scholarly journals Approximations to seismic AVA responses: Validity and potential in glaciological applications

Geophysics ◽  
2016 ◽  
Vol 81 (1) ◽  
pp. WA1-WA11 ◽  
Author(s):  
Adam D. Booth ◽  
Ezgi Emir ◽  
Anja Diez
Keyword(s):  
Incident Angle ◽  
P Wave ◽  
Curve Matching ◽  
Weak Interface ◽  
Amplitude Variation ◽  
Seismic Properties ◽  
The Future ◽  
Transverse Isotropic ◽  
Comparable Accuracy ◽  
Amplitude Variation With Angle

Amplitude-variation-with-angle (AVA) methods establish the seismic properties of material either side of a reflective interface, and their use is growing in glaciology. The AVA response of an interface is defined by the complex Knott-Zoeppritz (K-Z) equations, numerous approximations to which we typically assume weak interface contrasts and isotropic propagation, inconsistent with the strong contrasts at glacier beds and the vertically transverse isotropic (VTI) fabrics were associated with englacial reflectivity. We considered the validity of a suite of approximate K-Z equations for the exact P-wave reflectivity [Formula: see text] of ice overlying bedrock, sediment and water, and englacial interfaces between isotropic and VTI ice. We found that the approximations of Aki-Richards, Shuey, and Fatti match exact glacier bed reflectivity to within [Formula: see text], smaller than the uncertainty in typical glaciological AVA analyses, but only for maximum incident angle [Formula: see text] limited to 30°. A stricter limit of [Formula: see text] offered comparable accuracy to a hydrocarbon benchmark case of shale overlying gas-charged sand. The VTI-compliant Rüger approximation accurately described englacial reflectivity, to within [Formula: see text], and it can be modified to give a quadratic expression in [Formula: see text] suitable for curve-matching operations. Having shown the circumstances under which AVA approximations were valid for glaciological applications, we have suggested that their interpretative advantages can be exploited in the future AVA interpretations.

Inversion of the seismic AVF/AVA signatures of highly attenuative targets

Geophysics ◽  
2011 ◽  
Vol 76 (1) ◽  
pp. R1-R14 ◽  
Author(s):  
Kristopher A. Innanen
Keyword(s):  
Reflection Coefficient ◽  
Wave Velocity ◽  
P Wave ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Amplitude Variation ◽  
P Wave Velocity ◽  
Amplitude Variation With Angle ◽  
Source Of Information ◽  
Two Parameter

Frequency-dependent seismic field data anomalies, appearing in association with low-[Formula: see text] targets, have, on occasion, been attributed to the presence of a strong absorptive reflection coefficient. This “absorptive reflectivity” represents a potent, and largely untapped, source of information for determining subsurface target properties. It would most likely be encountered where a predominantly elastic/nonattenuating overburden suddenly is interrupted by a highly attenuative target. Series expansions of absorptive reflection coefficients about small parameter contrasts and incidence angles can expose these anomalies to analysis, either frequency-by-frequency (amplitude variation with frequency [AVF]) or angle-by-angle (amplitude variation with angle of incidence [AVA]). Within this framework, variations in P-wave velocity and [Formula: see text] can be estimated separately through a range of direct formulas, both linear and with nonlinear corrections. The latter come to the fore when a contrast from an incidence medium [Formula: see text] (i.e., acoustic/elastic) to a target medium [Formula: see text] is encountered, in which case the linearized estimate can be in error by as much as 50%. Algorithmically, it is a differencing of the reflection coefficient across frequencies that separates [Formula: see text] variations from variations in other parameters. This holds for both two-parameter (P-wave velocity and [Formula: see text]) problems and five-parameter anelastic problems, and would appear to be a general feature of direct absorptive inversion.

Interpreting azimuthal Fourier coefficients for anisotropic and fracture parameters

2015 ◽  
Vol 3 (3) ◽  
pp. ST9-ST27 ◽  
Author(s):  
Jonathan E. Downton ◽  
Benjamin Roure
Keyword(s):  
Fourier Coefficients ◽  
P Wave ◽  
Amplitude Variation ◽  
Data Set ◽  
Amplitude Variation With Offset ◽  
Fracture Parameters ◽  
Isotropic Media ◽  
Transverse Isotropic ◽  
Axis Of Symmetry ◽  
Vertical Fractures

Amplitude variation with offset and azimuth (AVOAz) analysis can be separated into two separate parts: amplitude variation with offset (AVO) analysis and amplitude variation with azimuth (AVAz) analysis. Useful information about fractures and anisotropy can be obtained just by examining the AVAz. The AVAz can be described as a sum of sinusoids of different periodicities, each characterized by its magnitude and phase. This sum is mathematically equivalent to a Fourier series, and hence the coefficients describing the AVAz response are azimuthal Fourier coefficients (FCs). This FC parameterization is purely descriptive. The aim of this paper is to help the interpreter understand what these coefficients mean in terms of anisotropic and fracture parameters for the case of P-wave reflectivity using a linearized approximation. The FC representation is valid for general anisotropy. However, to gain insight into the significance of FCs, more restrictive assumptions about the anisotropy or facture system must be assumed. In the case of transverse isotropic media with a horizontal axis of symmetry, the P-wave reflectivity linearized approximation may be rewritten in terms of azimuthal FCs with the magnitude and phase of the different FCs corresponding to traditional AVAz attributes. Linear slip theory is used to show that the FCs can be interpreted similarly for the cases of a single set of parallel vertical fractures in isotropic media and in transverse isotropic media with a vertical axis of symmetry (VTI). The magnitude of the FCs depends on the fracture weakness parameters and the background media. For the case of vertical fractures in a VTI background, the AVOAz inverse problem is underdetermined, so extra information must be incorporated to determine how the weights are modified due to this background anisotropy. We evaluated this on a 3D data set from northwest Louisiana for which the main target was the Haynesville shale.

