inversion method is implemented to the simultaneous estimation of rock porosity, rock-matrix modulus, density and fluid modulus. Besides, the Laplace probability model and differential evolution, Markov chain Monte Carlo algorithm is utilized for the stochastic simulation within Bayesian framework. Models and field data examples demonstrate that the simultaneous optimizations of multiple Markov chains can achieve the efficient simulation of the posterior probability density distribution of model parameters, which is helpful for the uncertainty analysis of the inversion and sets a theoretical fundament for reservoir characterization and fluid discrimination.

scholarly journals Data-driven method for an improved linearised AVO inversion

2020 ◽  
Author(s):  
Liping Niu ◽  
Jianhua Geng ◽  
Xinming Wu ◽  
Luanxiao Zhao ◽  
Hong Zhang
Keyword(s):  
Contrast Media ◽  
Seismic Inversion ◽  
Poor Quality ◽  
Data Driven ◽  
Inversion Method ◽  
Model Parameters ◽  
Reflection Coefficients ◽  
S Wave ◽  
Avo Inversion ◽  
Strong Contrast

Abstract Linearised approximations of the Zoeppritz equation are widely used for amplitude versus offset (AVO) forward modelling and prestack seismic inversion. However, current linearised approximations typically exhibit large errors for strong-contrast media and large incidence angles (even for those less than the critical angle), leading to poor quality estimation of elastic parameters. We therefore develop a data-driven method to improve the linearised AVO approximation, based on the concept that the inaccuracy of the conventional linearised AVO forward operator is solely responsible for generating residuals of the PP reflection coefficients calculated by the conventional linearised approximation compared with using the Zoeppritz equation. Therefore, if true model parameters from well-logging data are known, the residuals of the PP reflection coefficients can be used to estimate linear modifications of the inaccurate linearised AVO forward operators at well sites. We apply estimated linear modifications to original inaccurately linearised forward operators to obtain an improved linear AVO operator (ILAO). Because ILAOs can only be estimated at the well sites by the data-driven method, we construct spatially variant ILAOs using structure-guided interpolation for those at a distance from the well sites. Numerical example results reveal that the improved linear AVO approximation is more accurate than the Aki–Richards approximation for strong-contrast media and large incident angles. Moreover, the accuracy and resolution of the inverted P- and S-wave velocities and density using ILAOs are higher than those using the conventional Aki–Richards operators. Finally, application to the field data successfully demonstrates the feasibility and effectiveness of the improved linearised AVO inversion method.

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.

Constrained nonlinear amplitude variation with offset inversion using Zoeppritz equations

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. R245-R255 ◽  
Author(s):  
Ali Gholami ◽  
Hossein S. Aghamiry ◽  
Mostafa Abbasi
Keyword(s):  
Nonlinear Equations ◽  
Wave Velocity ◽  
Seismic Data ◽  
P Wave ◽  
Simultaneous Estimation ◽  
Model Parameters ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Zoeppritz Equations ◽  
Avo Inversion

The inversion of prestack seismic data using amplitude variation with offset (AVO) has received increased attention in the past few decades because of its key role in estimating reservoir properties. AVO is mainly governed by the Zoeppritz equations, but traditional inversion techniques are based on various linear or quasilinear approximations to these nonlinear equations. We have developed an efficient algorithm for nonlinear AVO inversion of precritical reflections using the exact Zoeppritz equations in multichannel and multi-interface form for simultaneous estimation of the P-wave velocity, S-wave velocity, and density. The total variation constraint is used to overcome the ill-posedness while solving the forward nonlinear model and to preserve the sharpness of the interfaces in the parameter space. The optimization is based on a combination of Levenberg’s algorithm and the split Bregman iterative scheme, in which we have to refine the data and model parameters at each iteration. We refine the data via the original nonlinear equations, but we use the traditional cost-effective linearized AVO inversion to construct the Jacobian matrix and update the model. Numerical experiments show that this new iterative procedure is convergent and converges to a solution of the nonlinear problem. We determine the performance and optimality of our nonlinear inversion algorithm with various simulated and field seismic data sets.

