Determination of relative angles and anisotropic resistivity using multicomponent induction logging data

We have developed a new algorithm that retrieves information about relative dip angle, relative azimuth angle, vertical resistivity, and horizontal resistivity from multicomponent EM induction logging data. To investigate how relative dip and azimuth angles affect multicomponent induction logging data, we performed a sensitivity analysis using an anisotropic whole space model. Based upon the sensitivity analysis, we designed a two‐step procedure to recover relative dip, relative azimuth, horizontal resistivity, and vertical resistivity. In the first step, the observed data are transformed into a new data set independent of the azimuth angle; a simultaneous inversion method recovers relative dip angle, vertical resistivity, and horizontal resistivity. In the second step, a 1D line search is performed to decide relative azimuth angle. Synthetic and field data tests indicate that the new inversion algorithm can extract information about relative dip and azimuth angles as well as the anisotropic resistivity structure from multicomponent induction loggingdata.

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

Geophysics ◽

10.1190/1.1443818 ◽

1995 ◽

Vol 60 (3) ◽

pp. 796-809 ◽

Cited By ~ 110

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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Simultaneous inversion of prestack seismic data for rock properties using simulated annealing

Geophysics ◽

10.1190/1.1527087 ◽

2002 ◽

Vol 67 (6) ◽

pp. 1877-1885 ◽

Cited By ~ 85

Author(s):

Xin‐Quan Ma

Keyword(s):

Simulated Annealing ◽

Seismic Data ◽

Low Frequency ◽

Optimization Procedure ◽

P Wave ◽

Rock Properties ◽

Inversion Method ◽

Inversion Algorithm ◽

Simultaneous Inversion ◽

Reflection Seismic

A new prestack inversion algorithm has been developed to simultaneously estimate acoustic and shear impedances from P‐wave reflection seismic data. The algorithm uses a global optimization procedure in the form of simulated annealing. The goal of optimization is to find a global minimum of the objective function, which includes the misfit between synthetic and observed prestack seismic data. During the iterative inversion process, the acoustic and shear impedance models are randomly perturbed, and the synthetic seismic data are calculated and compared with the observed seismic data. To increase stability, constraints have been built into the inversion algorithm, using the low‐frequency impedance and background Vs/Vp models. The inversion method has been successfully applied to synthetic and field data examples to produce acoustic and shear impedances comparable to log data of similar bandwidth. The estimated acoustic and shear impedances can be combined to derive other elastic parameters, which may be used for identifying of lithology and fluid content of reservoirs.

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Simultaneous inversion of PP and PS seismic data

Geophysics ◽

10.1190/1.2194533 ◽

2006 ◽

Vol 71 (3) ◽

pp. R1-R10 ◽

Cited By ~ 51

Author(s):

Helene Hafslund Veire ◽

Martin Landrø

Keyword(s):

Seismic Data ◽

Reservoir Characterization ◽

Model Building ◽

Joint Inversion ◽

P Wave ◽

Inversion Method ◽

System Of Equations ◽

S Wave ◽

Data Set ◽

Simultaneous Inversion

Elastic parameters derived from seismic data are valuable input for reservoir characterization because they can be related to lithology and fluid content of the reservoir through empirical relationships. The relationship between physical properties of rocks and fluids and P-wave seismic data is nonunique. This leads to large uncertainties in reservoir models derived from P-wave seismic data. Because S- waves do not propagate through fluids, the combined use of P-and S-wave seismic data might increase our ability to derive fluid and lithology effects from seismic data, reducing the uncertainty in reservoir characterization and thereby improving 3D reservoir model-building. We present a joint inversion method for PP and PS seismic data by solving approximated linear expressions of PP and PS reflection coefficients simultaneously using a least-squares estimation algorithm. The resulting system of equations is solved by singular-value decomposition (SVD). By combining the two independent measurements (PP and PS seismic data), we stabilize the system of equations for PP and PS seismic data separately, leading to more robust parameter estimation. The method does not require any knowledge of PP and PS wavelets. We tested the stability of this joint inversion method on a 1D synthetic data set. We also applied the methodology to North Sea multicomponent field data to identify sand layers in a shallow formation. The identified sand layers from our inverted sections are consistent with observations from nearby well logs.

