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.

An Adaptive Stratified Joint PP and PS AVA Inversion Using Accurate Jacobian Matrix

Geophysics ◽  
2021 ◽  
pp. 1-145
Author(s):  
Xiaobo Liu ◽  
Jingyi Chen ◽  
Jing Zeng ◽  
Fuping Liu ◽  
Handong Huang ◽  
...  
Keyword(s):  
Seismic Data ◽  
Jacobian Matrix ◽  
Incidence Angle ◽  
P Wave ◽  
Rock Properties ◽  
Inversion Method ◽  
S Wave ◽  
Zoeppritz Equations ◽  
Wave Velocities ◽  
Strong Contrast

Amplitude variation with incidence angle (AVA) analysis is an essential tool for discriminating lithology in the hydrocarbon reservoirs. Compared with the traditional AVA inversion using only P-wave information, joint AVA inversion using PP and PS seismic data provides better estimation of rock properties (e.g., density, P- and S-wave velocities). At present, the most used AVA inversions depend on the approximations of Zoeppritz equations (e.g., Shuey and Aki-Richards approximations), which are not suitable for formations with strong contrast interfaces and seismic data with large incidence angles. Based on the previous derivation of accurate Jacobian matrix, we find that the sign of each partial derivative of reflection coefficient with respect to P-, S-wave velocities and density changes across the interface, represents good indicator for the reflection interfaces. Accordingly, we propose an adaptive stratified joint PP and PS AVA inversion using the accurate Jacobian matrix that can automatically obtain the layer information and can be further used as a constraint in the inversion of in-layer rock properties (density, P- and S-wave velocities). Due to the use of the exact Zoeppritz equations and accurate Jacobian matrix, this proposed inversion method is more accurate than traditional AVA inversion methods, has higher computational efficiency and can be applied to seismic wide-angle reflection data or seismic data acquired for formations with strong contrast interfaces. The model study shows that this proposed inversion method works better than the classical Shuey and Aki-Richards approximations at estimating reflection interfaces and in-layer rock properties. It also works well in handling a part of the complex Marmousi 2 model and real seismic data.

P- and S-wave attenuation logs from monopole sonic data

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 755-765 ◽  
Author(s):  
Xinhua Sun ◽  
Xiaoming Tang ◽  
C. H. (Arthur) Cheng ◽  
L. Neil Frazer
Keyword(s):  
Wave Attenuation ◽  
Fluid Velocity ◽  
P Wave ◽  
Reservoir Rock ◽  
Rock Properties ◽  
S Wave ◽  
Intrinsic Attenuation ◽  
Modified Method ◽  
Receiver Array ◽  
Attenuation Profiles

In this paper, a modification of an existing method for estimating relative P-wave attenuation is proposed. By generating synthetic waveforms without attenuation, the variation of geometrical spreading related to changes in formation properties with depth can be accounted for. With the modified method, reliable P- and S-wave attenuation logs can be extracted from monopole array acoustic waveform log data. Synthetic tests show that the P- and S-wave attenuation values estimated from synthetic waveforms agree well with their respective model values. In‐situ P- and S-wave attenuation profiles provide valuable information about reservoir rock properties. Field data processing results show that this method gives robust estimates of intrinsic attenuation. The attenuation profiles calculated independently from each waveform of an eight‐receiver array are consistent with one another. In fast formations where S-wave velocity exceeds the borehole fluid velocity, both P-wave attenuation ([Formula: see text]) and S-wave attenuation ([Formula: see text]) profiles can be obtained. P- and S-wave attenuation profiles and their comparisons are presented for three reservoirs. Their correlations with formation lithology, permeability, and fractures are also presented.

