scholarly journals Linearized Frequency-Dependent Reflection Coefficient and Attenuated Anisotropic Characteristics of Q-VTI Model

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8506
Author(s):  
Yahua Yang ◽  
Xingyao Yin ◽  
Bo Zhang ◽  
Danping Cao ◽  
Gang Gao
Keyword(s):  
Reflection Coefficient ◽  
Seismic Wave ◽  
Incident Angle ◽  
Transversely Isotropic ◽  
P Wave ◽  
Reference Frequency ◽  
Quality Factors ◽  
S Wave ◽  
Reservoir Properties ◽  
Simultaneous Inversion

Seismic wave exhibits the characteristics of anisotropy and attenuation while propagating through the fluid-bearing fractured or layered reservoirs, such as fractured carbonate and shale bearing oil or gas. We derive a linearized reflection coefficient that simultaneously considers the effects of anisotropy and attenuation caused by fractures and fluids. Focusing on the low attenuated transversely isotropic medium with a vertical symmetry axis (Q-VTI) medium, we first express the complex stiffness tensors based on the perturbation theory and the linear constant Q model at an arbitrary reference frequency, and then we derive the linearized approximate reflection coefficient of P to P wave. It decouples the P- and S-wave inverse quality factors, and Thomsen-style attenuation-anisotropic parameters from complex P- and S-wave velocity and complex Thomsen anisotropic parameters. By evaluating the reflection coefficients around the solution point of the interface of two models, we analyze the characteristics of reflection coefficient vary with the incident angle and frequency and the effects of different Thomsen anisotropic parameters and attenuation factors. Moreover, we realize the simultaneous inversion of all parameters in the equation using an actual well log as a model. We conclude that the derived reflection coefficient may provide a theoretical tool for the seismic wave forward modeling, and again it can be implemented to predict the reservoir properties of fractures and fluids based on diverse inversion methods of seismic data.

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.

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.

Seismic reflectivity of hydraulic fractures approximated by thin fluid layers

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. T79-T87 ◽  
Author(s):  
A. Oelke ◽  
D. Alexandrov ◽  
I. Abakumov ◽  
S. Glubokovskikh ◽  
R. Shigapov ◽  
...  
Keyword(s):  
Analytical Solutions ◽  
Fluid Layer ◽  
Synthetic Data ◽  
P Wave ◽  
Hydraulic Fractures ◽  
Reflection Coefficients ◽  
S Wave ◽  
Reservoir Properties ◽  
Thin Fluid ◽  
Theoretical Results

We have analyzed the angle-dependent reflectivity of microseismic wavefields at a hydraulic fracture, which we modeled as an ideal thin fluid layer embedded in an elastic, isotropic solid rock. We derived full analytical solutions for the reflections of an incident P-wave, the P-P and P-S reflection coefficients, as well as for an incident S-wave, and the S-S and S-P reflection coefficients. The rather complex analytical solutions were then approximated and we found that these zero-thickness limit approximations are in good agreement with the linear slip model, representing a fracture at slip contact. We compared the analytical solutions for the P-P reflections with synthetic data that were derived using finite-difference modeling and found that the modeling confirmed our theoretical results. For typical parameters of microseismic monitoring by hydraulic fracturing, e.g., a layer thickness of [Formula: see text] and frequencies of [Formula: see text], the reflection coefficients depend on the Poisson’s ratio. Furthermore, the reflection coefficients of an incident S-wave are remarkably high. Theoretical results suggested that it is feasible to image hydraulic fractures using microseismic events as a source and to solve the inverse problem, that is, to interpret reflection coefficients extracted from microseismic data in terms of reservoir properties.