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Bayesian linearized AVO inversion

Geophysics ◽

10.1190/1.1543206 ◽

2003 ◽

Vol 68 (1) ◽

pp. 185-198 ◽

Cited By ~ 450

Author(s):

Arild Buland ◽

Henning Omre

Keyword(s):

Wave Velocity ◽

Posterior Distribution ◽

Acoustic Impedance ◽

Velocity Ratio ◽

P Wave ◽

Inversion Method ◽

Inversion Algorithm ◽

S Wave ◽

Data Set ◽

Avo Inversion

A new linearized AVO inversion technique is developed in a Bayesian framework. The objective is to obtain posterior distributions for P‐wave velocity, S‐wave velocity, and density. Distributions for other elastic parameters can also be assessed—for example, acoustic impedance, shear impedance, and P‐wave to S‐wave velocity ratio. The inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the Zoeppritz equation. The solution is represented by a Gaussian posterior distribution with explicit expressions for the posterior expectation and covariance; hence, exact prediction intervals for the inverted parameters can be computed under the specified model. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero. With realistic noise levels, acoustic impedance was the best determined parameter, while the inversion provided practically no information about the density. The inversion algorithm has also been tested on a real 3‐D data set from the Sleipner field. The results show good agreement with well logs, but the uncertainty is high.

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3D induced-polarization data inversion for complex resistivity

Geophysics ◽

10.1190/1.3560156 ◽

2011 ◽

Vol 76 (3) ◽

pp. F157-F171 ◽

Cited By ~ 32

Author(s):

Michael Commer ◽

Gregory A. Newman ◽

Kenneth H. Williams ◽

Susan S. Hubbard

Keyword(s):

Environmental Remediation ◽

Large Scale ◽

Forward Modeling ◽

Induced Polarization ◽

Inversion Method ◽

Data Sets ◽

Inversion Algorithm ◽

Data Set ◽

Complex Resistivity ◽

Data Inversion

The conductive and capacitive material properties of the subsurface can be quantified through the frequency-dependent complex resistivity. However, the routine three-dimensional (3D) interpretation of voluminous induced polarization (IP) data sets still poses a challenge due to large computational demands and solution nonuniqueness. We have developed a flexible methodology for 3D (spectral) IP data inversion. Our inversion algorithm is adapted from a frequency-domain electromagnetic (EM) inversion method primarily developed for large-scale hydrocarbon and geothermal energy exploration purposes. The method has proven to be efficient by implementing the nonlinear conjugate gradient method with hierarchical parallelism and by using an optimal finite-difference forward modeling mesh design scheme. The method allows for a large range of survey scales, providing a tool for both exploration and environmental applications. We experimented with an image focusing technique to improve the poor depth resolution of surface data sets with small survey spreads. The algorithm’s underlying forward modeling operator properly accounts for EM coupling effects; thus, traditionally used EM coupling correction procedures are not needed. The methodology was applied to both synthetic and field data. We tested the benefit of directly inverting EM coupling contaminated data using a synthetic large-scale exploration data set. Afterward, we further tested the monitoring capability of our method by inverting time-lapse data from an environmental remediation experiment near Rifle, Colorado. Similar trends observed in both our solution and another 2D inversion were in accordance with previous findings about the IP effects due to subsurface microbial activity.

