Perturbation analysis of an explicit wavefield separation scheme for P‐ and S‐waves

Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1972-1982 ◽  
Author(s):  
Remco Muijs ◽  
Klaus Holliger ◽  
Johan O. A. Robertsson
Keyword(s):  
Explicit Calculation ◽  
Angle Of Incidence ◽  
Separation Scheme ◽  
S Wave ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
S Waves ◽  
Wave Separation ◽  
Small Phase ◽  
Wavefield Decomposition

Dense spatial recording patterns of three‐component (3C) receivers allow for direct wavefield decomposition through explicit calculation of divergence and curl of the recorded elastic wavefield. Since this approach is based upon the observation of small phase shifts, it requires highly accurate deployment of the receiver configurations. To study the feasibility of a recently proposed P/S‐wave separation scheme, we systematically assess the effects of position and orientation errors of one or several geophones within the recording pattern on technique performance. We find that realistic deployment errors can significantly affect estimates of the divergence and curl of particle velocity. The errors induced by mispositioned or misoriented geophones differ for each of the geophones that make up a pattern. Moreover, the inaccuracies vary with the angle of incidence, potentially affecting analysis procedures applied to the data at a later stage, such as amplitude variation with offset (AVO). Based on a relative L1‐criterion, the position of each receiver needs to be accurate within 10% of the length of the sides of the configuration to obtain meaningful divergence and curl estimates. Furthermore, the output is particularly sensitive to misorientations of geophones, requiring that the orientations of all geophones be accurate within 2°. These observations point to significant difficulties when applying this technique. To alleviate this problem, we present an approach to detect and compensate for such deployment‐related inaccuracies prior to explicit P/S‐wave separation. This strategy is based on a pyramid‐shaped receiver configuration and relies on minimizing the differences between the divergence and curl estimates calculated over the pyramid and each of the four subtetrahedra that comprise the pyramid.

Characterization of naturally fractured Arbuckle Group in the Wellington Field, Kansas, using S-wave amplitude variation with offset

2017 ◽  
Vol 5 (1) ◽  
pp. T49-T63 ◽  
Author(s):  
Menal Gupta ◽  
Kyle Spikes ◽  
Bob Hardage
Keyword(s):  
Wave Amplitude ◽  
Anisotropy Parameter ◽  
P Wave ◽  
Fracture Density ◽  
S Wave ◽  
Amplitude Variation ◽  
Fracture Characterization ◽  
Amplitude Variation With Offset ◽  
S Waves ◽  
Arbuckle Group

S-wave amplitude variation with offset (AVO) analysis is sensitive to the presence of fractures and can provide a high-resolution seismic-based fracture characterization as compared with traditionally used traveltime-based methods. To determine viable attributes for estimation of properties such as spatial density and fluid fill of fractures, S-wave AVO modeling and analysis is carried out in the Wellington Field, Kansas, where 9C-2D seismic data have been acquired. Analysis is performed on the Ordovician fractured-carbonate interval called the Arbuckle Group, which is being considered for [Formula: see text] sequestration. AVO modeling of the Arbuckle interval indicates that differences in AVO intercepts of different S-wave polarizations can estimate S-wave anisotropy parameter [Formula: see text], which gives an estimate of fracture density. In addition, modeling suggests that AVO gradients of [Formula: see text] and [Formula: see text] waves can be used to derive a seismic attribute to discriminate fluid fill in fractures, provided good-quality S-wave gathers are available. The intercept anisotropy (IA) attribute obtained from AVO intercepts of S-waves provides fracture density estimates within the Arbuckle Group. These estimates are consistent with the field-wide, low-frequency observations from seismic velocities and spatially limited, high-frequency estimates obtained from drill cores and sonic and borehole-image logs. The IA attribute highlights possible high-permeability zones in the Upper and Lower Arbuckle suitable for [Formula: see text] injection. The Middle Arbuckle indicates low fracture density, potentially acting as a baffle to vertical flow and providing a seal for the Lower Arbuckle. The gradient anisotropy attribute obtained from the AVO gradient of S-waves suggests that most fractures in the Arbuckle are brine saturated. This attribute has a potential application in monitoring the movement of a [Formula: see text] plume in the Arbuckle Group when time-lapse data become available. These results demonstrate that S-wave AVO attributes can supplement the P-wave derived subsurface properties and significantly reduce uncertainties in subsurface fracture characterization.

