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Title: Modeling Frequency–Independent Q Viscoacoustic Wave Propagation in Heterogeneous Media

Abstract

Quantifying the attenuation of seismic waves propagating in the Earth interior is critical to study the subsurface structure. Previous studies have proposed fractional anelastic wave equations to model the frequency–independent Q seismic wave propagation. Such wave equations involve fractional derivatives that pose computational challenges for the numerical schemes in terms of accuracy and efficiency when dealing with heterogeneous Earth media. To tackle these challenges, here we derive a new viscoacoustic wave equation, where the power terms of the fractional Laplacian operators are spatially independent, thus accurate and efficient methods (e.g., the Fourier pseudospectral method) can be adopted. Our derivation enables the resultant equation to capture both amplitude and phase signatures of the anelastic wave propagation by matching the complex wave numbers for all the frequencies of interest. We verify the derivation by comparing the dispersion curves of both the attenuation factor and the phase velocity produced by the new wave equation with their theoretical values as well as the Pierre Shale in situ measurements. Following that, we use a synthetic attenuating gas chimney model to demonstrate the attenuation effects on seismic waveforms and then construct the Q–compensated reverse time migration to undo these effects for seismic image enhancement. Finally, wemore » find that our forward modeling results can characterize the spatiotemporal attenuation effects revealed in the Frio–II CO2 injection time–lapse seismic monitoring data. Here, we expect this proposed equation to be useful to quantify the attenuation in seismic data to push the resolution limits of seismic imaging and inversion.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]
  1. Pennsylvania State Univ., University Park, PA (United States)
Publication Date:
Research Org.:
Pennsylvania State Univ., University Park, PA (United States)
Sponsoring Org.:
USDOE Office of Fossil Energy (FE); National Science Foundation (NSF)
Contributing Org.:
Penn State University
OSTI Identifier:
1569481
Alternate Identifier(s):
OSTI ID: 1574085
Grant/Contract Number:  
FE0031544; EAR 1919650
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Geophysical Research. Solid Earth
Additional Journal Information:
Journal Volume: 124; Journal Issue: 11; Journal ID: ISSN 2169-9313
Publisher:
American Geophysical Union
Country of Publication:
United States
Language:
English
Subject:
25 ENERGY STORAGE; seismology; wave propagation; attenuation

Citation Formats

Xing, Guangchi, and Zhu, Tieyuan. Modeling Frequency–Independent Q Viscoacoustic Wave Propagation in Heterogeneous Media. United States: N. p., 2019. Web. doi:10.1029/2019JB017985.
Xing, Guangchi, & Zhu, Tieyuan. Modeling Frequency–Independent Q Viscoacoustic Wave Propagation in Heterogeneous Media. United States. https://doi.org/10.1029/2019JB017985
Xing, Guangchi, and Zhu, Tieyuan. 2019. "Modeling Frequency–Independent Q Viscoacoustic Wave Propagation in Heterogeneous Media". United States. https://doi.org/10.1029/2019JB017985. https://www.osti.gov/servlets/purl/1569481.
@article{osti_1569481,
title = {Modeling Frequency–Independent Q Viscoacoustic Wave Propagation in Heterogeneous Media},
author = {Xing, Guangchi and Zhu, Tieyuan},
abstractNote = {Quantifying the attenuation of seismic waves propagating in the Earth interior is critical to study the subsurface structure. Previous studies have proposed fractional anelastic wave equations to model the frequency–independent Q seismic wave propagation. Such wave equations involve fractional derivatives that pose computational challenges for the numerical schemes in terms of accuracy and efficiency when dealing with heterogeneous Earth media. To tackle these challenges, here we derive a new viscoacoustic wave equation, where the power terms of the fractional Laplacian operators are spatially independent, thus accurate and efficient methods (e.g., the Fourier pseudospectral method) can be adopted. Our derivation enables the resultant equation to capture both amplitude and phase signatures of the anelastic wave propagation by matching the complex wave numbers for all the frequencies of interest. We verify the derivation by comparing the dispersion curves of both the attenuation factor and the phase velocity produced by the new wave equation with their theoretical values as well as the Pierre Shale in situ measurements. Following that, we use a synthetic attenuating gas chimney model to demonstrate the attenuation effects on seismic waveforms and then construct the Q–compensated reverse time migration to undo these effects for seismic image enhancement. Finally, we find that our forward modeling results can characterize the spatiotemporal attenuation effects revealed in the Frio–II CO2 injection time–lapse seismic monitoring data. Here, we expect this proposed equation to be useful to quantify the attenuation in seismic data to push the resolution limits of seismic imaging and inversion.},
doi = {10.1029/2019JB017985},
url = {https://www.osti.gov/biblio/1569481}, journal = {Journal of Geophysical Research. Solid Earth},
issn = {2169-9313},
number = 11,
volume = 124,
place = {United States},
year = {Fri Oct 18 00:00:00 EDT 2019},
month = {Fri Oct 18 00:00:00 EDT 2019}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 29 works
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Figures / Tables:

Figure 1 Figure 1: The workflow of the derivation process of the new viscoacoustic wave equation. We start from the Taylor expansions for each term of Equation (6). Different colors indicate the co-efficients of different terms while the solid and dashed borders correspond to real and imaginary parts, respectively. The processes markedmore » by numbers are: (1) plug the Taylor expansion expressions into Equation (6) and formulate the 6 x 6 linear system problem; (2) analytically solve the linear system and obtain a complicated closed form representation of $$\tilde{β}$$, which is a function of γ; (3) apply a second Taylor expansion with respect to γ and preserve the leading term; (4) convert the dimension-normalized parameters$$\tilde{β}$$ back to β .« less

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