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Simultaneous reconstruction of 1-D susceptibility and conductivity from electromagnetic data

Geophysics ◽

10.1190/1.1444528 ◽

1999 ◽

Vol 64 (1) ◽

pp. 33-47 ◽

Cited By ~ 31

Author(s):

Zhiyi Zhang ◽

Douglas W. Oldenburg

Keyword(s):

Cost Function ◽

Objective Functions ◽

Inversion Algorithm ◽

Data Set ◽

Circular Loop ◽

Simultaneous Inversion ◽

The Earth ◽

Simultaneous Reconstruction ◽

Single Data ◽

The Cost

In this paper, we develop an inversion algorithm to simultaneously recover 1-D distributions of electric conductivity and magnetic susceptibility from a single data set. The earth is modeled as a series of homogeneous layers of known thickness with constant but unknown conductivities and susceptibilities. The medium of interest is illuminated by a horizontal circular loop source located above the surface of the earth. The secondary signals from the earth are received by a circular loop receiver located some distance from the source. The model objective function in the inversion, which we refer to as the cost function, is a weighted sum of model objective functions of conductivity and susceptibility. We minimize this cost function subject to the data constraints and show how the choice of weights for the model objective functions of conductivity and susceptibility affects the results of the inversion through 1-D synthetic examples. We also invert 3-D synthetic and field data. From these examples we conclude that simultaneous inversion of electromagnetic (EM) data can provide useful information about the conductivity and susceptibility distributions.

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Geostatistical inversion of prestack seismic data for the joint estimation of facies and impedances using stochastic sampling from Gaussian mixture posterior distributions

Geophysics ◽

10.1190/geo2016-0670.1 ◽

2017 ◽

Vol 82 (4) ◽

pp. M55-M65 ◽

Cited By ~ 19

Author(s):

Xiaozheng Lang ◽

Dario Grana

Keyword(s):

Elastic Properties ◽

Posterior Distribution ◽

Seismic Data ◽

Gaussian Mixture ◽

Seismic Inversion ◽

Joint Estimation ◽

Inversion Method ◽

Inversion Algorithm ◽

Data Set ◽

Geostatistical Approach

We have developed a seismic inversion method for the joint estimation of facies and elastic properties from prestack seismic data based on a geostatistical approach. The objectives of our inversion methodology are to sample from the posterior distribution of seismic properties and to simultaneously classify the lithology conditioned by seismic data. The inversion algorithm is a sequential Gaussian mixture inversion based on Bayesian linearized amplitude variation with offset inverse theory and sequential geostatistical simulations. The stochastic approach to the inversion allows generating multiple elastic models that match the seismic data. To mathematically represent the multimodal behavior of elastic properties due to their variations within different lithologies, we adopt a Gaussian mixture distribution for the prior model of the elastic properties and we use the prior probability of the facies as weights of the Gaussian components of the mixture. The solution of the inverse problem is achieved by deriving the explicit analytical expression of the posterior distribution of the elastic properties and facies and by sampling from this distribution according to a spatial correlation model. The inversion methodology has been validated using well logs and synthetic seismic data with different noise levels, and it is then applied to a real 3D seismic data set in North Sea.

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A simultaneous inversion for background velocity and impedance maps

Geophysics ◽

10.1190/1.1442855 ◽

1990 ◽

Vol 55 (4) ◽

pp. 458-469 ◽

Cited By ~ 29

Author(s):

D. Cao ◽

W. B. Beydoun ◽

S. C. Singh ◽

A. Tarantola

Keyword(s):

Traditional Approach ◽

Waveform Inversion ◽

Synthetic Data ◽

Inversion Method ◽

Nonlinear Inversion ◽

Seismic Velocities ◽

Inversion Algorithm ◽

Seismic Reflection Data ◽

Simultaneous Inversion ◽

Highly Nonlinear

Full‐waveform inversion of seismic reflection data is highly nonlinear because of the irregular form of the function measuring the misfit between the observed and the synthetic data. Since the nonlinearity results mainly from the parameters describing seismic velocities, an alternative to the full nonlinear inversion is to have an inversion method which remains nonlinear with respect to velocities but linear with respect to impedance contrasts. The traditional approach is to decouple the nonlinear and linear parts by first estimating the background velocity from traveltimes, using either traveltime inversion or velocity analysis, and then estimating impedance contrasts from waveforms, using either waveform inversion or conventional migration. A more sophisticated strategy is to obtain both the subsurface background velocities and impedance contrasts simultaneously by using a single least‐squares norm waveform‐fit criterion. The background velocity that adequately represents the gross features of the medium is parameterized using a sparse grid, whereas the impedance contrasts use a dense grid. For each updated velocity model, the impedance contrasts are computed using a linearized inversion algorithm. For a 1-D velocity background, it is very efficient to perform inversion in the f-k domain by using the WKBJ and Born approximations. The method performs well both with synthetic and field data.

