Bayesian linearized AVO inversion

Geophysics ◽  
2003 ◽  
Vol 68 (1) ◽  
pp. 185-198 ◽  
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.

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.

Nonlinear waveform inversion of plane‐wave seismograms in stratified elastic media

Geophysics ◽  
1991 ◽  
Vol 56 (5) ◽  
pp. 664-674 ◽  
Author(s):  
F. Kormendi ◽  
M. Dietrich
Keyword(s):  
Plane Wave ◽  
Least Squares ◽  
Wave Velocity ◽  
Generalized Least Squares ◽  
P Wave ◽  
Gradient Algorithm ◽  
Stratified Medium ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Frequency Wave

We present a method for determining the elastic parameters of a horizontally stratified medium from its plane‐wave reflectivity. The nonlinear inverse problem is iteratively solved by using a generalized least‐squares formalism. The proposed method uses the (relatively) fast convergence properties of the conjugate gradient algorithm and achieves computational efficiency through analytical solutions for calculating the reference and perturbational wavefields. The solution method is implemented in the frequency‐wave slowness domain and can be readily adapted to various source‐receiver configurations. The behavior of the algorithm conforms to the predictions of generalized least‐squares inverse theory: the inversion scheme yields satisfactory results as long as the correct velocity trends are introduced in the starting model. In practice, the inversion algorithm should be applied first in the precritical region because of the strong nonlinear behavior of postcritical data with respect to velocity perturbations. The suggested inversion strategy consists of first inverting for the density and P‐wave velocity (or P‐wave impedance) by considering plane waves in the low slowness region (near‐normal angles of incidence), then in optimizing for the S‐wave velocity by progressively including contributions from the high slowness region (steep angles of incidence). Numerical experiments performed with noise‐free synthetic data prove that the proposed inversion method satisfactorialy reconstructs the elastic properties of a stratified medium from a limited set of plane‐wave components, at a reasonable computing cost.

High-resolution three-term AVO inversion by means of a Trivariate Cauchy probability distribution

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. R43-R55 ◽  
Author(s):  
Wubshet Alemie ◽  
Mauricio D. Sacchi
Keyword(s):  
High Resolution ◽  
Wave Velocity ◽  
P Wave ◽  
S Wave ◽  
Avo Inversion ◽  
P Wave Velocity ◽  
Multivariate Gaussian ◽  
Density Perturbations ◽  
Gaussian Prior ◽  
Scale Matrix

Three-term AVO inversion can be used to estimate P-wave velocity, S-wave velocity, and density perturbations from reflection seismic data. The density term, however, exhibits little sensitivity to amplitudes and, therefore, its inversion is unstable. One way to stabilize the density term is by including a scale matrix that provides correlation information between the three unknown AVO parameters. We investigate a Bayesian procedure to include sparsity and a scale matrix in the three-term AVO inversion problem. To this end, we model the prior distribution of the AVO parameters via a Trivariate Cauchy distribution. We found an iterative algorithm to solve the Bayesian inversion and, in addition, comparisons are provided with the classical inversion approach that uses a Multivariate Gaussian prior. It is important to point out that the Multivariate Gaussian prior allows us to include the correlation of the AVO parameters in the solution of the inverse problem. The Trivariate Cauchy prior not only permits us to incorporate correlation but also leads to high-resolution (broadband) P-wave velocity, S-wave velocity, and density perturbations.

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.

Amplitude variation with offset inversion using the reflectivity method

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. R185-R195 ◽  
Author(s):  
Hongxing Liu ◽  
Jingye Li ◽  
Xiaohong Chen ◽  
Bo Hou ◽  
Li Chen
Keyword(s):  
Wave Velocity ◽  
P Wave ◽  
Transmission Losses ◽  
Amplitude Variation ◽  
Data Set ◽  
Amplitude Variation With Offset ◽  
Avo Inversion ◽  
Propagation Effects ◽  
Reflectivity Method ◽  
Internal Multiples

Most existing amplitude variation with offset (AVO) inversion methods are based on the Zoeppritz’s equation or its approximations. These methods assume that the amplitude of seismic data depends only on the reflection coefficients, which means that the wave-propagation effects, such as geometric spreading, attenuation, transmission loss, and multiples, have been fully corrected or attenuated before inversion. However, these requirements are very strict and can hardly be satisfied. Under a 1D assumption, reflectivity-method-based inversions are able to handle transmission losses and internal multiples. Applications of these inversions, however, are still time-consuming and complex in computation of differential seismograms. We have evaluated an inversion methodology based on the vectorized reflectivity method, in which the differential seismograms can be calculated from analytical expressions. It is computationally efficient. A modification is implemented to transform the inversion from the intercept time and ray-parameter domain to the angle-gather domain. AVO inversion is always an ill-posed problem. Following a Bayesian approach, the inversion is stabilized by including the correlation of the P-wave velocity, S-wave velocity, and density. Comparing reflectivity-method-based inversion with Zoeppritz-based inversion on a synthetic data and a real data set, we have concluded that reflectivity-method-based inversion is more accurate when the propagation effects of transmission losses and internal multiples are not corrected. Model testing has revealed that the method is robust at high noise levels.

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.