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.

Direct vector-field method to obtain angle-domain common-image gathers from isotropic acoustic and elastic reverse time migration

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB135-WB149 ◽  
Author(s):  
Qunshan Zhang ◽  
George A. McMechan
Keyword(s):  
Direct Method ◽  
Incident Angle ◽  
Field Method ◽  
Propagation Direction ◽  
P Wave ◽  
Common Source ◽  
Spatial Gradient ◽  
Reverse Time ◽  
S Wave ◽  
Time Migration

We have developed an alternative (new) method to produce common-image gathers in the incident-angle domain by calculating wavenumbers directly from the P-wave polarization rather than using the dominant wavenumber as the normal to the source wavefront. In isotropic acoustic media, the wave propagation direction can be directly calculated as the spatial gradient direction of the acoustic wavefield, which is parallel to the wavenumber direction (the normal to the wavefront). Instantaneous wavenumber, obtained via a novel Hilbert transform approach, is used to calculate the local normal to the reflectors in the migrated image. The local incident angle is produced as the difference between the propagation direction and the normal to the reflector. By reordering the migrated images (over all common-source gathers) with incident angle, common-image gathers are produced in the incident-angle domain. Instantaneous wavenumber takes the place of the normal to the reflector in the migrated image. P- and S-wave separations allow both PP and PS common-image gathers to be calculated in the angle domain. Unlike the space-shift image condition for calculating the common-image gather in angle domain, we use the crosscorrelation image condition, which is substantially more efficient. This is a direct method, and is less dependent on the data quality than the space-shift method. The concepts were successfully implemented and tested with 2D synthetic acoustic and elastic examples, including a complicated (Marmousi2) model that illustrates effects of multipathing in angle-domain common-image gathers.

Rock-physics templates based on seismic Q

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. MR13-MR23 ◽  
Author(s):  
Stefano Picotti ◽  
José M. Carcione ◽  
Jing Ba
Keyword(s):  
Quality Factor ◽  
Acoustic Impedance ◽  
Rock Physics ◽  
P Wave ◽  
Gas Oil ◽  
Seismic Properties ◽  
Gas Saturation ◽  
Seismic Quality Factor ◽  
Porosity And Permeability ◽  
Higher Sensitivity

We build rock-physics templates (RPTs) for reservoir rocks based on seismic quality factors. In these templates, the effects of partial saturation, porosity, and permeability on the seismic properties are described by generalizing the Johnson mesoscopic-loss model to a distribution of gas-patch sizes in brine- and oil-saturated rocks. This model addresses the wave-induced fluid flow attenuation mechanism, by which part of the energy of the fast P-wave is converted into the slow P (Biot) diffusive mode. We consider patch sizes, whose probability density function is defined by a normal (Gaussian) distribution. The complex bulk modulus of the composite medium is obtained with the Voigt-Reuss-Hill average, and we show that the results are close to those obtained with the Hashin-Shtrikman average. The templates represent the seismic dissipation factor (reciprocal of seismic quality factor) as a function of the P-wave velocity, acoustic impedance, and [Formula: see text] (P to S velocity ratio), for isolines of saturation, porosity, and permeability. They differentiate between oil and brine on the basis of the quality factor, with the gas-brine case showing more dissipation than the gas-oil case. We obtain sensitivity maps of the seismic properties to gas saturation and porosity for brine and oil. Unlike the gas-brine case, which shows higher sensitivity of attenuation to gas saturation, the gas-oil case shows higher sensitivity to porosity, and higher acoustic impedance and [Formula: see text] sensitivity values versus saturation. The RPTs can be used for a robust sensitivity analysis, which provides insights on seismic attributes for hydrocarbon detection and reservoir delineation. The templates are also relevant for studies related to [Formula: see text]-storage monitoring.