Two-step joint PP- and PS-wave three-term amplitude-variation with offset inversion

2016 ◽  
Vol 4 (4) ◽  
pp. T613-T625 ◽  
Author(s):  
Qizhen Du ◽  
Bo Zhang ◽  
Xianjun Meng ◽  
Chengfeng Guo ◽  
Gang Chen ◽  
...  
Keyword(s):  
Reflection Coefficient ◽  
Wave Reflection ◽  
Coefficient Matrix ◽  
P Wave ◽  
Inversion Method ◽  
S Wave ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Avo Inversion ◽  
Pp Wave

Three-term amplitude-variation with offset (AVO) inversion generally suffers from instability when there is limited prior geologic or petrophysical constraints. Two-term AVO inversion shows higher instability compared with three-term AVO inversion. However, density, which is important in the fluid-type estimation, cannot be recovered from two-term AVO inversion. To reliably predict the P- and S-waves and density, we have developed a robust two-step joint PP- and PS-wave three-term AVO-inversion method. Our inversion workflow consists of two steps. The first step is to estimate the P- and S-wave reflectivities using Stewart’s joint two-term PP- and PS-AVO inversion. The second step is to treat the P-wave reflectivity obtained from the first step as the prior constraint to remove the P-wave velocity related-term from the three-term Aki-Richards PP-wave approximated reflection coefficient equation, and then the reduced PP-wave reflection coefficient equation is combined with the PS-wave reflection coefficient equation to estimate the S-wave and density reflectivities. We determined the effectiveness of our method by first applying it to synthetic models and then to field data. We also analyzed the condition number of the coefficient matrix to illustrate the stability of the proposed method. The estimated results using proposed method are superior to those obtained from three-term AVO inversion.

scholarly journals Travel-Time Inversion Method of Converted Shear Waves Using RayInvr Algorithm

2021 ◽  
Vol 11 (8) ◽  
pp. 3571
Author(s):  
Genggeng Wen ◽  
Kuiyuan Wan ◽  
Shaohong Xia ◽  
Huilong Xu ◽  
Chaoyan Fan ◽  
...  
Keyword(s):  
Travel Time ◽  
Wave Velocity ◽  
P Wave ◽  
Inversion Method ◽  
Time Inversion ◽  
Ocean Bottom Seismometer ◽  
S Wave ◽  
S Waves ◽  
Inversion Model ◽  
Travel Time Inversion

The detailed studies of converted S-waves recorded on the Ocean Bottom Seismometer (OBS) can provide evidence for constraining lithology and geophysical properties. However, the research of converted S-waves remains a weakness, especially the S-waves’ inversion. In this study, we applied a travel-time inversion method of converted S-waves to obtain the crustal S-wave velocity along the profile NS5. The velocities of the crust are determined by the following four aspects: (1) modelling the P-wave velocity, (2) constrained sediments Vp/Vs ratios and S-wave velocity using PPS phases, (3) the correction of PSS phases’ travel-time, and (4) appropriate parameters and initial model are selected for inversion. Our results show that the vs. and Vp/Vs of the crust are 3.0–4.4 km/s and 1.71–1.80, respectively. The inversion model has a similar trend in velocity and Vp/Vs ratios with the forward model, due to a small difference with ∆Vs of 0.1 km/s and ∆Vp/Vs of 0.03 between two models. In addition, the high-resolution inversion model has revealed many details of the crustal structures, including magma conduits, which further supports our method as feasible.

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

Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1877-1885 ◽  
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.

Useful approximations for converted‐wave AVO

Geophysics ◽  
2001 ◽  
Vol 66 (6) ◽  
pp. 1721-1734 ◽  
Author(s):  
Antonio C. B. Ramos ◽  
John P. Castagna
Keyword(s):  
Wave Velocity ◽  
Random Noise ◽  
P Wave ◽  
Rock Properties ◽  
Negative Slope ◽  
High Contrast ◽  
Fractional Change ◽  
S Wave ◽  
Converted Wave ◽  
Low Contrast

