Stochastic joint inversion of 2D seismic and seismoelectric signals in linear poroelastic materials: A numerical investigation

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. N19-N31 ◽  
Author(s):  
Abderrahim Jardani ◽  
André Revil ◽  
Evert Slob ◽  
Walter Söllner
Keyword(s):  
Bulk Modulus ◽  
Posterior Probability ◽  
Solid Phase ◽  
Joint Inversion ◽  
Layer Boundary ◽  
Partially Saturated ◽  
Poroelastic Materials ◽  
Posterior Probability Density ◽  
Porous Frame ◽  
Horizontal Layers

The interpretation of seismoelectrical signals is a difficult task because coseismic and seismoelectric converted signals are recorded simultaneously and the seismoelectric conversions are typically several orders of magnitude smaller than the coseismic electrical signals. The seismic and seismoelectric signals are modeled using a finite-element code with perfectly matched layer boundary conditions assuming a linear poroelastic body. We present a stochastic joint inversion of the seismic and seismoelectrical data based on the adaptive Metropolis algorithm, to obtain the posterior probability density functions of the material properties of each geologic unit. This includes the permeability, porosity, electrical conductivity, bulk modulus of the dry porous frame, bulk modulus of the fluid, bulk modulus of the solid phase, and shear modulus of the formations. A test of this approach is performed with a synthetic model comprising two horizontal layers and a reservoir partially saturated with oil, which is embedded in the second layer. The result of the joint inversion shows that we can invert the permeability of the reservoir and its mechanical properties.

scholarly journals The influence of the pore shape on the bulk modulus and the Biot coefficient of fluid-saturated porous rocks

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
A. P. S. Selvadurai ◽  
A. P. Suvorov
Keyword(s):  
Bulk Modulus ◽  
Pore Space ◽  
Pore Shape ◽  
Porous Rocks ◽  
Partially Saturated ◽  
Biot Coefficient ◽  
Stress Partitioning ◽  
Oblate Spheroids ◽  
Poroelastic Materials ◽  
Applied Stresses

Abstract Fluid-saturated rocks are multi-phasic materials and the mechanics of partitioning the externally applied stresses between the porous skeleton of the rock and the interstitial fluids has to take into consideration the mechanical behaviour of the phases. In these studies the porosity of the multi-phasic material is important for estimating the multi-phasic properties and most studies treat the porosity as a scalar measure without addressing the influence of pore shape and pore geometry. This paper shows that both the overall bulk modulus of a porous medium and the Biot coefficient depend on the shape of the pores. Pores with shapes resembling either thin oblate spheroids or spheres are considered. The Mori–Tanaka and the self-consistent methods are used to estimate the overall properties and the results are compared with experimental data. The pore density and the aspect ratio of the spheroidal pores influence the porosity of the geomaterials. For partially saturated rocks, the equivalent bulk modulus of the fluid–gas mixture occupying the pore space can also be obtained. The paper also examines the influence of the pore shape in estimating the Biot coefficient that controls the stress partitioning in fluid-saturated poroelastic materials.

Geophysical signal processing using sequential Bayesian techniques

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. V87-V100 ◽  
Author(s):  
Caglar Yardim ◽  
Peter Gerstoft ◽  
Zoi-Heleni Michalopoulou
Keyword(s):  
Posterior Probability ◽  
Signal To Noise Ratio ◽  
Multiple Model ◽  
Nonstationary Processes ◽  
Ensemble Kalman Filters ◽  
Bayesian Techniques ◽  
Strongly Nonlinear ◽  
Posterior Probability Density ◽  
Geophysical Signal ◽  
Seismic Measurements

Sequential Bayesian techniques enable tracking of evolving geophysical parameters via sequential observations. They provide a formulation in which the geophysical parameters that characterize dynamic, nonstationary processes are continuously estimated as new data become available. This is done by using prediction from previous estimates of geophysical parameters, updates stemming from physical and statistical models that relate seismic measurements to the unknown geophysical parameters. In addition, these techniques provide the evolving uncertainty in the estimates in the form of posterior probability density functions. In addition to the particle filters (PFs), extended, unscented, and ensemble Kalman filters (EnKFs) were evaluated. The filters were compared via reflector and nonvolcanic tremor tracking examples. Because there are numerous geophysical problems in which the environmental model itself is not known or evolves with time, the concept of model selection and its filtering implementation were introduced. A multiple model PF was then used to track an unknown number of reflectors from seismic interferometry data. We found that when the equations that define the geophysical problem are strongly nonlinear, a PF was needed. The PF outperformed all Kalman filter variants, especially in low signal-to-noise ratio tremor cases. However, PFs are computationally expensive. The EnKF is most appropriate when the number of parameters is large. Because each technique is ideal under different conditions, they complement each other and provide a useful set of techniques for solving sequential geophysical inversion problems.

