Simultaneous inversion for model geometry and elastic parameters

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 182-190 ◽  
Author(s):  
Yanghua Wang
Keyword(s):  
Joint Inversion ◽  
Real Data ◽  
Structural Effect ◽  
P Wave ◽  
Inversion Method ◽  
S Wave ◽  
Elastic Parameters ◽  
Simultaneous Inversion ◽  
Avo Analysis ◽  
The North

Both traveltimes and amplitudes in reflection seismology are used jointly in an inversion to simultaneously invert for the interface geometry and the elastic parameters at the reflectors. The inverse problem has different physical dimensions in both data and model spaces. Practical approaches are proposed to tackle the dimensional difficulties. In using the joint inversion, which may properly take care of the structural effect, one potentially improves the estimates of the subsurface elastic parameters in the traditional analysis of amplitude variation with offset (AVO). Analysis of the elastic parameters estimated, using the ratio of s-wave to P-wave velocity contrasts and the deviation of this parameter from a normal background trend, promises to have application in AVO analysis. The inversion method is demonstrated by application to real data from the North Sea.

Simultaneous inversion of PP and PS seismic data

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. R1-R10 ◽  
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.

Seismic simultaneous inversion using a multidamped subspace method

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. R1-R10 ◽  
Author(s):  
Jinyue Liu ◽  
Yanghua Wang
Keyword(s):  
Fourier Coefficients ◽  
Hessian Matrix ◽  
Wave Impedance ◽  
Seismic Inversion ◽  
P Wave ◽  
Inversion Method ◽  
Subspace Method ◽  
S Wave ◽  
Elastic Parameters ◽  
Simultaneous Inversion

Seismic inversion of amplitude variation with offset (AVO) plays a key role in seismic interpretation and reservoir characterization. The AVO inversion should be a simultaneous inversion that inverts for three elastic parameters simultaneously: the P-wave impedance, S-wave impedance, and density. Using only seismic P-wave reflection data with a limited source-receiver offset range, the AVO simultaneous inversion can obtain two elastic parameters reliably, but it is difficult to invert for the third parameter, usually the density term. To address this difficulty in the AVO simultaneous inversion, we used a subspace inversion method in which we partitioned the elastic parameters into different subspaces. We parameterized each single elastic parameter with a truncated Fourier series and inverted for the Fourier coefficients. Because the Fourier coefficients of different wavenumber components have different sensitivities, we grouped the Fourier coefficients of low-, medium-, and high-wavenumber components into different subspaces. We further assigned different damping factors to the Hessian matrix corresponding to different wavenumber components within each subspace. This inversion scheme is referred to as a multidamped subspace method. Synthetic and field seismic data examples confirmed that the AVO simultaneous inversion with this multidamped subspace method is capable of producing reliable estimation of the three elastic parameters simultaneously.

Shear‐wave velocity and density estimation from PS-wave AVO analysis: Application to an OBS dataset from the North Sea

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1446-1454 ◽  
Author(s):  
Side Jin ◽  
G. Cambois ◽  
C. Vuillermoz
Keyword(s):  
Wave Velocity ◽  
North Sea ◽  
Random Noise ◽  
P Wave ◽  
S Wave ◽  
Data Set ◽  
Avo Analysis ◽  
The North ◽  
Avo Inversion ◽  
The North Sea

S-wave velocity and density information is crucial for hydrocarbon detection, because they help in the discrimination of pore filling fluids. Unfortunately, these two parameters cannot be accurately resolved from conventional P-wave marine data. Recent developments in ocean‐bottom seismic (OBS) technology make it possible to acquire high quality S-wave data in marine environments. The use of (S)-waves for amplitude variation with offset (AVO) analysis can give better estimates of S-wave velocity and density contrasts. Like P-wave AVO, S-wave AVO is sensitive to various types of noise. We investigate numerically and analytically the sensitivity of AVO inversion to random noise and errors in angles of incidence. Synthetic examples show that random noise and angle errors can strongly bias the parameter estimation. The use of singular value decomposition offers a simple stabilization scheme to solve for the elastic parameters. The AVO inversion is applied to an OBS data set from the North Sea. Special prestack processing techniques are required for the success of S-wave AVO inversion. The derived S-wave velocity and density contrasts help in detecting the fluid contacts and delineating the extent of the reservoir sand.

scholarly journals Azimuthal Attenuation Elastic Impedance Inversion for Fluid and Fracture Characterization Based on Modified Linear-Slip Theory

Geofluids ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18
Author(s):  
Xinpeng Pan ◽  
Guangzhi Zhang ◽  
Yian Cui
Keyword(s):  
Porous Medium ◽  
Wave Attenuation ◽  
Real Data ◽  
Seismic Attenuation ◽  
P Wave ◽  
Inversion Method ◽  
S Wave ◽  
Fracture Characterization ◽  
Fractured Porous Medium ◽  
Elastic Impedance

The seismic attenuation should be considered while accounting for the effect of anisotropy on the seismic wave propagating through a saturated fractured porous medium. Based on the modified linear-slip theory and anisotropic Gassmann’s equation, we derive an analytical expression for a linearized PP-wave reflection coefficient and an azimuthal attenuation elastic impedance (AAEI) equation in terms of fluid/porosity term, shear modulus, density, dry normal and tangential fracture weaknesses, and compressional (P-wave) and shear (S-wave) attenuation parameters in a weak-attenuation isotropic background rock containing one single set of vertical aligned fractures. We then propose an AAEI inversion method to characterize the characteristics of fluids and fractures using two kinds of constrained regularizations in such a fractured porous medium. The proposed approach is finally confirmed by both the synthetic and real data sets acquired over a saturated fractured porous reservoir.