Converted‐wave amplitude versus offset (AVO) behavior may be fit with a cubic relationship between reflection coefficient and ray parameter. Attributes extracted using this form can be directly related to elastic parameters with low‐contrast or high‐contrast approximations to the Zoeppritz equations. The high‐contrast approximation has the advantage of greater accuracy; the low‐contrast approximation is analytically simpler. The two coefficients of the low‐contrast approximation are a function of the average ratio of compressional‐to‐shear‐wave velocity (α/β) and the fractional changes in S‐wave velocity and density (Δβ/β and Δρ/ρ). Because of its simplicity, the low‐contrast approximation is subject to errors, particularly for large positive contrasts in P‐wave velocity associated with negative contrasts in S‐wave velocity. However, for incidence angles up to 40° and models confined to |Δβ/β| < 0.25, the errors in both coefficients are relatively small. Converted‐wave AVO crossplotting of the coefficients of the low‐contrast approximation is a useful interpretation technique. The background trend in this case has a negative slope and an intercept proportional to the α/β ratio and the fractional change in S‐wave velocity. For constant α/β ratio, an attribute trace formed by the weighted sum of the coefficients of the low‐contrast approximation provides useful estimates of the fractional change in S‐wave velocity and density. Using synthetic examples, we investigate the sensitivity of these parameters to random noise. Integrated P‐wave and converted‐wave analysis may improve estimation of rock properties by combining extracted attributes to yield fractional contrasts in P‐wave and S‐wave velocities and density. Together, these parameters may provide improved direct hydrocarbon indication and can potentially be used to identify anomalies caused by low gas saturations.

Converted-wave model building and imaging based on common-focus-point methodology

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. U139-U149
Author(s):  
Hongwei Liu ◽  
Mustafa Naser Al-Ali ◽  
Yi Luo
Keyword(s):  
Elastic Wave ◽  
Wave Velocity ◽  
Seismic Data ◽  
Model Building ◽  
P Wave ◽  
Rock Properties ◽  
S Wave ◽  
Converted Wave ◽  
Seismic Images ◽  
Focus Point

Seismic images can be viewed as photographs for underground rocks. These images can be generated from different reflections of elastic waves with different rock properties. Although the dominant seismic data processing is still based on the acoustic wave assumption, elastic wave processing and imaging have become increasingly popular in recent years. A major challenge in elastic wave processing is shear-wave (S-wave) velocity model building. For this reason, we have developed a sequence of procedures for estimating seismic S-wave velocities and the subsequent generation of seismic images using converted waves. We have two main essential new supporting techniques. The first technique is the decoupling of the S-wave information by generating common-focus-point gathers via application of the compressional-wave (P-wave) velocity on the converted seismic data. The second technique is to assume one common VP/ VS ratio to approximate two types of ratios, namely, the ratio of the average earth layer velocity and the ratio of the stacking velocity. The benefit is that we reduce two unknown ratios into one, so it can be easily scanned and picked in practice. The PS-wave images produced by this technology could be aligned with the PP-wave images such that both can be produced in the same coordinate system. The registration between the PP and PS images provides cross-validation of the migrated structures and a better estimation of underground rock and fluid properties. The S-wave velocity, computed from the picked optimal ratio, can be used not only for generating the PS-wave images, but also to ensure well registration between the converted-wave and P-wave images.

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.

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.

Direct nonlinear inversion of multiparameter 1D elastic media using the inverse scattering series

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCD15-WCD27 ◽  
Author(s):  
Haiyan Zhang ◽  
Arthur B. Weglein
Keyword(s):  
Wave Velocity ◽  
Material Properties ◽  
Value Added ◽  
P Wave ◽  
Added Value ◽  
Inversion Method ◽  
Elastic Media ◽  
Nonlinear Inversion ◽  
Model Matching ◽  
S Wave

In the direct nonlinear inversion method and in algorithms for 1D elastic media, P-wave velocity, S-wave velocity, and density are depth dependent. “Direct nonlinear” means that the method uses explicit formulas that (1) input data and directly output changes in material properties without the need for indirect procedures such as model matching, searching, optimization, or other assumed aligned objectives or proxies and that (2) the algorithms recognize and directly invert the intrinsic nonlinear relationship between changes in material properties and the recorded reflection wavefields. To achieve full elastic inversion, all components of data (such as PP, SP, and SS data) are needed. The method assumes that only data and reference medium propertiesare input, and terms in the inverse series for moving mislocated reflectors resulting from the linear inverse term are separated from amplitude correction terms. Although in principle this direct inversion approach requires all components of elastic data, synthetic tests indicate that a consistent value-added result may be achieved given only PP data measurements, as long as the PP data are used to approximately synthesize the PS and SP components. Further value would be derived from measuring all components of the data as the method requires. If all components of data are available, one consistent method can solve for all of the second terms (the first terms beyond linear). The explicit nonlinear inversion formulas provide an unambiguous data requirement message as well as conceptual and practical added value beyond both linear approaches and all indirect methods.

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