scholarly journals Efficient Probabilistic Joint Inversion of Direct Current Resistivity and Small-Loop Electromagnetic Data

Algorithms ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 144
Author(s):  
Christin Bobe ◽  
Daan Hanssens ◽  
Thomas Hermans ◽  
Ellen Van De Vijver
Keyword(s):  
Direct Current ◽  
Field Data ◽  
Joint Inversion ◽  
Dc Resistivity ◽  
Data Sets ◽  
Electrical Conductivities ◽  
Posterior Probability Density ◽  
Posterior Probability Density Function ◽  
Efficient Alternative ◽  
Synthetic Studies

Often, multiple geophysical measurements are sensitive to the same subsurface parameters. In this case, joint inversions are mostly preferred over two (or more) separate inversions of the geophysical data sets due to the expected reduction of the non-uniqueness in the joint inverse solution. This reduction can be quantified using Bayesian inversions. However, standard Markov chain Monte Carlo (MCMC) approaches are computationally expensive for most geophysical inverse problems. We present the Kalman ensemble generator (KEG) method as an efficient alternative to the standard MCMC inversion approaches. As proof of concept, we provide two synthetic studies of joint inversion of frequency domain electromagnetic (FDEM) and direct current (DC) resistivity data for a parameter model with vertical variation in electrical conductivity. For both studies, joint results show a considerable improvement for the joint framework over the separate inversions. This improvement consists of (1) an uncertainty reduction in the posterior probability density function and (2) an ensemble mean that is closer to the synthetic true electrical conductivities. Finally, we apply the KEG joint inversion to FDEM and DC resistivity field data. Joint field data inversions improve in the same way seen for the synthetic studies.

Poroelasticity of Fluid-Saturated Nanoporous Media

2009 ◽  
Vol 614 ◽  
pp. 35-40 ◽  
Author(s):  
Vincent Pensée ◽  
Qi Chang He ◽  
H. Le Quang
Keyword(s):  
Bulk Modulus ◽  
Size Effects ◽  
Solid Phase ◽  
Hollow Spheres ◽  
Pore Surface ◽  
Nanoporous Media ◽  
Surface Stresses ◽  
Effective Bulk Modulus ◽  
Nanometric Size

The purpose of this work is to extend the equations of linear poroelasticity to the case of materials with nanopores. We consider a model of microstructure which corresponds to an assemblage of hollow spheres saturated by a fluid. The solid phase is linearly elastic and isotropic; pores are assumed to be of nanometric size. To account for the pore surface stresses, the Young-Laplace model is used. The nanopore size effects on the effective bulk modulus, Biot’ modulus and coefficient are shown. When pores are sufficiently large, the classical relations of linear poroelasticity are retrieved.

Seismic signatures of reservoir transport properties and pore fluid distribution

Geophysics ◽  
1994 ◽  
Vol 59 (8) ◽  
pp. 1222-1236 ◽  
Author(s):  
Nabil Akbar ◽  
Gary Mavko ◽  
Amos Nur ◽  
Jack Dvorkin
Keyword(s):  
Bulk Modulus ◽  
Solid Phase ◽  
Low Frequency ◽  
Pore Fluid ◽  
Fluid Distribution ◽  
Geometrical Factor ◽  
Velocity Versus ◽  
Frequency Limit ◽  
Local Flow ◽  
Wave Induced