Long-offset AVO inversion of PP reflections from plane interfaces using effective reflection coefficients

Geophysics ◽  
2011 ◽  
Vol 76 (6) ◽  
pp. C65-C79 ◽  
Author(s):  
Lyubov Skopintseva ◽  
Milana Ayzenberg ◽  
Martin Landrø ◽  
Tatyana Nefedkina ◽  
Arkady M. Aizenberg
Keyword(s):  
Reflection Coefficient ◽  
Plane Wave ◽  
Seismic Waves ◽  
Wave Reflection ◽  
Point Sources ◽  
Model Parameters ◽  
Reflection Coefficients ◽  
Avo Inversion ◽  
Long Offset ◽  
Head Waves

A conventional amplitude variation with offset (AVO) inversion is based on geometrical seismics which exploit plane-wave reflection coefficients to describe the reflection phenomenon. Widely exploited linearizations of plane-wave coefficients are mostly valid at pre-critical offsets for media with almost flat and weak-contrast interfaces. Existing linearizations do not account for the seismic frequency range by ignoring the frequency content of the wavelet, which is a strong assumption. Plane-wave reflection coefficients do not fully describe the reflection of seismic waves at near-critical and post-critical offsets, because reflected seismic waves are typically generated by point sources. We propose an improved approach to AVO inversion, which is based on effective reflection coefficients (ERCs). ERCs generalize plane-wave coefficients for seismic waves generated by point sources and therefore more accurately describe near-critical and post-critical reflections where head waves are generated. Moreover, they are frequency-dependent and incorporate the local curvatures of the wavefront and the reflecting interface. In our study, we neglect the effect of interface curvature and demonstrate the advantages of our approach on synthetic data for a simple model with a plane interface separating two isotropic half-spaces. A comparison of the inversion results obtained with our approach and the results from an AVO inversion method based on the exact plane-wave reflection coefficient suggests that our method is superior, in particular for long-offset ranges which extend to and beyond the critical angle. We thus propose that long offsets can be successfully exploited in an AVO inversion under the correct assumption about the reflection coefficient. Such long-offset AVO inversion shows the potential of outperforming a conventional moderate-offset AVO inversion in the accuracy of estimated model parameters.

Joint facies and reservoir properties inversion

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. M15-M24 ◽  
Author(s):  
Dario Grana
Keyword(s):  
Seismic Data ◽  
Joint Inversion ◽  
Convex Combination ◽  
Real Data ◽  
Joint Estimation ◽  
Reservoir Rock ◽  
Inversion Method ◽  
Simultaneous Estimation ◽  
Model Parameters ◽  
Reservoir Properties

I have developed a joint inversion of seismic data for the simultaneous estimation of facies and reservoir properties, such as porosity, mineralogy, and saturation. The inversion method is a Bayesian approach for the joint estimation of facies and reservoir rock/fluid properties based on the statistical assumption of mixtures of nonparametric distributions of the model parameters. A mixture distribution is a convex combination of distributions. In the approach, I use a mixture of [Formula: see text] nonparametric distributions, where [Formula: see text] is the number of facies, and the weights of the combination represent the probability of the facies. The statistical assumptions in the proposed Bayesian inversion allow modeling multimodal and nonsymmetric distributions of the model parameters because they are not restricted to specific shapes of the probability distributions and allow modeling multimodal distributions caused by the presence of different facies and nonlinear relations between reservoir properties and elastic data. The inversion can be applied to elastic properties from well logs or derived from seismic data, and they can be combined with traditional Bayesian linearized AVO inversion. The method provides the point-by-point posterior distribution of facies and reservoir properties, as well as the most-likely models and its associated uncertainty, and it is successfully applied to real data.