Approximations to the Zoeppritz equations and their use in AVO analysis

Geophysics ◽  
1999 ◽  
Vol 64 (6) ◽  
pp. 1920-1927 ◽  
Author(s):  
Yanghua Wang
Keyword(s):  
Linear Approximation ◽  
Wave Velocity ◽  
Order Approximation ◽  
Quadratic Function ◽  
P Wave ◽  
S Wave ◽  
Elastic Parameters ◽  
Amplitude Variation With Offset ◽  
Zoeppritz Equations ◽  
Avo Analysis

To efficiently invert seismic amplitudes for elastic parameters, pseudoquartic approximations to the Zoeppritz equations are derived to calculate P-P-wave reflection and transmission coefficients as a function of the ray parameter p. These explicit expressions have a compact form in which the coefficients of the p2 and p4 terms are given in terms of the vertical slownesses. The amplitude coefficients are also represented as a quadratic function of the elastic contrasts at an interface and are compared to the linear approximation used in conventional amplitude variation with offset (AVO) analysis, which can invert for only two elastic parameters. Numerical analysis with the second‐order approximation shows that the condition number of the Fréchet matrix for three elastic parameters is improved significantly from using a linear approximation. Therefore, those quadratic approximations can be used directly with amplitude information to estimate not only two but three parameters: P-wave velocity contrast, S-wave velocity contrast, and the ratio of S-wave and P-wave velocities at an interface.

scholarly journals Quadri-joint inversion: Method and application to the Big Sky 9C 3D data set in northern Montana

2018 ◽  
Vol 6 (4) ◽  
pp. SN101-SN118 ◽  
Author(s):  
Vincent Clochard ◽  
Bryan C. DeVault ◽  
David Bowen ◽  
Nicolas Delépine ◽  
Kanokkarn Wangkawong
Keyword(s):  
Reservoir Characterization ◽  
Joint Inversion ◽  
Wave Impedance ◽  
P Wave ◽  
Seismic Survey ◽  
Time Shift ◽  
Inversion Method ◽  
S Wave ◽  
Data Set ◽  
Long Term Storage

The Kevin Dome [Formula: see text] storage project, located in northern Montana, attempted to characterize the Duperow Formation as a potential long-term storage zone for injected [Formula: see text]. A multicomponent (9C) seismic survey was acquired for the Big Sky Carbon Sequestration Partnership over a portion of the Kevin Dome using P- and S-wave sources. Prestack migrated PP, PS, SH, and SV data sets were generated. We then applied several stratigraphic inversion workflows using one or several kinds of seismic wavefield at the same time resulting in joint inversions of each data set. The aim of our study is to demonstrate the benefits of doing quadri-joint inversion of PP-, PS-, SH-, and SV-wavefields for the recovery of the elastic earth parameters, especially the S-wave impedance and density. These are crucial parameters because they can help determine lithology and porefill in the reservoir characterization workflow. Because the inversion workflow always uses the original seismic data recorded in its own time domain, it is necessary to compute registration laws between PP-PS-, PP-SH-, and PP-SV-wavefields using a time shift computation procedure (warping) based on inverted S-wave impedances from inversion of a single wavefield. This generated a significant improvement over methods that rely on attempting to match trace waveforms that may have a different phase, frequency content, and polarity. Finally, we wanted to investigate the reliability of the quadri-joint inversion results in the Bakken/Banff Formations, which have less lateral geologic variation than the underlying Duperow target. This interval shares many of the geophysical characterization challenges common to shale reservoirs in other North American basins. We computed geomechanical parameters, such as Poisson’s ratio and Young’s modulus, which are a proxy for brittleness. Comparison of these results with independent laboratory measurements in the Bakken interval demonstrates the superiority of the quadri-joint inversion method to the traditional inversion using P-wave data only.

Bayesian lithology and fluid prediction from seismic prestack data

Geophysics ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. C13-C21 ◽  
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.