We investigate the effects of permeability, frequency, and fluid distribution on the viscoelastic behavior of rock. The viscoelastic response of rock to seismic waves depends on the relative motion of pore fluid with respect to the solid phase. Fluid motion depends, in part, on the internal wave‐induced pore pressure distribution that relates to the pore micro‐structure of rock and the scales of saturation. We consider wave‐induced squirt fluid flow at two scales: (1) local microscopic flow at the smallest scale of saturation heterogeneity (e.g., within a single pore) and (2) macroscopic flow at a larger scale of fluid‐saturated and dry patches. We explore the circumstances under which each of these mechanisms prevails. We examine such flows under the conditions of uniform confining (bulk) compression and obtain the effective dynamic bulk modulus of rock. The solutions are formulated in terms of generalized frequencies that depend on frequency, saturation, fluid and gas properties, and on the macroscopic properties of rock such as permeability, porosity, and dry bulk modulus. The study includes the whole range of saturation and frequency; therefore, we provide the missing link between the low‐frequency limit (Gassmann’s formula) and the high‐frequency limit given by Mavko and Jizba. Further, we compare our model with Biot’s theory and introduce a geometrical factor whose numeric value gives an indication as to whether local fluid squirt or global (squirt and/or Biot’s) mechanisms dominate the viscoelastic properties of porous materials. The important results of our theoretical modeling are: (1) a hysteresis of acoustic velocity versus saturation resulting from variations in fluid distributions, and (2) two peaks of acoustic wave attenuation—one at low frequency (caused by global squirt‐flow) and another at higher frequency (caused by local flow). Both theoretical results are compared with experimental data.

Joint inversion of nuclear magnetic resonance data from partially saturated rocks using a triangular pore model

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. JM15-JM28 ◽  
Author(s):  
Thomas Hiller ◽  
Norbert Klitzsch
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Pore Size Distribution ◽  
Pore Size ◽  
Size Distribution ◽  
Joint Inversion ◽  
Nmr Relaxation ◽  
Relaxation Data ◽  
Surface Relaxivity ◽  
Partially Saturated

Measurement of nuclear magnetic resonance (NMR) relaxation is a well-established laboratory/borehole method to characterize the storage and transport properties of rocks due to its direct sensitivity to the corresponding pore-fluid content (water/oil) and pore sizes. Using NMR, the correct estimation of, e.g., permeability strongly depends on the underlying pore model. Usually, one assumes spherical or cylindrical pores for interpreting NMR relaxation data. To obtain surface relaxivity and thus, the pore-size distribution, a calibration procedure by, e.g., mercury intrusion porosimetry or gas adsorption has to be used. Recently, a joint inversion approach was introduced that used NMR measurements at different capillary pressures/saturations (CPS) to derive surface relaxivity and pore-size distribution (PSD) simultaneously. We further extend this approach from a bundle of parallel cylindrical capillaries to capillaries with triangular cross sections. With this approach, it is possible to account for residual or trapped water within the pore corners/crevices of partially saturated pores. In addition, we have developed a method that allows determining the shape of these triangular capillaries by using NMR measurements at different levels of drainage and imbibition. We show the applicability of our approach on synthetic and measured data sets and determine how the combination of NMR and CPS significantly improves the interpretation of NMR relaxation data on fully and partially saturated porous media.

A New Traceability Method for Sudden Water Pollution Accidents

2013 ◽  
Vol 807-809 ◽  
pp. 1570-1574 ◽  
Author(s):  
Hai Dong Yang ◽  
Dong Guo Shao ◽  
Bi Yu Liu
Keyword(s):  
Water Pollution ◽  
Probability Distribution ◽  
Numerical Experiments ◽  
Posterior Probability ◽  
Recognition Accuracy ◽  
Average Error ◽  
Bayesian Mcmc ◽  
Posterior Probability Distribution ◽  
Posterior Probability Density ◽  
Sudden Water Pollution

Pollution point source identification for the non-shore emission which is the main form of sudden water pollution incident is considered in this paper. Firstly, the source traceability of sudden water pollution accidents is taken as the Bayesian estimation problem; secondly, the posterior probability distribution of the source's parameters are deduced; thirdly, the marginal posterior probability density is obtained by using a new traceability method; finally, this proposed method is compared with Bayesian-MCMC by numerical experiments. The conclusions are as following: the new traceability method can reduce the iterations, improve the recognition accuracy, and reduce the overall average error obviously and it is more stable and robust than Bayesian-MCMC and can identify sudden water pollution accidents source effectively. Therefore, it provides a new idea and method to solve the difficulty of traceability problems in sudden water pollution accidents.

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