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Multidimensional inversion of loop-loop frequency-domain EM data for resistivity and magnetic susceptibility

Geophysics ◽

10.1190/1.3503652 ◽

2010 ◽

Vol 75 (6) ◽

pp. F213-F223 ◽

Cited By ~ 22

Author(s):

Yutaka Sasaki ◽

Jung-Ho Kim ◽

Seong-Jun Cho

Keyword(s):

Magnetic Susceptibility ◽

Frequency Domain ◽

Synthetic Data ◽

Staggered Grid ◽

Data Sets ◽

Inversion Algorithm ◽

Simultaneous Inversion ◽

Small Loop ◽

Em Induction ◽

Airborne Em

Electromagnetic (EM) induction measurements are affected by resistivity and magnetic susceptibility. Thus, inverting EM data for resistivity alone can give misleading models if susceptible effects are strong. An inversion algorithm is presented to simultaneously recover multidimensional distributions of resistivity and susceptibility from various types of loop-loop frequency-domain EM data. The algorithm adopts a staggered-grid finite-difference method for the 3D forward solutions and computes the sensitivities with respect to resistivity and susceptibility from the forward solutions using the reciprocity principle. The algorithm is tested on synthetic data sets from ground-based small-loop, airborne, and Slingram EM surveys. It is shown that the simultaneous inversion of the small-loop EM data collected at a singleheight is unstable and likely to produce unreliable susceptibility models because the effect of susceptibility is nearly independent of the frequency. However, if the data are obtained for multiple heights or different loop configurations, simultaneous inversion can produce more reliable susceptibility and resistivity models even if the data are contaminated by offset errors. It is also shown that although the simultaneous inversion of airborne EM data is relatively stable, adding data obtained at different heights helps to increase the reliability of the resistivity and susceptibility models. Among the loop-loop EM methods discussed here, the Slingram method is relatively insensitive to susceptibility anomalies and thus cannot be used to recover the susceptibility distribution via inversion even if the data are obtained using different loop configurations.

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Bayesian lithology and fluid prediction from seismic prestack data

Geophysics ◽

10.1190/1.2842150 ◽

2008 ◽

Vol 73 (3) ◽

pp. C13-C21 ◽

Cited By ~ 75

Author(s):

Arild Buland ◽

Odd Kolbjørnsen ◽

Ragnar Hauge ◽

Øyvind Skjæveland ◽

Kenneth Duffaut

Keyword(s):

Seismic Data ◽

Rock Physics ◽

Real Data ◽

Feasibility Analysis ◽

Bayesian Inversion ◽

Inversion Method ◽

Elastic Parameters ◽

Data Set ◽

Prior Probabilities ◽

Simultaneous Inversion

A fast Bayesian inversion method for 3D lithology and fluid prediction from prestack seismic data, and a corresponding feasibility analysis were developed and tested on a real data set. The objective of the inversion is to find the probabilities for different lithology-fluid classes from seismic data and geologic knowledge. The method combines stochastic rock physics relations between the elastic parameters and the different lithology-fluid classes with the results from a fast Bayesian seismic simultaneous inversion from seismic data to elastic parameters. A method for feasibility analysis predicts the expected modification of the prior probabilities to posterior probabilities for the different lithology-fluid classes. The feasibility analysis can be carried out before the seismic data are analyzed. Both the feasibility method and the seismic lithology-fluid probability inversion were applied to a prospect offshore Norway. The analysis improves the probability for gas sand from 0.1 to about 0.2–0.4 with seismic data.

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