Bayesian closed-skew Gaussian inversion of seismic AVO data for elastic material properties

Bayesian closed-skew Gaussian inversion is defined as a generalization of traditional Bayesian Gaussian inversion, which is used frequently in seismic amplitude-versus-offset (AVO) inversion. The new model captures skewness in the variables of interest; hence, the posterior model for log-transformed elastic material properties given seismic AVO data might be a skew probability density function. The model is analytically tractable, and this makes it applicable in high-dimensional 3D inversion problems. Assessment of the posterior models in high dimensions requires numerical approximations, however. The Bayesian closed-skew Gaussian inversion approach has been applied on real elastic material properties from a well in the Sleipner field in the North Sea. A comparison with results from traditional Bayesian Gaussian inversion shows that the mean square error of predictions of P-wave and S-wave velocities are reduced by a factor of two, although somewhat less for density predictions.

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

Geophysics ◽

10.1190/1.1444833 ◽

2000 ◽

Vol 65 (5) ◽

pp. 1446-1454 ◽

Cited By ~ 33

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.

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

Geophysics ◽

10.1190/1.1444965 ◽

2001 ◽

Vol 66 (3) ◽

pp. 755-762 ◽

Cited By ~ 9

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.

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Three-component amplitude versus offset analysis

Exploration Geophysics ◽

10.1071/eg989257 ◽

1989 ◽

Vol 20 (2) ◽

pp. 257

Author(s):

D.R. Miles ◽

G. Gassaway ◽

L. Bennett ◽

R. Brown

Keyword(s):

Seismic Data ◽

P Wave ◽

S Wave ◽

Converted Wave ◽

P Waves ◽

S Waves ◽

Avo Analysis ◽

Avo Inversion ◽

Amplitude Versus Offset ◽

Converted Waves

Three-component (3-C) amplitude versus offset (AVO) inversion is the AVO analysis of the three major energies in the seismic data, P-waves, S-waves and converted waves. For each type of energy the reflection coefficients at the boundary are a function of the contrast across the boundary in velocity, density and Poisson's ratio, and of the angle of incidence of the incoming wave. 3-C AVO analysis exploits these relationships to analyse the AVO changes in the P, S, and converted waves. 3-C AVO analysis is generally done on P, S, and converted wave data collected from a single source on 3-C geophones. Since most seismic sources generate both P and S-waves, it follows that most 3-C seismic data may be used in 3-C AVO inversion. Processing of the P-wave, S-wave and converted wave gathers is nearly the same as for single-component P-wave gathers. In split-spread shooting, the P-wave and S-wave energy on the radial component is one polarity on the forward shot and the opposite polarity on the back shot. Therefore to use both sides of the shot, the back shot must be rotated 180 degrees before it can be stacked with the forward shot. The amplitude of the returning energy is a function of all three components, not just the vertical or radial, so all three components must be stacked for P-waves, then for S-waves, and finally for converted waves. After the gathers are processed, reflectors are picked and the amplitudes are corrected for free-surface effects, spherical divergence and the shot and geophone array geometries. Next the P and S-wave interval velocities are calculated from the P and S-wave moveouts. Then the amplitude response of the P and S-wave reflections are analysed to give Poisson's ratio. The two solutions are then compared and adjusted until they match each other and the data. Three-component AVO inversion not only yields information about the lithologies and pore-fluids at a specific location; it also provides the interpreter with good correlations between the P-waves and the S-waves, and between the P and converted waves, thus greatly expanding the value of 3-C seismic data.

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Anisotropic correction of sonic logs in wells with large relative dip

Geophysics ◽

10.1190/1.2789776 ◽

2008 ◽

Vol 73 (1) ◽

pp. E1-E5 ◽

Cited By ~ 16

Author(s):

Lev Vernik

Keyword(s):

Reservoir Characterization ◽

Low Frequency ◽

P Wave ◽

Amplitude Variation With Offset ◽

Seismic Amplitude ◽

Avo Inversion ◽

Pore Pressure Prediction ◽

Siliciclastic Rocks ◽

Dip Angle ◽

Sonic Logs

Seismic reservoir characterization and pore-pressure prediction projects rely heavily on the accuracy and consistency of sonic logs. Sonic data acquisition in wells with large relative dip is known to suffer from anisotropic effects related to microanisotropy of shales and thin-bed laminations of sand, silt, and shale. Nonetheless, if anisotropy parameters can be related to shale content [Formula: see text] in siliciclastic rocks, then I show that it is straightforward to compute the anisotropy correction to both compressional and shear logs using [Formula: see text] and the formation relative dip angle. The resulting rotated P-wave sonic logs can be used to enhance time-depth ties, velocity to effective stress transforms, and low-frequency models necessary for prestack seismic amplitude variation with offset (AVO) inversion.