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.

scholarly journals Phased array compaction cell for measurement of the transversely isotropic elastic properties of compacting sediments

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. WA113-WA123 ◽  
Author(s):  
Kurt T. Nihei ◽  
Seiji Nakagawa ◽  
Frederic Reverdy ◽  
Larry R. Myer ◽  
Luca Duranti ◽  
...  
Keyword(s):  
Elastic Properties ◽  
Phased Array ◽  
Transversely Isotropic ◽  
P Wave ◽  
S Wave ◽  
P Waves ◽  
Array Measurements ◽  
Experimental Apparatus ◽  
Marine Sediment Sample ◽  
Plane P Waves

Sediments undergoing compaction typically exhibit transversely isotropic (TI) elastic properties. We present a new experimental apparatus, the phased array compaction cell, for measuring the TI elastic properties of clay-rich sediments during compaction. This apparatus uses matched sets of P- and S-wave ultrasonic transducers located along the sides of the sample and an ultrasonic P-wave phased array source, together with a miniature P-wave receiver on the top and bottom ends of the sample. The phased array measurements are used to form plane P-waves that provide estimates of the phase velocities over a range of angles. From these measurements, the five TI elastic constants can be recovered as the sediment is compacted, without the need for sample unloading, recoring, or reorienting. This paper provides descriptions of the apparatus, the data processing, and an application demonstrating recovery of the evolving TI properties of a compacting marine sediment sample.

Inversion of reflection traveltimes for transverse isotropy

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1095-1107 ◽  
Author(s):  
Ilya Tsvankin ◽  
Leon Thomsen
Keyword(s):  
Wave Velocity ◽  
Vertical Velocity ◽  
Joint Inversion ◽  
Transverse Isotropy ◽  
Taylor Series Expansion ◽  
High Sensitivity ◽  
Transversely Isotropic ◽  
P Wave ◽  
S Wave ◽  
Quartic Term

In anisotropic media, the short‐spread stacking velocity is generally different from the root‐mean‐square vertical velocity. The influence of anisotropy makes it impossible to recover the vertical velocity (or the reflector depth) using hyperbolic moveout analysis on short‐spread, common‐midpoint (CMP) gathers, even if both P‐ and S‐waves are recorded. Hence, we examine the feasibility of inverting long‐spread (nonhyperbolic) reflection moveouts for parameters of transversely isotropic media with a vertical symmetry axis. One possible solution is to recover the quartic term of the Taylor series expansion for [Formula: see text] curves for P‐ and SV‐waves, and to use it to determine the anisotropy. However, this procedure turns out to be unstable because of the ambiguity in the joint inversion of intermediate‐spread (i.e., spreads of about 1.5 times the reflector depth) P and SV moveouts. The nonuniqueness cannot be overcome by using long spreads (twice as large as the reflector depth) if only P‐wave data are included. A general analysis of the P‐wave inverse problem proves the existence of a broad set of models with different vertical velocities, all of which provide a satisfactory fit to the exact traveltimes. This strong ambiguity is explained by a trade‐off between vertical velocity and the parameters of anisotropy on gathers with a limited angle coverage. The accuracy of the inversion procedure may be significantly increased by combining both long‐spread P and SV moveouts. The high sensitivity of the long‐spread SV moveout to the reflector depth permits a less ambiguous inversion. In some cases, the SV moveout alone may be used to recover the vertical S‐wave velocity, and hence the depth. Success of this inversion depends on the spreadlength and degree of SV‐wave velocity anisotropy, as well as on the constraints on the P‐wave vertical velocity.

scholarly journals Evidence for deep icequakes in an Alpine glacier

2000 ◽  
Vol 31 ◽  
pp. 85-90 ◽  
Author(s):  
N. Deichmann ◽  
J. Ansorge ◽  
F. Scherbaum ◽  
A. Aschwanden ◽  
F. Bernard ◽  
...  
Keyword(s):  
Rayleigh Wave ◽  
Three Dimensional ◽  
Focal Depth ◽  
Vertical Component ◽  
Swiss Alps ◽  
P Wave ◽  
S Wave ◽  
Glacier Surface ◽  
Simultaneous Inversion ◽  
Wave Velocities

