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.

Frequency-dependent spherical-wave nonlinear AVO inversion in elastic media

2020 ◽  
Vol 223 (2) ◽  
pp. 765-776
Author(s):  
Guangsen Cheng ◽  
Xingyao Yin ◽  
Zhaoyun Zong
Keyword(s):  
Reflection Coefficient ◽  
Wave Reflection ◽  
Fresnel Zone ◽  
Spherical Wave ◽  
Inversion Method ◽  
Elastic Media ◽  
Amplitude Variation With Offset ◽  
Avo Inversion ◽  
Well Location ◽  
The Stability

SUMMARY The plane-wave reflection coefficient (PRC) plays a remarkable role in conventional amplitude variation with offset (AVO) analysis and inversion. Compared with the widely exploited PRC that breaks down at the near- and supercritical incidence angles, the spherical-wave reflection coefficient (SRC) can overcome the influence of wide-angle reflection and give an accurate description of the actual seismic wave reflection phenomenon based on spherical-wave fronts. However, SRC is not widely used in AVO inversion due to its nonlinearity and computational complexity. In our study, the characteristics of frequency–depth-dependent monochromatic SRC are discussed and a novel three-parameter SRC is derived. Compared with the conventional six-parameter SRC, the novel three-parameter SRC improves the stability of spherical-wave AVO inversion. In addition, the concept of SRC within the Fresnel zone is proposed, and the accuracy of SRC within the Fresnel zone in the deep subsurface is tested. Finally, a nonlinear spherical-wave AVO inversion method for elastic media is proposed, which can make full use of all frequency components of wavelet. The robustness of the proposed method is verified by the application on synthetic seismogram with white Gaussian noise. The feasibility and practicability of this method are verified by comparing the spherical-wave AVO inversion results with the filtered well logs at the known well location.

Frequency-Dependent Spherical-Wave Reflection in Acoustic Media: Analysis and Inversion

2017 ◽  
Vol 174 (4) ◽  
pp. 1759-1778 ◽  
Author(s):  
Jingnan Li ◽  
Shangxu Wang ◽  
Jingbo Wang ◽  
Chunhui Dong ◽  
Sanyi Yuan
Keyword(s):  
Wave Reflection ◽  
Spherical Wave ◽  
Media Analysis ◽  
Frequency Dependent ◽  
Acoustic Media ◽  
And Inversion

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 A novel expression of the spherical-wave reflection coefficient at a plane interface

2017 ◽  
Vol 211 (2) ◽  
pp. 700-717 ◽  
Author(s):  
Jingnan Li ◽  
Shangxu Wang ◽  
Yonghui Tao ◽  
Chunhui Dong ◽  
Genyang Tang
Keyword(s):  
Reflection Coefficient ◽  
Complex Plane ◽  
Wave Reflection ◽  
Incidence Angle ◽  
Velocity Ratio ◽  
Spherical Wave ◽  
Density Ratio ◽  
Plane Interface ◽  
Analytical Equation ◽  
Wave Number

Abstract The spherical-wave reflection coefficient (SRC) describes the reflection strength when seismic waves emanating from a point source impinge on an interface. In this study, the SRC at a plane interface between two infinite half-spaces is investigated. We derive an analytical equation of the SRC when kR → 0 (k is the wave number and R is the wave propagation distance). It only depends on the density ratio; it is independent of the velocity ratio and incidence angle. On the other hand, we find that the SRCs at different kR lie along an elliptical curve on the complex plane (the complex plane is a geometric representation of the complex numbers established by the real axis and perpendicular imaginary axis). Based on this feature, we construct a new analytical equation for the reflected spherical wave with high accuracy, which is applicable to both small and large kR. Using the elliptical distribution of the SRCs for a series of frequencies recorded at only one spatial location, the density and velocity ratios can be extracted. This study complements the spherical-wave reflection theory and provides a new basis for acoustic parameters inversion, particularly density inversion.

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