A data-driven amplitude variation with offset inversion method via learned dictionaries and sparse representation

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. R725-R748 ◽  
Author(s):  
Bin She ◽  
Yaojun Wang ◽  
Jiandong Liang ◽  
Zhining Liu ◽  
Chengyun Song ◽  
...  
Keyword(s):  
Sparse Representation ◽  
Prior Information ◽  
Data Driven ◽  
Inversion Method ◽  
Model Parameters ◽  
Well Log ◽  
Elastic Parameters ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Avo Inversion

Amplitude variation with offset (AVO) inversion is a typical ill-posed inverse problem. To obtain a stable and unique solution, regularization techniques relying on mathematical models from prior information are commonly used in conventional AVO inversion methods (hence the name model-driven methods). Due to the difference between prior information and the actual geology, these methods often have difficulty achieving satisfactory accuracy and resolution. We have developed a novel data-driven inversion method for the AVO inversion problem. This method can effectively extract useful knowledge from well-log data, including sparse dictionaries of elastic parameters and sparse representation of subsurface model parameters. Lateral continuity of subsurface geology allows for the approximation of model parameters for a work area using the learned dictionaries. Instead of particular mathematical models, a sparse representation is used to constrain the inverse problem. Because no assumption is made about the model parameters, we consider this a data-driven method. The general process of the algorithm is as follows: (1) using well-log data as the training samples to learn the sparse dictionary of each elastic parameter, (2) imposing a sparse representation constraint on the objective function, making the elastic parameters be sparsely represented over the learned dictionary, and (3) solving the objective function by applying a coordinate-descent algorithm. Tests on several synthetic examples and field data demonstrate that our algorithm is effective in improving the resolution and accuracy of solutions and is adaptable to various geologies.

A direct nonlinear AVO inversion method based on Lamé parameters

2017 ◽  
Author(s):  
Cheng Guangsen ◽  
Xingyao Yin ◽  
Zhaoyun Zong
Keyword(s):  
Inversion Method ◽  
Avo Inversion

scholarly journals refnx: neutron and X-ray reflectometry analysis in Python

2019 ◽  
Vol 52 (1) ◽  
pp. 193-200 ◽  
Author(s):  
Andrew R. J. Nelson ◽  
Stuart W. Prescott
Keyword(s):  
Bayesian Approach ◽  
Volume Fraction ◽  
Scattering Length ◽  
Distribution Functions ◽  
Monte Carlo Algorithm ◽  
Reproducible Research ◽  
Model Parameters ◽  
X Ray ◽  
Multiple Data Sets ◽  
Parameter Constraints

refnx is a model-based neutron and X-ray reflectometry data analysis package written in Python. It is cross platform and has been tested on Linux, macOS and Windows. Its graphical user interface is browser based, through a Jupyter notebook. Model construction is modular, being composed from a series of components that each describe a subset of the interface, parameterized in terms of physically relevant parameters (volume fraction of a polymer, lipid area per molecule etc.). The model and data are used to create an objective, which is used to calculate the residuals, log-likelihood and log-prior probabilities of the system. Objectives are combined to perform co-refinement of multiple data sets and mixed-area models. Prior knowledge of parameter values is encoded as probability distribution functions or bounds on all parameters in the system. Additional prior probability terms can be defined for sets of components, over and above those available from the parameters alone. Algebraic parameter constraints are available. The software offers a choice of fitting approaches, including least-squares (global and gradient-based optimizers) and a Bayesian approach using a Markov-chain Monte Carlo algorithm to investigate the posterior distribution of the model parameters. The Bayesian approach is useful for examining parameter covariances, model selection and variability in the resulting scattering length density profiles. The package is designed to facilitate reproducible research; its use in Jupyter notebooks, and subsequent distribution of those notebooks as supporting information, permits straightforward reproduction of analyses.

scholarly journals The Impact of Employer Attitude to Green Commuting Plans on Reducing Car Driving: A Mixed Method Analysis

