AVO and AVA inversion for fractured reservoir characterization

Geophysics ◽  
2002 ◽  
Vol 67 (1) ◽  
pp. 300-306 ◽  
Author(s):  
Matteo Mario Beretta ◽  
Giancarlo Bernasconi ◽  
Giuseppe Drufuca
Keyword(s):  
Reservoir Characterization ◽  
Spectral Component ◽  
Plane Waves ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Fractured Reservoir ◽  
Fracture Density ◽  
P Waves ◽  
Data Set ◽  
Inversion Procedure

Seismic wave reflection amplitudes are used to detect fluids and fracture properties in reservoirs. This paper studies the characterization of a vertically fractured fluid‐filled reservoir by analyzing the reflection amplitudes of P‐waves with varying incident and azimuthal angles. The reservoir is modeled as a horizontal transversely isotropic medium embedded in an isotropic background, and the linearized P‐waves reflection coefficient are considered. The conditioning of the inverse problem is analyzed, and fracture density is found to be the best conditioned parameter. Using diffraction tomography under the Born approximation, an inversion procedure is proposed in the transformed k–ω domain to detect fracture density variations within the reservoir. Seismic data are rearranged in pairs of incident and reflected plane waves, enlightening only one spectral component of the fracture density field at a time. Only the observable spectral components are inverted. Moreover, working in the transformed domain, picking reflection amplitudes is not required. An example of the inversion applied to a synthetic data set is presented. The limitation of source and receiver numbers and the finite bandwidth of the wavelet produce a loss of resolution, but the overall fracture density variations are recovered correctly.

Stacking-velocity tomography for tilted orthorhombic media

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. C171-C180 ◽  
Author(s):  
Qifan Liu ◽  
Ilya Tsvankin
Keyword(s):  
Parameter Estimation ◽  
Subsurface Layer ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
P Waves ◽  
Additional Information ◽  
Reflection Data ◽  
Anisotropic Layers ◽  
Zero Offset ◽  
Velocity Tomography

Tilted orthorhombic (TOR) models are typical for dipping anisotropic layers, such as fractured shales, and can also be due to nonhydrostatic stress fields. Velocity analysis for TOR media, however, is complicated by the large number of independent parameters. Using multicomponent wide-azimuth reflection data, we develop stacking-velocity tomography to estimate the interval parameters of TOR media composed of homogeneous layers separated by plane dipping interfaces. The normal-moveout (NMO) ellipses, zero-offset traveltimes, and reflection time slopes of P-waves and split S-waves ([Formula: see text] and [Formula: see text]) are used to invert for the interval TOR parameters including the orientation of the symmetry planes. We show that the inversion can be facilitated by assuming that the reflector coincides with one of the symmetry planes, which is a common geologic constraint often employed for tilted transversely isotropic media. This constraint makes the inversion for a single TOR layer feasible even when the initial model is purely isotropic. If the dip plane is also aligned with one of the symmetry planes, we show that the inverse problem for [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-waves can be solved analytically. When only [Formula: see text]-wave data are available, parameter estimation requires combining NMO ellipses from a horizontal and dipping interface. Because of the increase in the number of independent measurements for layered TOR media, constraining the reflector orientation is required only for the subsurface layer. However, the inversion results generally deteriorate with depth because of error accumulation. Using tests on synthetic data, we demonstrate that additional information such as knowledge of the vertical velocities (which may be available from check shots or well logs) and the constraint on the reflector orientation can significantly improve the accuracy and stability of interval parameter estimation.

scholarly journals Seismic AVOA Inversion for Weak Anisotropy Parameters and Fracture Density in a Monoclinic Medium

2020 ◽  
Vol 10 (15) ◽  
pp. 5136 ◽  
Author(s):  
Zijian Ge ◽  
Shulin Pan ◽  
Jingye Li
Keyword(s):  
Fractured Rock ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
P Wave ◽  
Inversion Method ◽  
Fracture Density ◽  
Weak Anisotropy ◽  
Amplitude Versus Offset ◽  
Porosity And Permeability ◽  
Transverse Isotropic