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.

AVA analysis after velocity-independent DMO and imaging

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 686-691 ◽  
Author(s):  
Gerald H. F. Gardner ◽  
Anat Canning
Keyword(s):  
Reflection Coefficient ◽  
Peak Amplitude ◽  
Angle Of Incidence ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
The Past ◽  
Reflectivity Function ◽  
Velocity Of Propagation ◽  
Zero Offset ◽  
Amplitude Versus

A common midpoint (CMP) gather usually provides amplitude variation with offset (AVO) information by displaying the reflectivity as the peak amplitude of symmetrical deconvolved wavelets. This puts a reflection coefficient R at every offset h, giving a function R(h). But how do we link h with the angle of incidence, θ, to get the reflectivity function, R(θ)? This is necessary for amplitude versus angle-of-incidence (AVA) analysis. One purpose of this paper is to derive formulas for this linkage after velocity-independent dip-moveout (DMO), done by migrating radial sections, and prestack zero-offset migration. Related studies of amplitude-preserving DMO in the past have dealt with constant-offset DMO but have not given the connection between offset and angle of incidence after processing. The results in the present paper show that the same reflectivity function can be extracted from the imaged volume whether it is produced using radial-trace DMO plus zero-offset migration, constant-offset DMO plus zero-offset migration, or directly by prestack, common-offset migration. The data acquisition geometry for this study consists of parallel, regularly spaced, multifold lines, and the velocity of propagation is constant. Events in the data are caused by an arbitrarily oriented 3-D plane reflector with any reflectivity function. The DMO operation transforms each line of data (m, h, t), i.e., midpoint, half-offset, and time, into an (m1, k, t1) space by Stolt-migrating each radial-plane section of the data, 2h = Ut, with constant velocity U/2. Merging the (m1, k, t1) spaces for all the lines forms an (x, y, k, t1) space, where the first two coordinates are the midpoint location, the third is the new half-offset, and the fourth is the time. Normal moveout (NMO) plus 3-D zero-offset migration of the subspace (x, y, t1) for each k creates a true-amplitude imaged volume (X, Y, k, T). Each peak amplitude in the volume is a reflection coefficient linked to an angle of incidence.

Reflection and refraction of elastic waves at a corrugated interface

1966 ◽  
Vol 56 (1) ◽  
pp. 201-221
Author(s):  
Shuzo Asano
Keyword(s):  
Wave Amplitude ◽  
Normal Incidence ◽  
P Wave ◽  
Irregular Waves ◽  
Angle Of Incidence ◽  
S Wave ◽  
Reflected Waves ◽  
S Waves ◽  
Significant Difference ◽  
Almost All

abstract The effect of a corrugated interface on wave propagation is considered by using the method that was first applied to acoustical gratings by Rayleigh. The problem is what happens when a plane P wave is incident on a corrugated interface that separates two semi-infinite media. As is well known, there are irregular (scattered) waves as well as regular waves. By assuming both the amplitude and the slope of a corrugated interface to be small, quantities of the order of the square of corrugation amplitude are taken into account. In the case of normal incidence for three models considered, the effect of corrugation on reflection is larger than the effect of corrugation on refraction; the amplitude of the regularly reflected waves decreases, and that of the regularly refracted waves and of the irregular waves increases, as the corrugation amplitude becomes larger. Generally, the larger the velocity contrast, the larger the variation of wave amplitude with the wavelength and the amplitude of corrugation. The S wave component generally becomes larger as the wavelength of corrugation becomes smaller. Boundary waves exist, depending upon the ratio of wavelength of corrugation to that of the incident wave. For a specified interface, it is possible that there is a significant difference in wave amplitude as a function of the elastic constants. In the case of oblique incidence, computation was carried out for angles of incidence smaller than 15° for one model. For these small angles of incidence, almost all results for the case of normal incidence still hold. Furthermore, it can be concluded that the effect of the angle of incidence on reflected S waves is larger than for the other waves and that large differences in the amplitudes of waves at different angles of incidence may be expected for the irregular waves.

