Seismic inversion using complex spherical-wave reflection coefficient at different offsets and frequencies

Geophysics ◽  
2021 ◽  
pp. 1-47
Author(s):  
Guangsen Cheng ◽  
Xingyao Yin ◽  
Zhaoyun Zong ◽  
Tongxing Xia ◽  
Jianli Wang ◽  
...  
Keyword(s):  
Reflection Coefficient ◽  
Wave Amplitude ◽  
Wave Reflection ◽  
Spherical Wave ◽  
Frequency Component ◽  
Seismic Inversion ◽  
Synthetic Seismogram ◽  
S Wave ◽  
Wave Inversion ◽  
Frequency Components

Compared with the plane-wave reflection coefficient, the spherical-wave reflection coefficient (SRC) can more accurately describe the reflected wavefield excited by a point source, especially in the case of low seismic frequency and short travel distance. However, unlike the widely used plane-wave amplitude-variation-with-offset/frequency (AVO/AVF) inversion, the practical application of spherical-wave AVO/AVF inversion in multilayer elastic media is still in the exploratory stage. One of the difficulties is how to fully use the amplitude and phase information of the complex-valued SRC and the spherical-wave response property of each frequency component to obtain the spherical-wave synthetic seismogram in multilayer elastic media. In view of this, we have developed a complex convolution model considering the amplitude and phase information of a SRC to obtain the complex synthetic seismogram of a certain frequency component. A simple harmonic superposition method is further developed. By superposing the complex synthetic seismograms of different frequency components, the synthetic seismogram of the full-frequency band can be obtained. In addition, a novel three-parameter SRC in terms of P- and S-wave moduli and density is derived. Based on the SRC and complex seismic traces with different offsets (or incidence angles) and frequency components, an inversion approach of complex spherical-wave amplitude and phase variation with offset and frequency is proposed. A noisy synthetic data example verifies the robustness of our complex spherical-wave inversion approach. Field data examples indicate that the P- and S-wave moduli estimated by the complex spherical-wave inversion approach can reasonably match the filtered well-logging data. Considering spherical waves rather than plane waves can improve the accuracy of seismic inversion results.

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.

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.

The domain of applicability of acoustic full-waveform inversion for marine seismic data

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCC91-WCC103 ◽  
Author(s):  
Christophe Barnes ◽  
Marwan Charara
Keyword(s):  
Seismic Data ◽  
Seismic Inversion ◽  
Three Dimensions ◽  
Acoustic Medium ◽  
Physical Parameters ◽  
S Wave ◽  
Data Set ◽  
Reflection Seismic ◽  
Wave Inversion ◽  
Full Wave

Marine reflection seismic data inversion is a compute-intensive process, especially in three dimensions. Approximations often are made to limit the number of physical parameters we invert for, or to speed up the forward modeling. Because the data often are dominated by unconverted P-waves, one popular approximation is to consider the earth as purely acoustic, i.e., no shear modulus. The material density sometimes is taken as a constant. Nonlinear waveform seismic inversion consists of iteratively minimizing the misfit between the amplitudes of the measured and the modeled data. Approximations, such as assuming an acoustic medium, lead to incorrect modeling of the amplitudes of the seismic waves, especially with respect to amplitude variation with offset (AVO), and therefore have a direct impact on the inversion results. For evaluation purposes, we have performed a series of inversions with different approximations and different constraints whereby the synthetic data set to recover is computed for a 1D elastic medium. A series of numerical experiments, although simple, help to define the applicability domain of the acoustic assumption. Acoustic full-wave inversion is applicable only when the S-wave velocity and the density fields are smooth enough to reduce the AVO effect, or when the near-offset seismograms are inverted with a good starting model. However, in many realistic cases, acoustic approximation penalizes the full-wave inversion of marine reflection seismic data in retrieving the acoustic parameters.

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.

Azimuthal Fourier coefficient inversion for horizontal and vertical fracture characterization in weakly orthorhombic media

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. C199-C214
Author(s):  
Guangzhi Zhang ◽  
Lin Li ◽  
Xinpeng Pan ◽  
Hengxin Li ◽  
Junzhou Liu ◽  
...  
Keyword(s):  
Reflection Coefficient ◽  
Wave Reflection ◽  
Bayesian Inversion ◽  
Model Parameters ◽  
Orthorhombic Symmetry ◽  
S Wave ◽  
Elastic Parameters ◽  
Vertical Fracture ◽  
Pp Wave ◽  
Vertical Fractures

Horizontally and vertically aligned fractures (joints) permeated in an isotropic background can give rise to a long-wavelength equivalent orthorhombic medium, which is common for naturally fractured reservoirs. We have developed a feasible approach to characterize the horizontal and vertical fractures using observed azimuthal seismic reflection data. For weak anisotropy, we assume that the horizontal and vertical fractures are decoupled. Using a linear-slip orthorhombic model, we first obtain analytic expressions for the effective elastic stiffness matrix and the corresponding perturbed matrix of an effective orthorhombic anisotropic elastic medium. Combining the scattering function and the perturbed matrix of the orthorhombic medium, we then derive a linearized PP-wave reflection coefficient of effective orthorhombic medium in terms of compressional-wave (P-wave) and shear-wave (S-wave) moduli, density, and horizontal- and vertical-fracture-induced normal and tangential weaknesses. To handle the inverse problem for multiple model parameters in an orthorhombic medium, we reexpress the linearized PP-wave reflection coefficient as a Fourier series. According to the sensitivity analysis of Fourier coefficients (FCs) to isotropic background elastic parameters and four fracture weaknesses, we finally establish a three-step inversion approach to describe the orthorhombic model, which involves (1) estimation of the FCs at different incidence angles from observed azimuthal seismic data and determination of the symmetry axis azimuth, (2) an iterative Bayesian inversion for isotropic background elastic parameters and fracture weaknesses of horizontal fractures from the zeroth-order FC, and (3) an iterative Bayesian inversion for fracture weaknesses of vertical fractures from the second-order FC. The proposed approach is validated by tests on synthetic and field data sets, which demonstrates that the inversion results of P- and S-wave moduli, density, and four fracture weaknesses are robust and reasonable for gas-bearing fractured reservoir characterization with orthorhombic symmetry.

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.

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