In shale gas development, fracture density is an important lithologic parameter to properly characterize reservoir reconstruction, establish a fracturing scheme, and calculate porosity and permeability. The traditional methods usually assume that the fracture reservoir is one set of aligned vertical fractures, embedded in an isotropic background, and estimate some alternative parameters associated with fracture density. Thus, the low accuracy caused by this simplified model, and the intrinsic errors caused by the indirect substitution, affect the estimation of fracture density. In this paper, the fractured rock of monoclinic symmetry assumes two non-orthogonal vertical fracture sets, embedded in a transversely isotropic background. Firstly, assuming that the fracture radius, width, and orientation are known, a new form of P-wave reflection coefficient, in terms of weak anisotropy (WA) parameters and fracture density, was obtained by substituting the stiffness coefficients of vertical transverse isotropic (VTI) background, normal, and tangential fracture compliances. Then, a linear amplitude versus offset and azimuth (AVOA) inversion method, of WA parameters and fracture density, was constructed by using Bayesian theory. Tests on synthetic data showed that WA parameters, and fracture density, are stably estimated in the case of seismic data containing a moderate noise, which can provide a reliable tool in fracture prediction.

Interpolation with Fourier-radial adaptive thresholding

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. WB95-WB102 ◽  
Author(s):  
William Curry
Keyword(s):  
Convex Sets ◽  
Plane Waves ◽  
Synthetic Data ◽  
Sampling Interval ◽  
Polar Coordinates ◽  
Adaptive Thresholding ◽  
Sampled Data ◽  
Data Set ◽  
Before And After ◽  
Reflectivity Data

Many interpolation methods are effective with regularly sampled or randomly sampled data, whereas the spatial sampling of seismic reflectivity data is typically neither regular nor random. Fourier-radial adaptive thresholding (FRAT) is a sparsity-promoting method in which the interpolated result is sparse in the frequency-wavenumber domain and is coherent in a manner consistent with that of a collection of unaliased plane waves. The sparsity and the desired pattern in the [Formula: see text] domain are promoted by iterative soft thresholding and adaptive weighting; data in the [Formula: see text] domain are transformed to polar coordinates and then low-pass filtered along the radial axis to generate the nonlinear weight. FRAT interpolates data that are randomly sampled and aliased; i.e., where the minimum distance between adjacent traces is greater than the Nyquist sampling interval. A conventional approach to solving this problem is to apply a cascade of two procedures: first a sparsity-based method, such as projection onto convex sets (POCS) to interpolate the data onto a regularly sampled but aliased grid, followed by a “beyond aliasing” approach such as Gülünay [Formula: see text] interpolation to further interpolate the regularly sampled POCS result. In a simple synthetic example of two dipping plane waves with irregular, aliased sampling, FRAT outperformed this cascaded approach. In another experiment, the Sigsbee2A prestack synthetic data set was sampled using the source geometry from a 3D offshore survey where POCS will have difficulty with the semiregularity of this sampling pattern. FRAT produced results superior to those of POCS before and after the data were migrated.

Building tilted transversely isotropic depth models using localized anisotropic tomography with well information

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. D27-D36 ◽  
Author(s):  
Andrey Bakulin ◽  
Marta Woodward ◽  
Dave Nichols ◽  
Konstantin Osypov ◽  
Olga Zdraveva
Keyword(s):  
Seismic Data ◽  
Model Building ◽  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Synthetic Data ◽  
Rock Physics ◽  
Transversely Isotropic ◽  
Data Set ◽  
Anisotropic Models ◽  
Well Data