Fracture-porosity inversion from P-wave AVOA data along 2D seismic lines: An example from the Austin Chalk of southeast Texas

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. B1-B7 ◽  
Author(s):  
Abdullatif A. Al-Shuhail
Keyword(s):  
Aspect Ratio ◽  
Wave Velocity ◽  
P Wave ◽  
S Wave ◽  
Amplitude Variation ◽  
Fracture Porosity ◽  
Amplitude Variation With Offset ◽  
P Wave Velocity ◽  
Austin Chalk ◽  
Southeast Texas

Vertical aligned fractures can significantly enhance the horizontal permeability of a tight reservoir. Therefore, it is important to know the fracture porosity and direction in order to develop the reservoir efficiently. P-wave AVOA (amplitude variation with offset and azimuth) can be used to determine these fracture parameters. In this study, I present a method for inverting the fracture porosity from 2D P-wave seismic data. The method is based on a modeling result that shows that the anisotropic AVO (amplitude variation with offset) gradient is negative and linearly dependent on the fracture porosity in a gas-saturated reservoir, whereas the gradient is positive and linearly dependent on the fracture porosity in a liquid-saturated reservoir. This assumption is accurate as long as the crack aspect ratio is less than 0.1 and the ratio of the P-wave velocity to the S-wave velocity is greater than 1.8 — two conditions that are satisfied in most naturally fractured reservoirs. The inversion then uses the fracture strike, the crack aspect ratio, and the ratio of the P-wave velocity to the S-wave velocity to invert the fracture porosity from the anisotropic AVO gradient after inferring the fluid type from the sign of the anisotropic AVO gradient. When I applied this method to a seismic line from the oil-saturated zone of the fractured Austin Chalk of southeast Texas, I found that the inversion gave a median fracture porosity of 0.21%, which is within the fracture-porosity range commonly measured in cores from the Austin Chalk.

Amplitude-variation-with-offset, elastic-impedence, and wave-equation synthetics — A modeling study

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. C1-C7 ◽  
Author(s):  
Subhashis Mallick
Keyword(s):  
Wave Equation ◽  
Incidence Angle ◽  
Synthetic Data ◽  
P Wave ◽  
Equation Modeling ◽  
Parameter Estimates ◽  
Angle Of Incidence ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Wave Modes

Amplitude-variation-with-offset (AVO) and elastic-impedance (EI) analysis use an approximate plane P-wave reflection coefficient as a function of angle of incidence. AVO and EI both can be used in a three-term or a two-term formulation. This study uses synthetic data to demonstrate that the P-wave primary reflections at large offsets can be contaminated by reflections from other wave modes that can affect the quality of three-term AVO or EI results. The coupling of P-waves and S-waves in seismic-wave propagation through finely layered media generates the interfering wave modes. A methodology such as prestack-wave-equation modeling can properly account for these coupling effects. Both AVO and EI also assume a convolutional model whose accuracy decreases as incidence angles increase. On the other hand, wave-equation modeling is based on the rigorous solution to the wave equation and is valid for any incidence angle. Because wave interference is minimal at small angles, a two-term AVO/EI analysis that restricts input from small angles is likely to give more reliable parameter estimates than a three-term analysis. A three-term AVO/EI analysis should be used with caution and should be calibrated against well data and other data before being used for quantitative analysis.

Computation of dry-rock VP/VS ratio, fluid property factor, and density estimation from amplitude-variation-with-offset inversion

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. R669-R679 ◽  
Author(s):  
Gang Chen ◽  
Xiaojun Wang ◽  
Baocheng Wu ◽  
Hongyan Qi ◽  
Muming Xia
Keyword(s):  
Reservoir Characterization ◽  
Synthetic Data ◽  
Pore Fluid ◽  
Inversion Method ◽  
S Wave ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Fluid Identification ◽  
Fluid Property ◽  
Avo Inversion