Joint inversion of logging-while-drilling multipole acoustic data to determine P- and S-wave velocities in unconsolidated slow formations

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. D553-D560 ◽  
Author(s):  
Yuan-Da Su ◽  
Can Jiang ◽  
Chun-Xi Zhuang ◽  
Song Xu ◽  
Xiao-Ming Tang
Keyword(s):  
Data Processing ◽  
Joint Inversion ◽  
P Wave ◽  
Inversion Method ◽  
Dispersion Characteristics ◽  
S Wave ◽  
Data Set ◽  
Acoustic Data ◽  
Wave Velocities ◽  
Logging While Drilling

We have developed a joint inversion method for logging-while-drilling (LWD) multipole acoustic data processing to simultaneously determine the formation of P- and S-wave velocities. The presence of the LWD tool strongly influences the dispersion characteristics of quadrupole and monopole leaky-P-waves, especially in unconsolidated slow formations. We have verified that an equivalent-tool theory can be adequately used to model the LWD multipole wave dispersion characteristics and can therefore be used to do forward modeling for the inversion. A major advantage of jointly inverting the multipole data sets, as compared with separately inverting each individual data set, is the reduction of uncertainties in the estimated formation of P- and S-wave velocities. We have applied the method to field data processing. The results found that the method not only corrected the dispersion effect in the quadrupole and leaky-P-wave data but also simultaneously obtained the formation of P- and S-wave velocities.

A new crustal shear-velocity model in Southwest China from joint seismological inversion and its implications for regional crustal dynamics

2019 ◽  
Author(s):  
Yan Yang ◽  
Huajian Yao ◽  
Hanxiao Wu ◽  
Ping Zhang ◽  
Maomao Wang
Keyword(s):  
Tibetan Plateau ◽  
Rayleigh Wave ◽  
Joint Inversion ◽  
Shear Velocity ◽  
P Wave ◽  
Tectonic Deformation ◽  
Inversion Method ◽  
Low Velocity ◽  
Sw China ◽  
S Period

SUMMARY Southwest (SW) China is located in a transition site from the active Tibetan Plateau to the stable Yangtze craton, which has complicated tectonic deformation and severe seismic hazards. We combine data from ambient noise, teleseismic body and surface waves, and petroleum wells to better constrain the crustal shear-velocity structure in SW China. We jointly invert the Rayleigh wave dispersion (5–40 s period), Rayleigh wave ZH ratio (20–60 s period), and P-wave receiver function for 114 permanent stations with a stepwise linearized joint inversion method. Compared to previous tomography results, we observe higher shear velocity in the sedimentary rocks within the Sichuan Basin, which is consistent with sonic logging measurements. Our model reveals widespread low-velocity zones in the mid-lower crust, and their boundaries correlate well with major fault systems. Between two main mid-crustal low-velocity channels, a prominent high-velocity region surrounded by earthquakes is observed in the inner zone of the Emeishan large igneous province (ELIP) and around the Anninghe-Zemuhe fault zone. These observations are comparable to regional tomography results using very dense arrays. Based on the results, we suggest that mid-lower crustal ductile flow and upper-crustal rigid fault movement play equally important roles in controlling the regional deformation styles and earthquake distribution in SW China. Our results also resolve thick crust-mantle transition zones beneath the eastern Tibetan Plateau and the inner zone of the ELIP due to ‘top-down’ and ‘bottom-up’ crust-mantle interactions, respectively. Our new model can serve as a reference crustal model of future high resolution model construction in SW China.

scholarly journals Variational Bayesian inversion of seismic attributes jointly for geologic facies and petrophysical rock properties

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. MR213-MR233 ◽  
Author(s):  
Muhammad Atif Nawaz ◽  
Andrew Curtis ◽  
Mohammad Sadegh Shahraeeni ◽  
Constantin Gerea
Keyword(s):  
Gaussian Mixture ◽  
Seismic Attributes ◽  
Joint Estimation ◽  
Training Data ◽  
P Wave ◽  
Rock Properties ◽  
Inversion Method ◽  
Computationally Efficient ◽  
S Wave ◽  
Well Data

Seismic attributes (derived quantities) such as P-wave and S-wave impedances and P-wave to S-wave velocity ratios may be used to classify subsurface volume of rock into geologic facies (distinct lithology-fluid classes) using pattern recognition methods. Seismic attributes may also be used to estimate subsurface petrophysical rock properties such as porosity, mineral composition, and pore-fluid saturations. Both of these estimation processes are conventionally carried out independent of each other and involve considerable uncertainties, which may be reduced significantly by a joint estimation process. We have developed an efficient probabilistic inversion method for joint estimation of geologic facies and petrophysical rock properties. Seismic attributes and petrophysical properties are jointly modeled using a Gaussian mixture distribution whose parameters are initialized by unsupervised learning using well-log data. Rock-physics models may be used in our method to augment the training data if the existing well data are limited; however, this is not required if sufficient well data are available. The inverse problem is solved using the Bayesian paradigm that models uncertainties in the form of probability distributions. Probabilistic inference is performed using variational optimization, which is a computationally efficient deterministic alternative to the commonly used sampling-based stochastic inference methods. With the help of a real data application from the North Sea, we find that our method is computationally efficient, honors expected spatial correlations of geologic facies, allows reliable detection of convergence, and provides full probabilistic results without stochastic sampling of the posterior distribution.

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