Tilted transverse isotropy (TTI) is increasingly recognized as a more geologically plausible description of anisotropy in sedimentary formations than vertical transverse isotropy (VTI). Although model-building approaches for VTI media are well understood, similar approaches for TTI media are in their infancy, even when the symmetry-axis direction is assumed known. We describe a tomographic approach that builds localized anisotropic models by jointly inverting surface-seismic and well data. We present a synthetic data example of anisotropic tomography applied to a layered TTI model with a symmetry-axis tilt of 45 degrees. We demonstrate three scenarios for constraining the solution. In the first scenario, velocity along the symmetry axis is known and tomography inverts for Thomsen’s [Formula: see text] and [Formula: see text] parame-ters. In the second scenario, tomography inverts for [Formula: see text], [Formula: see text], and velocity, using surface-seismic data and vertical check-shot traveltimes. In contrast to the VTI case, both these inversions are nonunique. To combat nonuniqueness, in the third scenario, we supplement check-shot and seismic data with the [Formula: see text] profile from an offset well. This allows recovery of the correct profiles for velocity along the symmetry axis and [Formula: see text]. We conclude that TTI is more ambiguous than VTI for model building. Additional well data or rock-physics assumptions may be required to constrain the tomography and arrive at geologically plausible TTI models. Furthermore, we demonstrate that VTI models with atypical Thomsen parameters can also fit the same joint seismic and check-shot data set. In this case, although imaging with VTI models can focus the TTI data and match vertical event depths, it leads to substantial lateral mispositioning of the reflections.

Conditional stochastic inversion of common-offset GPR reflection data

Geophysics ◽  
2021 ◽  
pp. 1-49
Author(s):  
Zhiwei Xu ◽  
James Irving ◽  
Yu Liu ◽  
Zhu Peimin ◽  
Klaus Holliger
Keyword(s):  
Ground Penetrating Radar ◽  
Synthetic Data ◽  
Field Measurements ◽  
Data Set ◽  
Stochastic Inversion ◽  
Reflection Data ◽  
Inversion Procedure ◽  
Borehole Logs ◽  
Ground Penetrating ◽  
Porosity Measurements

We present a stochastic inversion procedure for common-offset ground-penetrating radar (GPR) reflection measurements. Stochastic realizations of subsurface properties that offer an acceptable fit to GPR data are generated via simulated annealing optimization. The realizations are conditioned to borehole porosity measurements available along the GPR profile, or equivalent measurements of another petrophysical property that can be related to the dielectric permittivity, as well as to geostatistical parameters derived from the borehole logs and the processed GPR image. Validation of our inversion procedure is performed on a pertinent synthetic data set and indicates that the proposed method is capable of reliably recovering strongly heterogeneous porosity structures associated with surficial alluvial aquifers. This finding is largely corroborated through application of the methodology to field measurements from the Boise Hydrogeophysical Research Site near Boise, Idaho, USA.

Seismic demigration/migration in the curvelet domain

Geophysics ◽  
2008 ◽  
Vol 73 (2) ◽  
pp. S35-S46 ◽  
Author(s):  
Hervé Chauris ◽  
Truong Nguyen
Keyword(s):  
Input Data ◽  
Plane Waves ◽  
Synthetic Data ◽  
Velocity Model ◽  
Local Velocity ◽  
Data Set ◽  
Migration Operator ◽  
Local Plane ◽  
Seismic Images

Curvelets can represent local plane waves. They efficiently decompose seismic images and possibly imaging operators. We study how curvelets are distorted after demigration followed by migration in a different velocity model. We show that for small local velocity perturbations, the demigration/migration is reduced to a simple morphing of the initial curvelet. The derivation of the expected curvature of the curvelets shows that it is easier to sparsify the demigration/migration operator than the migration operator. An application on a 2D synthetic data set, generated in a smooth heterogeneous velocity model and with a complex reflectivity, demonstrates the usefulness of curvelets to predict what a migrated image would become in a locally different velocity model without the need for remigrating the full input data set. Curvelets are thus well suited to study the sensitivity of a prestack depth-migrated image with respect to the heterogeneous velocity model used for migration.

