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.

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.

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.

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.

Frequency‐wavenumber elastic inversion of marine seismic data

Geophysics ◽  
1994 ◽  
Vol 59 (12) ◽  
pp. 1868-1881 ◽  
Author(s):  
Huasheng Zhao ◽  
Bjørn Ursin ◽  
Lasse Amundsen
Keyword(s):  
Wave Velocity ◽  
Reference Data ◽  
Jacobian Matrix ◽  
Synthetic Data ◽  
Velocity Model ◽  
P Wave ◽  
Stratified Medium ◽  
Inversion Method ◽  
S Wave ◽  
Time Space

We present an inversion method for determining the velocities, densities, and layer thicknesses of a horizontally stratified medium with an acoustic layer at the top and a stack of elastic layers below. The multioffset reflection response of the medium generated by a compressional point source is transformed from the time‐space domain into the frequency‐wavenumber domain where the inversion is performed by minimizing the difference between the reference data and the modeled data using a least‐squares technique. The forward modeling is based on the reflectivity method where the solution for each frequency‐wavenumber component is found by computing the generalized reflection and transmission matrices recursively. The gradient of the objective function is computed from analytical expressions of the Jacobian matrix derived directly from the recursive modeling equations. The partial derivatives of the reflection response of the stratified medium are then computed simultaneously with the reflection response by layer‐recursive formulas. The limited‐aperture and discretization effects in time and space of the reference data are included by applying a pair of frequency and wavenumber dependent filters to the predicted data and to the Jacobian matrix at each iteration. Numerical experiments performed with noise‐free synthetic data prove that the proposed inversion method satisfactorily reconstructs the elastic parameters of a stratified medium. The low‐frequency trends of the S‐wave velocity and density are found when the initial P‐wave velocity model gives approximately correct traveltimes. The convergence of the iterative minimization algorithm is fast.

Petroacoustics and composition of presalt rocks from Santos Basin

2019 ◽  
Vol 38 (5) ◽  
pp. 342-348 ◽  
Author(s):  
Guilherme Fernandes Vasquez ◽  
Marcio José Morschbacher ◽  
Camila Wense Dias dos Anjos ◽  
Yaro Moisés Parisek Silva ◽  
Vanessa Madrucci ◽  
...  
Keyword(s):  
Clay Minerals ◽  
Chemical Elements ◽  
Pore Space ◽  
Rock Physics ◽  
P Wave ◽  
Rock Properties ◽  
Tectonic Activity ◽  
S Wave ◽  
Wave Velocities ◽  
Lacustrine Carbonate

The deposition of the presalt section from Santos Basin began when Gondwana started to break up and South America and Africa were separating. Initial synrift carbonate deposits affected by relatively severe tectonic activity evolved to a lacustrine carbonate environment during the later stages of basin formation. Although the reservoirs are composed of carbonate rocks, the occurrence of faults and the intense colocation of igneous rocks served as a source of chemical elements uncommon in typical carbonate environments. Consequently, beyond the presence of different facies with complex textures and pore geometries, the presalt reservoir rocks present marked compositional and microstructural variability. Therefore, rock-physics modeling is used to understand and interpret the extensive laboratory measurements of P-wave velocities, S-wave velocities, and density that we have undertaken on the presalt carbonate cores from Santos Basin. We show that quartz and exotic clay minerals (such as stevensite and other magnesium-rich clay minerals), which have different values of elastic moduli and Poisson's ratio as compared to calcite and dolomite, may introduce noticeable “Poisson's reflectivity anomalies” on prestack seismic data. Moreover, although the authors concentrate their attention on composition, it will become clear that pore-space geometry also may influence seismic rock properties of presalt carbonate reservoirs.

Predicting reservoir quality in the Bakken Formation, North Dakota, using petrophysics and 3C seismic data

2020 ◽  
Vol 8 (4) ◽  
pp. T851-T868
Author(s):  
Andrea G. Paris ◽  
Robert R. Stewart
Keyword(s):  
North Dakota ◽  
Seismic Data ◽  
Rock Physics ◽  
P Wave ◽  
Well Logs ◽  
Reservoir Quality ◽  
Bakken Formation ◽  
S Wave ◽  
Converted Wave ◽  
Wave Velocities

Combining rock-property analysis with multicomponent seismic imaging can be an effective approach for reservoir quality prediction in the Bakken Formation, North Dakota. The hydrocarbon potential of shale is indicated on well logs by low density, high gamma-ray response, low compressional-wave (P-wave) and shear-wave (S-wave) velocities, and high neutron porosity. We have recognized the shale intervals by cross plotting sonic velocities versus density. Intervals with total organic carbon (TOC) content higher than 10 wt% deviate from lower TOC regions in the density domain and exhibit slightly lower velocities and densities (<2.30 g/cm3). We consider TOC to be the principal factor affecting changes in the density and P- and S-wave velocities in the Bakken shales, where VP/ VS ranges between 1.65 and 1.75. We generate the synthetic seismic data using an anisotropic version of the Zoeppritz equations, including estimated Thomsen’s parameters. For the tops of the Upper and Lower Bakken, the amplitude shows a negative intercept and a positive gradient, which corresponds to an amplitude variation with offset of class IV. The P-impedance error decreases by 14% when incorporating the converted-wave information in the inversion process. A statistical approach using multiattribute analysis and neural networks delimits the zones of interest in terms of P-impedance, density, TOC content, and brittleness. The inverted and predicted results show reasonable correlations with the original well logs. The integration of well log analysis, rock physics, seismic modeling, constrained inversions, and statistical predictions contributes to identifying the areas of highest reservoir quality within the Bakken Formation.