AbstractTo obtain more reliable information about the focal-depth distribution of icequakes, in April 1997 we operated an array of seven portable digital seismographs on Unteraargletscher, central Swiss Alps. Over 5000 events were detected by at least two instruments during the 9 day recording period. P-wave velocities (3770 m f) were determined from several calibration shots detonated at the glacier surface as well as in a 49 m deep borehole, whereas S-wave velocities (1860 ms–1) were derived from a simultaneous inversion for Vp/Vs6 applied to 169 icequakes. So far, hypocentral locations have been calculated for over 300 icequakes. Besides confirming the occurrence of shallow events associated with the opening of crevasses, our results show that a small but significant fraction of the hypocenters are located at or near the glacier bed. One event was found at an intermediate depth of about 120 m. Three-dimensional particle-motion diagrams of both explosions and icequakes clearly demonstrate that all vertical component seismograms from shallow sources are dominated by the Rayleigh wave. On the other hand, for events occurring at depths greater than about 40 m, the Rayleigh wave disappears almost entirely. Therefore, a qualitative analysis of the signal character provides direct information on the focal depth of an event and was used as an independent check of the locations obtained from traditional arrival-time inversions. Thus, our results demonstrate that deep icequakes do occur and that simple rheological models, according to which brittle deformation is restricted to the uppermost part of a glacier, may need revision.

SIMULTANEOUS INVERSION FOR S-WAVE VELOCITY DENSITY FROM THE SV-SV WAVE

Geophysics ◽  
2020 ◽  
pp. 1-50
Author(s):  
Feng Zhang
Keyword(s):  
Wave Velocity ◽  
Oil And Gas ◽  
Incident Angle ◽  
Inversion Method ◽  
S Wave ◽  
Simultaneous Inversion ◽  
Pp Wave ◽  
Velocity Information ◽  
Using Data ◽  
Two Parameters

Knowledge of shear-wave velocity ( Vs) and density ( ρ) is essential for oil and gas reservoir detection and characterization. However, reliable recovery of both parameters, especially density, from the reflected PP-wave data is a difficult issue, because this inverse problem is highly illconditioned. The reflected SV-SV wave is easier to process than the PS-wave, and can provide better estimates of Vs and ρ than the PP-wave, because it is more sensitive to these parameters than the PP-wave. I present a simultaneous inversion for Vs and ρ based on a modified approximation of the SV-SV wave reflection coefficient. The modified equation includes only two parameters (natural logarithms of Vs and ρ) to be inverted, and it has high accuracy even at large incident angles and for strong impedance contrasts. I show that simultaneous inversion based on the modified approximation is well-posed when using data of small-to-moderate incident angle (20°-30°), and the misfit function can be easily regularized. The new simultaneous inversion method is applied to a SV-SV wave prestack dataset acquired from a 2D ninecomponent survey. The field data example demonstrates that the proposed method can recover stable and high-resolution density and S-wave velocity information, which can be used to investigate rock mineral composition, porosity and fluid content.

Simultaneous inversion of PP and PS seismic data

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. R1-R10 ◽  
Author(s):  
Helene Hafslund Veire ◽  
Martin Landrø
Keyword(s):  
Seismic Data ◽  
Reservoir Characterization ◽  
Model Building ◽  
Joint Inversion ◽  
P Wave ◽  
Inversion Method ◽  
System Of Equations ◽  
S Wave ◽  
Data Set ◽  
Simultaneous Inversion

Elastic parameters derived from seismic data are valuable input for reservoir characterization because they can be related to lithology and fluid content of the reservoir through empirical relationships. The relationship between physical properties of rocks and fluids and P-wave seismic data is nonunique. This leads to large uncertainties in reservoir models derived from P-wave seismic data. Because S- waves do not propagate through fluids, the combined use of P-and S-wave seismic data might increase our ability to derive fluid and lithology effects from seismic data, reducing the uncertainty in reservoir characterization and thereby improving 3D reservoir model-building. We present a joint inversion method for PP and PS seismic data by solving approximated linear expressions of PP and PS reflection coefficients simultaneously using a least-squares estimation algorithm. The resulting system of equations is solved by singular-value decomposition (SVD). By combining the two independent measurements (PP and PS seismic data), we stabilize the system of equations for PP and PS seismic data separately, leading to more robust parameter estimation. The method does not require any knowledge of PP and PS wavelets. We tested the stability of this joint inversion method on a 1D synthetic data set. We also applied the methodology to North Sea multicomponent field data to identify sand layers in a shallow formation. The identified sand layers from our inverted sections are consistent with observations from nearby well logs.

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