Reflection coefficient frequency-dependent inversion of a planar interface with spherical waves: Using critical and post-critical angles

2021 ◽  
pp. 104522
Author(s):  
Binpeng Yan ◽  
Shangxu Wang ◽  
Yongzhen Ji ◽  
Nuno Vieira da Silva ◽  
Xingguo Huang
Keyword(s):  
Reflection Coefficient ◽  
Planar Interface ◽  
Frequency Dependent ◽  
Spherical Waves

Inversion of differences in frequency components of azimuthal seismic data for indicators of oil-bearing fractured reservoirs based on an attenuative cracked model

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. R163-R175
Author(s):  
Huaizhen Chen ◽  
Junxiao Li ◽  
Kristopher A. Innanen
Keyword(s):  
Reflection Coefficient ◽  
Stiffness Matrix ◽  
Fractured Reservoirs ◽  
P Wave ◽  
Parameter Estimates ◽  
Fluid Viscosity ◽  
Mathematical Form ◽  
Data Set ◽  
Frequency Dependent ◽  
Frequency Components

Based on a model of attenuative cracked rock, we have derived a simplified and frequency-dependent stiffness matrix associated with (1) a rock volume containing aligned and partially saturated cracks and (2) a new indicator of oil-bearing fractured reservoirs, which is related to pressure relaxation in cracked rocks and influenced by fluid viscosity and saturation. Starting from the mathematical form of a perturbation in this stiffness matrix across a reflecting interface separating two attenuative cracked media, we set up a linearized P-wave to P-wave reflection coefficient as an azimuthally and frequency-dependent function of dry rock elastic properties, dry fracture weaknesses, and the new indicator. By varying this reflection coefficient with azimuthal angle, we derive a further expression referred to as the quasidifference in elastic impedance, or [Formula: see text], which is primarily affected by the dry fracture weaknesses and the new indicator. An inversion approach is established to use differences in frequency components of seismic amplitudes to estimate these weaknesses and the indicator based on the derived [Formula: see text]. In synthetic inversion tests, we determine that the approach produces interpretable parameter estimates in the presence of data with a moderate signal-to-noise ratio (S/N). Testing on a real data set suggests that reliable fracture weakness and indicator are generated by the approach; fractured and oil-bearing reservoirs are identified through a combination of the dry fracture weakness and the new indicator.

Frequency-dependent spherical-wave reflection coefficient inversion in acoustic media: Theory to practice

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. R425-R435
Author(s):  
Binpeng Yan ◽  
Shangxu Wang ◽  
Yongzhen Ji ◽  
Xingguo Huang ◽  
Nuno V. da Silva
Keyword(s):  
Reflection Coefficient ◽  
Wave Reflection ◽  
Incident Angle ◽  
Spherical Wave ◽  
Frequency Dependent ◽  
Amplitude Variation With Offset ◽  
Reflection Data ◽  
Alternative Approach ◽  
Acoustic Media ◽  
The Time Domain

As an approximation of the spherical-wave reflection coefficient (SRC), the plane-wave reflection coefficient does not fully describe the reflection phenomenon of a seismic wave generated by a point source. The applications of SRC to improve analyses of seismic data have also been studied. However, most of the studies focus on the time-domain SRC and its benefit to using the long-offset information instead of the dependency of SRC on frequency. Consequently, we have investigated and accounted for the frequency-dependent spherical-wave reflection coefficient (FSRC) and analyzed the feasibility of this type of inversion. Our inversion strategy requires a single incident angle using reflection data for inverting the density and velocity ratios, which is distinctly different from conventional inversion methods using amplitude variation with offset. Hence, this investigation provides an alternative approach for estimating media properties in some contexts, especially when the range of aperture of the reflection angles is limited. We apply the FSRC theory to the inversion of noisy synthetic and field data using a heuristic algorithm. The multirealization results of the inversion strategy are consistent with the feasibility analysis and demonstrate the potential of the outlined method for practical application.

A method for predicting the reflection and refraction of spherical waves across a planar interface

1994 ◽  
Vol 76 (1) ◽  
pp. 25-32 ◽  
Author(s):  
J. R. Furlong ◽  
Catherine F. Westbury ◽  
E. A. Phillips
Keyword(s):  
Planar Interface ◽  
Spherical Waves ◽  
Reflection And Refraction

Estimating elastic properties and attenuation factor from different frequency components of observed seismic data

2019 ◽  
Vol 220 (2) ◽  
pp. 794-805
Author(s):  
Huaizhen Chen
Keyword(s):  
Reflection Coefficient ◽  
Elastic Properties ◽  
Seismic Data ◽  
Wave Attenuation ◽  
Attenuation Factor ◽  
P Wave ◽  
S Wave ◽  
Data Set ◽  
Frequency Dependent ◽  
Frequency Components

SUMMARY Based on an attenuation model, we first express frequency-dependent P- and S-wave attenuation factors as a function of P-wave maximum attenuation factor, and then we re-express P- and S-wave velocities in anelastic media and derive frequency-dependent stiffness parameters in terms of P-wave maximum attenuation factor. Using the derived stiffness parameters, we propose frequency-dependent reflection coefficient in terms of P- and S-wave moduli at critical frequency and P-wave maximum attenuation factor for the case of an interface separating two attenuating media. Based on the derived reflection coefficient, we establish an approach to utilize different frequency components of observed seismic data to estimate elastic properties (P- and S-wave moduli and density) and attenuation factor, and following a Bayesian framework, we construct the objective function and an iterative method is employed to solve the inversion problem. Tests on synthetic data confirm that the proposed approach makes a stable and robust estimation of unknown parameters in the case of seismic data containing a moderate noise/error. Applying the proposed approach to a real data set illustrates that a reliable attenuation factor is obtained from observed seismic data, and the ability of distinguishing oil-bearing reservoirs is improved combining the estimated elastic properties and P-wave attenuation factor.

scholarly journals Quantum entanglement and statistics of photons on a beam splitter in the form of coupled waveguides

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
D. N. Makarov ◽  
E. S. Gusarevich ◽  
A. A. Goshev ◽  
K. A. Makarova ◽  
S. N. Kapustin ◽  
...  
Keyword(s):  
Reflection Coefficient ◽  
Transmission Coefficient ◽  
Quantum Entanglement ◽  
Beam Splitter ◽  
Photon Statistics ◽  
Frequency Dependent ◽  
Coupled Waveguides

AbstractIt is well known that a beam splitter (BS) can be used as a source of photon quantum entanglement. This is due to the fact that the statistics of photons changes at the output ports of the BS. Usually, quantum entanglement and photon statistics take into account the constancy of the reflection coefficient R or the transmission coefficient T of the BS, where $$R + T = 1$$ R + T = 1 . It has recently been shown that if BS is used in the form of coupled waveguides, the coefficients R and T will depend on the photon frequencies. In this paper, it is shown that the quantum entanglement and statistics of photons at the output ports of a BS can change significantly if a BS is used in the form of coupled waveguides, where the coefficients R and T are frequency-dependent.

Sign in / Sign up

Export Citation Format

Share Document