Estimating shear‐wave velocities from P-wave and converted‐wave data

Geophysics ◽  
1999 ◽  
Vol 64 (2) ◽  
pp. 504-507 ◽  
Author(s):  
Franklyn K. Levin
Keyword(s):  
Wave Velocity ◽  
Seismic Data ◽  
P Wave ◽  
S Wave ◽  
Converted Wave ◽  
Wave Data ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
P Wave Velocity ◽  
Growing Body

Tessmer and Behle (1988) show that S-wave velocity can be estimated from surface seismic data if both normal P-wave data and converted‐wave data (P-SV) are available. The relation of Tessmer and Behle is [Formula: see text] (1) where [Formula: see text] is the S-wave velocity, [Formula: see text] is the P-wave velocity, and [Formula: see text] is the converted‐wave velocity. The growing body of converted‐wave data suggest a brief examination of the validity of equation (1) for velocities that vary with depth.

Interpreter's Corner

2021 ◽  
Vol 40 (6) ◽  
pp. 454-459
Author(s):  
David J. Went
Keyword(s):  
Seismic Data ◽  
Incidence Angle ◽  
Seismic Inversion ◽  
P Wave ◽  
Data Sets ◽  
Oil Sand ◽  
S Wave ◽  
Seismic Line ◽  
The Difference ◽  
Amplitude Variation With Angle

Global empirical relationships of P-wave to S-wave and density for sandstones and shales are used to model two-term amplitude variation with angle at various depths of burial in a typically compacting siliciclastic basin. Data from the normally pressured Tertiary strata of Judd Basin, Atlantic Margin, West of Shetland, are used as a control. For a typical prospect depth of 1750 m below mudline, forward models of angle-dependent reflectivity reveal that discrimination of lithology (shale and brine sand) and fluid (oil sand) is optimally resolved at a 47° incidence angle (θ). This is equivalent to an angle of 28° on an intercept-gradient crossplot. Repeat experiments at other depths produce similar results but with the angle for optimal lithology and fluid determination shifting slightly with increasing depth. Background trends in seismic data crossplots of intercept versus gradient are typically overprinted by noise that has a disproportionate effect on the gradient. This study suggests that the difference between the noise and background rock-property trend is relatively small, such that in most modern seismic data sets, anomalies should be identifiable on time-windowed crossplots and equivalent weighted stacks. It is proposed that a seismic inversion for relative extended elastic impedance at a 45° incidence angle should capture most anomalies of interest in frontier basins with simple burial histories. An example is illustrated from a seismic line in Mozambique.

scholarly journals On The Low-Frequency Elastic Response of Pierre Shale During Temperature Cycles

2021 ◽  
Author(s):  
Stian Rørheim ◽  
Andreas Bauer ◽  
Rune M Holt
Keyword(s):  
Wave Velocity ◽  
Low Frequency ◽  
P Wave ◽  
Rock Properties ◽  
Fluid Viscosity ◽  
S Wave ◽  
Temperature Cycles ◽  
Wave Velocities ◽  
Young’S Moduli ◽  
P Wave Velocity

Summary The impact of temperature on elastic rock properties is less-studied and thus less-understood than that of pressure and stress. Thermal effects on dispersion are experimentally observed herein from seismic to ultrasonic frequencies: Young’s moduli and Poisson’s ratios plus P- and S-wave velocities are determined by forced-oscillation (FO) from 1 to 144 Hz and by pulse-transmission (PT) at 500 kHz. Despite being the dominant sedimentary rock type, shales receive less experimental attention than sandstones and carbonates. To our knowledge, no other FO studies on shale at above ambient temperatures exist. Temperature fluctuations are enforced by two temperature cycles from 20 via 40 to 60○C and vice versa. Measured rock properties are initially irreversible but become reversible with increasing number of heating and cooling segments. Rock property-sensitivity to temperature is likewise reduced. It is revealed that dispersion shifts towards higher frequencies with increasing temperature (reversible if decreased), Young’s moduli and P-wave velocity moduli and P-wave velocity maxima occur at 40○C for frequencies below 56 Hz, and S-wave velocities remain unchanged with temperature (if the first heating segment is neglected) at seismic frequencies. In comparison, ultrasonic P- and S-wave velocities are found to decrease with increasing temperatures. Behavioural differences between seismic and ultrasonic properties are attributed to decreasing fluid viscosity with temperature. We hypothesize that our ultrasonic recordings coincide with the transition-phase separating the low- and high-frequency regimes while our seismic recordings are within the low-frequency regime.

Sign in / Sign up

Export Citation Format

Share Document