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EXTRACTING SUB-SURFACE INFORMATION FROM LONG OFFSET P-WAVE DATA—A CHEAPER ALTERNATIVE TO MULTICOMPONENT OBC FOR EXPLORATION?

The APPEA Journal ◽

10.1071/aj01038 ◽

2002 ◽

Vol 42 (1) ◽

pp. 627

Author(s):

R.G. Williams ◽

G. Roberts ◽

K. Hawkins

Keyword(s):

Seismic Energy ◽

Higher Order ◽

P Wave ◽

S Wave ◽

Additional Information ◽

Wave Data ◽

Wave Velocities ◽

Avo Inversion ◽

Long Offset ◽

Multicomponent Data

Seismic energy that has been mode converted from pwave to s-wave in the sub-surface may be recorded by multi-component surveys to obtain information about the elastic properties of the earth. Since the energy converted to s-wave is missing from the p-wave an alternative to recording OBC multi-component data is to examine p-wave data for the missing energy. Since pwave velocities are generally faster than s-wave velocities, then for a given reflection point the converted s-wave signal reaches the surface at a shorter offset than the equivalent p-wave information. Thus, it is necessary to record longer offsets for p-wave data than for multicomponent data in order to measure the same information.A non-linear, wide-angle (including post critical) AVO inversion has been developed that allows relative changes in p-wave velocities, s-wave velocities and density to be extracted from long offset p-wave data. To extract amplitudes at long offsets for this inversion it is necessary to image the data correctly, including correcting for higher order moveout and possibly anisotropy if it is present.The higher order moveout may itself be inverted to yield additional information about the anisotropy of the sub-surface.

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

Geophysics ◽

10.1190/1.3554627 ◽

2011 ◽

Vol 76 (3) ◽

pp. R43-R55 ◽

Cited By ~ 142

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.

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

Interpretation ◽

10.1190/int-2016-0056.1 ◽

2016 ◽

Vol 4 (4) ◽

pp. T613-T625 ◽

Cited By ~ 1

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.

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Fracture detection using azimuthal variation of P-wave moveout from orthogonal seismic survey lines

Geophysics ◽

10.1190/1.1444626 ◽

1999 ◽

Vol 64 (4) ◽

pp. 1193-1201 ◽

Cited By ~ 34

Author(s):

Xiang‐Yang Li

Keyword(s):

P Wave ◽

Seismic Survey ◽

Fracture Detection ◽

Data Set ◽

The North ◽

High Impedance ◽

Impedance Contrast ◽

The North Sea ◽

Marine Exploration ◽

Orthogonal Pairs

An algorithm is proposed for determining the fracture orientation based on the azimuthal variations in the P-wave reflection moveout for a target interval. The differential moveout between orthogonal survey lines from the bottom of a given target shows cos 2ϕ variations with the line azimuth ϕ measured from the fracture strike for a fixed offset. A configuration of four intersecting survey lines may be used to quantify the fracture strike. The four lines form two orthogonal pairs, and the fracture strike can be obtained by analyzing the crossplot of the two corresponding pairs of the differential moveouts. An offset‐depth ratio (x/z) of 1.0 or greater (up to 1.5) is often required to quantify the moveout difference reliably. The sensitivity of the method is further enhanced by low/high impedance contrast at the top target interface but is greatly reduced by high/low impedance contrast. The method may be particularly useful in marine exploration with repeated surveys of various vintages where continuous azimuthal coverage is often not available. A data set from the North Sea is used to illustrate the technique.

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Amplitude variation with offset inversion using acoustic-elastic local solver

Geophysics ◽

10.1190/geo2019-0108.1 ◽

2020 ◽

Vol 85 (3) ◽

pp. R251-R262 ◽

Cited By ~ 1

Author(s):

Ligia Elena Jaimes-Osorio ◽

Alison Malcolm ◽

Ali Gholami

Keyword(s):