2014 ◽  
Vol 26 (2) ◽  
pp. 109-119 ◽  
Author(s):  
Chuan Ding ◽  
Chao Liu ◽  
Yaoyu Lin ◽  
Yaowu Wang
Keyword(s):  
Co2 Emissions ◽  
Mixed Method ◽  
Latent Variables ◽  
Choice Model ◽  
Mode Choice ◽  
Car Ownership ◽  
Simultaneous Estimation ◽  
Model Parameters ◽  
Employer Attitudes ◽  
The Impact

Reducing car trips and promoting green commuting modes are generally considered important solutions to reduce the increase of energy consumption and transportation CO2 emissions. One potential solution for alleviating transportation CO2 emissions has been to identify a role for the employer through green commuter programs. This paper offers an approach to assess the effects of employer attitudes towards green commuting plans on commuter mode choice and the intermediary role car ownership plays in the mode choice decision process. A mixed method which extends the traditional discrete choice model by incorporating latent variables and mediating variables with a structure equation model was used to better understand the commuter mode choice behaviour. The empirical data were selected from Washington-Baltimore Regional Household Travel Survey in 2007-2008, including all the trips from home to workplace during the morning hours. The model parameters were estimated using the simultaneous estimation approach and the integrated model turns out to be superior to the traditional multinomial logit (MNL) model accounting for the impact of employer attitudes towards green commuting. The direct and indirect effects of socio-demographic attributes and employer attitudes towards green commuting were estimated. Through the structural equation modelling with mediating variable, this approach confirmed the intermediary nature of car ownership in the choice process. The results found in this paper provide helpful information for transportation and planning policymakers to test the transportation and planning policies effects and encourage green commuting reducing transportation CO2 emissions.

A New Inversion Method Using a Modified Bat Algorithm for Analysis of Seismic Refraction Data in Dam Site Investigation

2019 ◽  
Vol 24 (2) ◽  
pp. 201-214
Author(s):  
Rashed Poormirzaee ◽  
Siamak Sarmady ◽  
Yusuf Sharghi
Keyword(s):  
Seismic Data ◽  
Seismic Refraction ◽  
Bat Algorithm ◽  
Inversion Method ◽  
Model Parameters ◽  
Inversion Algorithm ◽  
Dam Site ◽  
Seismic Refraction Data ◽  
Modified Bat Algorithm ◽  
Refraction Data

Similar to any other geophysical method, seismic refraction method faces non-uniqueness in the estimation of model parameters. Recently, different nonlinear seismic processing techniques have been introduced, particularly for seismic inversion. One of the recently developed metaheuristic algorithms is bat optimization algorithm (BA). Standard BA is usually quick at the exploitation of the solution, while its exploration ability is relatively poor. In order to improve exploration ability of BA, in the current study, a hybrid metaheuristic algorithm by inclusion a mutation operator into BA, so-called mutation based bat algorithm (MBA), is introduced to inversion of seismic refraction data. The efficiency and stability of the proposed inversion algorithm were tested on different synthetic cases. Finally, the MBA inversion algorithm was applied to a real dataset acquired from Leylanchay dam site at East-Azerbaijan province, Iran, to determine alluvium depth. Then, the performance of MBA on both synthetic and real datasets was compared with standard BA. Moreover, the dataset was further processed following a tomographic approach and the results were compared to the results of the proposed MBA inversion method. In general, the MBA inversion results were superior to standard BA inversion and results of MBA were in good agreement with available boreholes data and geological sections at the dam site. The analysis of the seismic data showed that the studied site comprises three distinct layers: a saturated alluvial, an unsaturated alluvial, and a dolomite bedrock. The measured seismic velocity across the dam site has a range of 400 to 3,500 m/s, with alluvium thickness ranging from 5 to 19 m. Findings showed that the proposed metaheuristic inversion framework is a simple, fast, and powerful tool for seismic data processing.

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