Seismic vertical transversely isotropic parameter inversion from P- and S-wave cross-borehole measurements in an aquifer environment

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. D101-D116
Author(s):  
Julius K. von Ketelhodt ◽  
Musa S. D. Manzi ◽  
Raymond J. Durrheim ◽  
Thomas Fechner
Keyword(s):  
Transversely Isotropic ◽  
P Wave ◽  
Perturbation Equation ◽  
S Wave ◽  
P Waves ◽  
Data Set ◽  
Near Surface ◽  
S Waves ◽  
Wave Measurements ◽  
Wave Splitting

Joint P- and S-wave measurements for tomographic cross-borehole analysis can offer more reliable interpretational insight concerning lithologic and geotechnical parameter variations compared with P-wave measurements on their own. However, anisotropy can have a large influence on S-wave measurements, with the S-wave splitting into two modes. We have developed an inversion for parameters of transversely isotropic with a vertical symmetry axis (VTI) media. Our inversion is based on the traveltime perturbation equation, using cross-gradient constraints to ensure structural similarity for the resulting VTI parameters. We first determine the inversion on a synthetic data set consisting of P-waves and vertically and horizontally polarized S-waves. Subsequently, we evaluate inversion results for a data set comprising jointly measured P-waves and vertically and horizontally polarized S-waves that were acquired in a near-surface ([Formula: see text]) aquifer environment (the Safira research site, Germany). The inverted models indicate that the anisotropy parameters [Formula: see text] and [Formula: see text] are close to zero, with no P-wave anisotropy present. A high [Formula: see text] ratio of up to nine causes considerable SV-wave anisotropy despite the low magnitudes for [Formula: see text] and [Formula: see text]. The SH-wave anisotropy parameter [Formula: see text] is estimated to be between 0.05 and 0.15 in the clay and lignite seams. The S-wave splitting is confirmed by polarization analysis prior to the inversion. The results suggest that S-wave anisotropy may be more severe than P-wave anisotropy in near-surface environments and should be taken into account when interpreting cross-borehole S-wave data.

Estimation of interval anisotropy parameters using velocity-independent layer stripping

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. WB117-WB127 ◽  
Author(s):  
Xiaoxiang Wang ◽  
Ilya Tsvankin
Keyword(s):  
Symmetry Plane ◽  
Synthetic Data ◽  
Single Layer ◽  
Transversely Isotropic ◽  
P Wave ◽  
Correlated Noise ◽  
Fractured Reservoir ◽  
Processing Parameter ◽  
Reflection Data ◽  
Error Amplification

Moveout analysis of long-spread P-wave data is widely used to estimate the key time-processing parameter [Formula: see text] in layered transversely isotropic media with a vertical symmetry axis (VTI). Inversion for interval [Formula: see text] values, however, suffers from instability caused by the trade-off between the effective moveout parameters and by subsequent error amplification during Dix-type layer stripping. We propose an alternative approach to nonhyperbolic moveout inversion based on the velocity-independent layer-stripping (VILS) method of Dewangan and Tsvankin. Also, we develop the 3D version of VILS and apply it to interval parameter estimation in orthorhombic media using wide-azimuth, long-spread data. If the overburden is laterally homogeneous and has a horizontal symmetry plane, VILS produces the exact interval traveltime-offset function in the target layer without knowledgeof the velocity field. Hence, Dix-type differentiation of moveout parameters used in existing techniques is replaced by the much more stable layer stripping of reflection traveltimes. The interval traveltimes are then inverted for the moveout parameters using the single-layer nonhyperbolic moveout equation. The superior accuracy and stability of the algorithm are illustrated on ray-traced synthetic data for typical VTI and orthorhombic models. Even small correlated noise in reflection traveltimes causes substantial distortions in the interval [Formula: see text] values computed by conventional Dix-type differentiation. In contrast, the output of VILS is insensitive to mild correlated traveltime errors. The algorithm is also tested on wide-azimuth P-wave reflection data recorded above a fractured reservoir at Rulison field in Colorado. The interval moveout parameters estimated by VILS in the shale layer above the reservoir are more plausible and less influenced by noise than those obtained by the Dix-type method.

scholarly journals Traces of the crustal units and the upper-mantle structure in the southwestern part of the East European Craton