Elastic Material ◽

Point Sources ◽

P Wave ◽

Reflection Coefficients ◽

Local Domain ◽

Amplitude Variation ◽

Amplitude Variation With Offset ◽

Zoeppritz Equations ◽

Avo Inversion ◽

Full Domain

Conventional amplitude variation with offset (AVO) inversion analysis uses the Zoeppritz equations, which are based on a plane-wave approximation. However, because real seismic data are created by point sources, wave reflections are better modeled by spherical waves than by plane waves. Indeed, spherical reflection coefficients deviate from planar reflection coefficients near the critical and postcritical angles, which implies that the Zoeppritz equations are not applicable for angles close to critical reflection in AVO analysis. Elastic finite-difference simulations provide a solution to the limitations of the Zoeppritz approximation because they can handle near- and postcritical reflections. We have used a coupled acoustic-elastic local solver that approximates the wavefield with high accuracy within a locally perturbed elastic subdomain of the acoustic full domain. Using this acoustic-elastic local solver, the local wavefield generation and inversion are much faster than performing a full-domain elastic inversion. We use this technique to model wavefields and to demonstrate that the amplitude from within the local domain can be used as a constraint in the inversion to recover elastic material properties. Then, we focus on understanding how much the amplitude and phase contribute to the reconstruction accuracy of the elastic material parameters ([Formula: see text], [Formula: see text], and [Formula: see text]). Our results suggest that the combination of amplitude and phase in the inversion helps with the convergence. Finally, we analyze elastic parameter trade-offs in AVO inversion, from which we find that to recover accurate P-wave velocities we should invert for [Formula: see text] and [Formula: see text] simultaneously with fixed density.

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Geochemical and petrophysical characterization of mantle metasomatism beneath the North Tanzanian Divergence, East African rift.

10.5194/egusphere-egu21-10603 ◽

2021 ◽

Author(s):

Adeline Clutier ◽

Fleurice Parat ◽

Michel Gregoire ◽

Benoit Gibert ◽

Stéphanie Gautier ◽

...

Keyword(s):

Wave Velocity ◽

Lithospheric Mantle ◽

East African Rift ◽

Mantle Xenoliths ◽

P Wave ◽

S Wave ◽

East African ◽

The North ◽

Alkaline Magmas ◽

African Rift

The North Tanzanian Divergence (NTD) is the prolongation of the eastern branch of the East African Rift and is a place of intense volcanism. Numerous volcanoes erupted deep subalkaline to highly alkaline magmas, including the particular active natrocarbonatite Oldoinyo Lengai. On the North-South axis (Natron to Manyara basins), three highly alkaline volcanoes, Pello Hills, Lashaine and Labait, erupted melilite magmas that originated from low degree of partial melting of asthenospheric mantle (depth > 120 km). The particularity of these volcanoes is that they sampled numerous mantle xenoliths during ascent. This represents a unique opportunity to study the composition and the rheology of lithospheric mantle. Mantle xenoliths are deep garnet-bearing peridotites (120 km depth), amphibole and phlogopite peridotites and phlogopitites. They contain abundant hydrous minerals as isolated crystals or veins that attest to an important metasomatism beneath the NTD. Previous geochemical and petrological studies have highlighted interactions of alkaline magmas and the thick cratonic lithosphere as metasomatic agent. However, the presence and composition of magmas, the degree of metasomatism, and the role of metasomatism on mantle rheology below the NTD is still debated.To characterize these previous parameters, in this study we performed geochemical and petrophysical analyses on metasomatized, fertile and refractory mantle xenoliths from Labait (on-craton volcano) and Pello Hills (in-rift volcano). Using mineral compositions and thermobarometer calibrations, we estimated the depth of mantle xenoliths between 40 and 140 km (14 to 47 kbar) and temperatures from 930 to 1340&#176;C. EBSD analysis on thin sections indicate that peridotites and amphibole/phlogopite-bearing mantle xenoliths display a moderate to strong deformation induced crystal preferred orientation. In contrast, weak mineral orientations have been observed in phlogopite-amphibole-clinopyroxene-bearing veins. Calculation of seismic properties using MTEX program show that peridotites are seismically anisotropic, up to 12.4% for P-wave velocity (Vp) and 6.8% for S-wave velocity (Vs). The Vp and Vs in hydrous veins are lower than in peridotites (Vp: 7.5-7.9 and 8.3-9.6 km/s; Vs: 4.4-4.6 and 5.0-5.3 km/s respectively) and therefore the Vp and Vs velocities decrease with the increasing proportion of metasomatic minerals. We estimate that a peridotite with 20 vol.% metasomatic vein has a velocity decrease of 3.5% for Vp and 2.9% for Vs, compared to a fertile peridotite.These geochemical and petrophysical approaches are important to understand P- and S-wave propagation in the lithospheric mantle beneath the NTD and more specifically in metasomatized lithospheric mantle. The new in situ data and models from mantle xenoliths will be compared to tomographic acquisition and discussed in term of temperature, presence of melt or metasomatism processes. Both petrophysical and geophysical data will help to precisely determine the structure and rheology of the lithospheric mantle, which may control the propagation of the rift at early stage rifting between the Tanzanian craton and the mobile Proterozoic belts.

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