The impact of common‐offset migration on porosity estimation by AVO inversion

Geophysics ◽  
2001 ◽  
Vol 66 (3) ◽  
pp. 755-762 ◽  
Author(s):  
Arild Buland ◽  
Martin Landrø
Keyword(s):  
P Wave ◽  
High Porosity ◽  
S Wave ◽  
Seismic Line ◽  
Data Set ◽  
The North ◽  
Avo Inversion ◽  
Time Migration ◽  
The Impact ◽  
Porosity Estimation

The impact of prestack time migration on porosity estimation has been tested on a 2-D seismic line from the Valhall/Hod area in the North Sea. Porosity is estimated in the Cretaceous chalk section in a two‐step procedure. First, P-wave and S-wave velocity and density are estimated by amplitude variation with offset (AVO) inversion. These parameters are then linked to porosity through a petrophysical rock data base based on core plug analysis. The porosity is estimated both from unmigrated and prestack migrated seismic data. For the migrated data set, a standard prestack Kirchhoff time migration is used, followed by simple angle and amplitude corrections. Compared to modern high‐cost, true amplitude migration methods, this approach is faster and more practical. The test line is structurally fairly simple, with a maximum dip of 5°; but the results differ significantly, depending on whether migration is applied prior to the inversion. The maximum difference in estimated porosity is of the order of 10% (about 50% relative change). High‐porosity zones estimated from the unmigrated data were not present on the porosity section estimated from the migrated data.

Full-waveform matching of VP and VS models from surface waves

2019 ◽  
Vol 218 (3) ◽  
pp. 1873-1891 ◽  
Author(s):  
Farbod Khosro Anjom ◽  
Daniela Teodor ◽  
Cesare Comina ◽  
Romain Brossier ◽  
Jean Virieux ◽  
...  
Keyword(s):  
Surface Waves ◽  
Wave Velocity ◽  
Real Data ◽  
Test Site ◽  
P Wave ◽  
S Wave ◽  
Surface Wave Dispersion ◽  
Data Set ◽  
Near Surface ◽  
Velocity Models

SUMMARY The analysis of surface wave dispersion curves (DCs) is widely used for near-surface S-wave velocity (VS) reconstruction. However, a comprehensive characterization of the near-surface requires also the estimation of P-wave velocity (VP). We focus on the estimation of both VS and VP models from surface waves using a direct data transform approach. We estimate a relationship between the wavelength of the fundamental mode of surface waves and the investigation depth and we use it to directly transform the DCs into VS and VP models in laterally varying sites. We apply the workflow to a real data set acquired on a known test site. The accuracy of such reconstruction is validated by a waveform comparison between field data and synthetic data obtained by performing elastic numerical simulations on the estimated VP and VS models. The uncertainties on the estimated velocity models are also computed.

Advances in surface-wave tomography for near-surface applications

2021 ◽  
Vol 40 (8) ◽  
pp. 567-575
Author(s):  
Myrto Papadopoulou ◽  
Farbod Khosro Anjom ◽  
Mohammad Karim Karimpour ◽  
Valentina Laura Socco
Keyword(s):  
Surface Wave ◽  
Wave Velocity ◽  
P Wave ◽  
Seismic Exploration ◽  
S Wave ◽  
Data Set ◽  
Near Surface ◽  
Processing Times ◽  
Spatial Coverage ◽  
Wave Tomography

Surface-wave (SW) tomography is a technique that has been widely used in the field of seismology. It can provide higher resolution relative to the classical multichannel SW processing and inversion schemes that are usually adopted for near-surface applications. Nevertheless, the method is rarely used in this context, mainly due to the long processing times needed to pick the dispersion curves as well as the inability of the two-station processing to discriminate between higher SW modes. To make it efficient and to retrieve pseudo-2D/3D S-wave velocity (VS) and P-wave velocity (VP) models in a fast and convenient way, we develop a fully data-driven two-station dispersion curve estimation, which achieves dense spatial coverage without the involvement of an operator. To handle higher SW modes, we apply a dedicated time-windowing algorithm to isolate and pick the different modes. A multimodal tomographic inversion is applied to estimate a VS model. The VS model is then converted to a VP model with the Poisson's ratio estimated through the wavelength-depth method. We apply the method to a 2D seismic exploration data set acquired at a mining site, where strong lateral heterogeneity is expected, and to a 3D pilot data set, recorded with state-of-the-art acquisition technology. We compare the results with the ones retrieved from classical multichannel analysis.

SH-SH wave inversion for S-wave velocity and density

Geophysics ◽  
2022 ◽  
pp. 1-59
Author(s):  
Fucai Dai ◽  
Feng Zhang ◽  
Xiangyang Li
Keyword(s):  
Wave Velocity ◽  
Inversion Method ◽  
Data Sets ◽  
Sh Wave ◽  
S Wave ◽  
Data Set ◽  
Sh Waves ◽  
Model Parameter ◽  
Wave Inversion ◽  
Impedance Contrast

SS-waves (SV-SV waves and SH-SH waves) are capable of inverting S-wave velocity ( VS) and density ( ρ) because they are sensitive to both parameters. SH-SH waves can be separated from multicomponent data sets more effectively than the SV-SV wave because the former is decoupled from the PP-wave in isotropic media. In addition, the SH-SH wave can be better modeled than the SV-SV wave in the case of strong velocity/impedance contrast because the SV-SV wave has multicritical angles, some of which can be quite small when velocity/ impedance contrast is strong. We derived an approximate equation of the SH-SH wave reflection coefficient as a function of VS and ρ in natural logarithm variables. The approximation has high accuracy, and it enables the inversion of VS and ρ in a direct manner. Both coefficients corresponding to VS and ρ are “model-parameter independent” and thus there is no need for prior estimate of any model parameter in inversion. Then, we developed an SH-SH wave inversion method, and demonstrated it by using synthetic data sets and a real SH-SH wave prestack data set from the west of China. We found that VS and ρ can be reliably estimated from the SH-SH wave of small angles.

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