Case study: Phase-component amplitude variation with angle

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. B285-B297
Author(s):  
Elita Selmara De Abreu ◽  
John Patrick Castagna ◽  
Gabriel Gil
Keyword(s):  
Thin Layer ◽  
Thin Layers ◽  
Phase Response ◽  
Study Phase ◽  
Phase Decomposition ◽  
Seismic Modeling ◽  
Phase Component ◽  
Amplitude Variation ◽  
High Impedance ◽  
Amplitude Variation With Angle

In detectable and isolated thin layers below seismic resolution, phase decomposition can theoretically be used to discriminate relatively high-impedance thin-layer responses from low-impedance reservoir responses. Phase decomposition can be used to isolate seismic amplitudes with a particular phase response or to decompose the seismic trace into symmetrical and antisymmetrical phase components. These components sum to form the original trace. Assuming zero-phase seismic data and normal American polarity, seismically thin layers that are high impedance relative to overlying and underlying half-spaces are seen on the [Formula: see text] phase component, whereas a relatively low-impedance thin layer will appear on the [Formula: see text] phase component. When such phase decomposition is applied to prestack attributes on a 2D line across a thin, 8 m thick, gas-saturated reservoir in the Western Canadian Sedimentary Basin of Alberta, Canada, amplitude-variation-with-angle is magnified on the [Formula: see text] phase component. The [Formula: see text] far-offset component allows the lateral extent of the reservoir to be better delineated. This amplification is also seen on the [Formula: see text] phase component of the gradient attribute. These results are corroborated by seismic modeling that indicates the same phase-component relationships for near- and far-angle stacks as are observed on the real data. Fluid substitution and seismic modeling indicate that, relative to full-phase data, the mixed-phase response observed in this study exhibits variations in fluid effects that are magnified and better observed at far angles on the [Formula: see text] phase component.

Petrophysical properties variation of bitumen-bearing carbonates at increasing temperatures from laboratory to model

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. MR297-MR308
Author(s):  
Roberta Ruggieri ◽  
Fabio Trippetta
Keyword(s):  
Central Italy ◽  
Carbonate Reservoir ◽  
P Wave ◽  
Petrophysical Properties ◽  
S Wave ◽  
Reservoir Properties ◽  
Velocity Change ◽  
Seismic Properties ◽  
Wave Velocities ◽  
Velocity Changes

Variations in reservoir seismic properties can be correlated to changes in saturated-fluid properties. Thus, the determination of variation in petrophysical properties of carbonate-bearing rocks is of interest to the oil exploration industry because unconventional oils, such as bitumen (HHC), are emerging as an alternative hydrocarbon reserve. We have investigated the temperature effects on laboratory seismic wave velocities of HHC-bearing carbonate rocks belonging to the Bolognano Formation (Majella Mountain, central Italy), which can be defined as a natural laboratory to study carbonate reservoir properties. We conduct an initial characterization in terms of porosity and density for the carbonate-bearing samples and then density and viscosity measurements for the residual HHC, extracted by HCl dissolution of the hosting rock. Acoustic wave velocities are recorded from ambient temperature to 90°C. Our acoustic velocity data point out an inverse relationship with temperature, and compressional (P) and shear (S) wave velocities show a distinct trend with increasing temperature depending on the amount of HHC content. Indeed, samples with the highest HHC content show a larger gradient of velocity changes in the temperature range of approximately 50°C–60°C, suggesting that the bitumen can be in a fluid state. Conversely, below approximately 50°C, the velocity gradient is lower because, at this temperature, bitumen can change its phase in a solid state. We also propose a theoretical model to predict the P-wave velocity change at different initial porosities for HHC-saturated samples suggesting that the velocity change mainly is related to the absolute volume of HHC.

scholarly journals Time-lapse monitoring of fluid-induced geophysical property variations within an unstable earthwork using P-wave refraction

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. EN17-EN27 ◽  
Author(s):  
Paolo Bergamo ◽  
Ben Dashwood ◽  
Sebastian Uhlemann ◽  
Russell Swift ◽  
Jonathan E. Chambers ◽  
...  
Keyword(s):  
Time Lapse ◽  
P Wave ◽  
Data Sets ◽  
Time Intervals ◽  
Total Period ◽  
Seismic Properties ◽  
Wave Refraction ◽  
Regular Time ◽  
Spatial Locations ◽  
Spatial Regularization

A significant portion of the UK’s transportation system relies on a network of geotechnical earthworks (cuttings and embankments) that were constructed more than 100 years ago, whose stability is affected by the change in precipitation patterns experienced over the past few decades. The vulnerability of these structures requires a reliable, cost- and time-effective monitoring of their geomechanical condition. We have assessed the potential application of P-wave refraction for tracking the seasonal variations of seismic properties within an aged clay-filled railway embankment, located in southwest England. Seismic data were acquired repeatedly along the crest of the earthwork at regular time intervals, for a total period of 16 months. P-wave first-break times were picked from all available recorded traces, to obtain a set of hodocrones referenced to the same spatial locations, for various dates along the surveyed period of time. Traveltimes extracted from each acquisition were then compared to track the pattern of their temporal variability. The relevance of such variations over time was compared with the data experimental uncertainty. The multiple set of hodocrones was subsequently inverted using a tomographic approach, to retrieve a time-lapse model of [Formula: see text] for the embankment structure. To directly compare the reconstructed [Formula: see text] sections, identical initial models and spatial regularization were used for the inversion of all available data sets. A consistent temporal trend for P-wave traveltimes, and consequently for the reconstructed [Formula: see text] models, was identified. This pattern could be related to the seasonal distribution of precipitation and soil-water content measured on site.

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.

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