Solid Earth ◽  
2014 ◽  
Vol 5 (2) ◽  
pp. 821-836 ◽  
Author(s):  
I. Janutyte ◽  
E. Kozlovskaya ◽  
M. Majdanski ◽  
P. H. Voss ◽  
M. Budraitis ◽  
...  
Keyword(s):  
Upper Mantle ◽  
Synthetic Data ◽  
Velocity Model ◽  
East European Craton ◽  
P Wave ◽  
Seismic Velocities ◽  
P Waves ◽  
Data Set ◽  
Teleseismic Tomography ◽  
East European

Abstract. The presented study is a part of the passive seismic experiment PASSEQ 2006–2008, which took place around the Trans-European Suture Zone (TESZ) from May 2006 to June 2008. The data set of 4195 manually picked arrivals of teleseismic P waves of 101 earthquakes (EQs) recorded in the seismic stations deployed to the east of the TESZ was inverted using the non-linear teleseismic tomography algorithm TELINV. Two 3-D crustal models were used to estimate the crustal travel time (TT) corrections. As a result, we obtain a model of P-wave velocity variations in the upper mantle beneath the TESZ and the East European Craton (EEC). In the study area beneath the craton, we observe up to 3% higher and beneath the TESZ about 2–3% lower seismic velocities compared to the IASP91 velocity model. We find the seismic lithosphere–asthenosphere boundary (LAB) beneath the TESZ at a depth of about 180 km, while we observe no seismic LAB beneath the EEC. The inversion results obtained with the real and the synthetic data sets indicate a ramp shape of the LAB in the northern TESZ, where we observe values of seismic velocities close to those of the craton down to about 150 km. The lithosphere thickness in the EEC increases going from the TESZ to the NE from about 180 km beneath Poland to 300 km or more beneath Lithuania. Moreover, in western Lithuania we find an indication of an upper-mantle dome. In our results, the crustal units are not well resolved. There are no clear indications of the features in the upper mantle which could be related to the crustal units in the study area. On the other hand, at a depth of 120–150 km we indicate a trace of a boundary of proposed palaeosubduction zone between the East Lithuanian Domain (EL) and the West Lithuanian Granulite Domain (WLG). Also, in our results, we may have identified two anorogenic granitoid plutons.

Estimation of modified fluid factor and dry fracture weaknesses using azimuthal elastic impedance

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. WA73-WA88 ◽  
Author(s):  
Huaizhen Chen ◽  
Yuxin Ji ◽  
Kristopher A. Innanen
Keyword(s):  
Reflection Coefficient ◽  
Synthetic Data ◽  
Tight Gas ◽  
Fracture Density ◽  
Fracture Detection ◽  
Data Set ◽  
Fluid Identification ◽  
Fluid Factor ◽  
Damped Least Squares ◽  
Elastic Impedance

We consider the problem of fluid identification and fracture detection in unconventional reservoir (tight gas sand and shale gas) characterization. We begin with a simplification of the stiffness parameters and the derivation of a linearized reflection coefficient and azimuthal elastic impedance (EI). The accuracy of the simplification is confirmed in application to gas-bearing fractured rocks with low porosity and small fracture density. We have developed a modified fluid factor that is more sensitive to fluid type and less influenced by porosity. A two-step inversion workflow is evaluated based on the derived linearized reflection coefficient and azimuthal EI, including (1) a damped least-squares inversion for azimuthal EI, constrained by an initial model, and (2) a Bayesian Markov chain Monte Carlo inversion for the modified fluid factor and dry fracture weaknesses. Stability and accuracy are examined with synthetic data, from which we conclude that the modified fluid factor and dry fracture weaknesses can be stably determined in the presence of moderate data error/noise. The stability of our approach is further confirmed on a fractured tight gas sand field data set, within which we observe that geologically reasonable parameters (Lamé constants, the modified fluid factor, and dry fracture weaknesses) are determined. We conclude that our inversion workflow and its underlying assumptions form realistic predictions/discriminations of reservoir fracture and fluid parameters.

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