Estimating the fluid property factor and density from amplitude-variation-with-offset (AVO) inversion is important for fluid identification and reservoir characterization. The fluid property factor can distinguish pore fluid in the reservoir and the density estimate aids in evaluating reservoir characteristics. However, if the scaling factor of the fluid property factor (the dry-rock [Formula: see text] ratio) is chosen inappropriately, the fluid property factor is not only related to the pore fluid, but it also contains a contribution from the rock skeleton. On the other hand, even if the angle gathers include large angles (offsets), a three-parameter AVO inversion struggles to estimate an accurate density term without additional constraints. Thus, we have developed an equation to compute the dry-rock [Formula: see text] ratio using only the P- and S-wave velocities and density of the saturated rock from well-logging data. This decouples the fluid property factor from lithology. We also developed a new inversion method to estimate the fluid property factor and density parameters, which takes full advantage of the high stability of a two-parameter AVO inversion. By testing on a portion of the Marmousi 2 model, we find that the fluid property factor calculated by the dry-rock [Formula: see text] ratio obtained by our method relates to the pore-fluid property. Simultaneously, we test the AVO inversion method for estimating the fluid property factor and density parameters on synthetic data and analyze the feasibility and stability of the inversion. A field-data example indicates that the fluid property factor obtained by our method distinguishes the oil-charged sand channels and the water-wet sand channel from the well logs.

Three-term amplitude-variation-with-offset projections

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. N51-N65 ◽  
Author(s):  
Vaughn Ball ◽  
Luis Tenorio ◽  
Christian Schiøtt ◽  
Michelle Thomas ◽  
J. P. Blangy
Keyword(s):  
Rock Physics ◽  
Projection Methods ◽  
Well Logs ◽  
Rock Properties ◽  
Inversion Method ◽  
Practical Implementation ◽  
Angle Of Incidence ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Maximum Angle

A three-term (3T) amplitude-variation-with-offset projection is a weighted sum of three elastic reflectivities. Parameterization of the weighting coefficients requires two angle parameters, which we denote by the pair [Formula: see text]. Visualization of this pair is accomplished using a globe-like cartographic representation, in which longitude is [Formula: see text], and latitude is [Formula: see text]. Although the formal extension of existing two-term (2T) projection methods to 3T methods is trivial, practical implementation requires a more comprehensive inversion framework than is required in 2T projections. We distinguish between projections of true elastic reflectivities computed from well logs and reflectivities estimated from seismic data. When elastic reflectivities are computed from well logs, their projection relationships are straightforward, and they are given in a form that depends only on elastic properties. In contrast, projection relationships between reflectivities estimated from seismic may also depend on the maximum angle of incidence and the specific reflectivity inversion method used. Such complications related to projections of seismic-estimated elastic reflectivities are systematized in a 3T projection framework by choosing an unbiased reflectivity triplet as the projection basis. Other biased inversion estimates are then given exactly as 3T projections of the unbiased basis. The 3T projections of elastic reflectivities are connected to Bayesian inversion of other subsurface properties through the statistical notion of Bayesian sufficiency. The triplet of basis reflectivities is computed so that it is Bayes sufficient for all rock properties in the hierarchical seismic rock-physics model; that is, the projection basis contains all information about rock properties that is contained in the original seismic.

Viscoelastic amplitude variation with offset equations with account taken of jumps in attenuation angle

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. N17-N29 ◽  
Author(s):  
Shahpoor Moradi ◽  
Kristopher A. Innanen
Keyword(s):  
Seismic Waves ◽  
Steam Injection ◽  
Seismic Wave Propagation ◽  
Type I ◽  
Amplitude Variation ◽  
Volume Scattering ◽  
Amplitude Variation With Offset ◽  
S Waves ◽  
Fluid Saturation ◽  
Special Cases

Anelastic properties of reservoir rocks are important and sensitive indicators of fluid saturation and viscosity changes due (for instance) to steam injection. The description of seismic waves propagating through viscoelastic continua is quite complex, involving a range of unique homogeneous and inhomogeneous modes. This is true even in the relatively simple theoretical environment of amplitude variation with offset (AVO) analysis. For instance, a complete treatment of the problem of linearizing the solutions of the low-loss viscoelastic Zoeppritz equations to obtain an extended Aki-Richards equations (one that is in accord with the appropriate complex Snell’s law) is lacking in the literature. Also missing is a clear analytical path allowing such forms to be reconciled with more general volume scattering pictures of viscoelastic seismic wave propagation. Our analysis, which provides these two missing elements, leads to approximate reflection and transmission coefficients for the P- and type-I S-waves. These involve additional, complex terms alongside those of the standard isotropic-elastic Aki-Richards equations. The extra terms were shown to have a significant influence on reflection strengths, particularly when the degree of inhomogeneity was high. The particular AVO forms we evaluated were finally shown to be special cases of potentials for volume scattering from viscoelastic inclusions.

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