the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Seismic wave modeling of fluidsaturated fractured porous rock: Including fluid pressure diffusion effects of discrete distributed largescale fractures
Abstract. The scattered seismic waves of fractured porous rock are strongly affected by the waveinduced fluid pressure diffusion effects between the compliant fractures and the stiffer embedding background. To include these poroelastic effects in seismic modeling, we develop a numerical scheme for discrete distributed largescale fractures embedded in fluidsaturated porous rock. Using Coates and Schoenberg’s local effective medium theory and Barbosa’s dynamic linear slip model characterized by complexvalued and frequencydependent fracture compliances, we derive the effective viscoelastic compliances in each spatial discretized cell by superimposing the compliances of the background and the fractures. The effective governing equations of the fractured porous rock are then characterized by the derived anisotropic, complexvalued, and frequencydependent effective compliances. We numerically solved the effective governing equations by mixedgrid stencil frequencydomain finitedifference method. The good consistency between the scattered waves off a single horizontal fracture calculated using our proposed scheme and those calculated using the poroelastic linear slip model shows that our modeling scheme can properly include the FPD effects. We also find that for a Ppoint source, the amplitudes of the scattered waves from a single horizontal fracture are strongly affected by the fluid stiffening effects due to fluid pressure diffusion, while for an Spoint source, the scattered waves are less sensitive to fluid pressure diffusion. In the case of the conjugate fracture system, the scattered waves from the bottom of the fractured reservoir and the reflected waves from the underlying formation are attenuated and dispersed by the FPD effects for both P and Spoint sources. The proposed numerical modeling scheme can also be used to improve migration quality and the estimation of fracture mechanical characteristics in inversion.

Notice on discussion status
The requested preprint has a corresponding peerreviewed final revised paper. You are encouraged to refer to the final revised version.

Preprint
(2508 KB)

The requested preprint has a corresponding peerreviewed final revised paper. You are encouraged to refer to the final revised version.
 Preprint
(2508 KB)  Metadata XML
 BibTeX
 EndNote
 Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed

RC1: 'Comment on egusphere20221388', Nicolas Barbosa, 11 Jul 2023
Review on:
Qi et al: Seismic wave modeling of fluidsaturated fractured porous rock: Including fluid pressure diffusion effects of discrete distributed largescale fractures
General comment:
Dear Editor and Authors,
I have completed the review of the abovementioned manuscript and would like to provide my feedback and suggestions for improvement.
The authors employ a numerical approach based on Coates and Schoenberg's "local effective medium theory" (1995) and Barbosa et al (2106) linear slip model (VLSM) to model seismic wave scattering in fluidsaturated fractured porous rock. The VLSM allows to account for waveinduced fluid pressure diffusion effects between individual fractures and the embedding background rock by considering complexvalued and frequencydependent fracture properties (i.e., compliances). The rest of the domain can be modeled using an elastic solid, which is the main advantage of the method compared to, for example, poroelastic ones.
The authors validate the approach for normal incidence (both P and S wave incidence) by comparing results with those of a fully poroelastic model in which fractures are represented using the interface model of Nakagawa and Schoenberg (2007). While the comparison with the fully poroelastic model is valid, the comparison with the elastic models described as LFLSM and HFLSM is not appropriate, as they do not model individual fractures. Nevertheless, I found this first part of the manuscript interesting as it aims at quantifying the importance of waveinduced fluid pressure diffusion (FPD) effects and is worth further development (e.g., inclined fracture case, see Specific comments).
In the second part of the work, the authors extend the application of their modeling approach to cases of multiple intersecting fractures. While this is a pertinent scenario, the VLSM does not allow properly reproducing the seismic response of hydraulically connected fractures. The authors do not seem to be aware of this critical assumption as they assume that this solution is "accurate" when comparing it to elastic models to assess FPD effects.
Overall, I think this work requires a major revision, in particular of the assumptions and models used. As a possible way to go, the authors could expand on the first part of the work related to individual fractures and consider notintersecting fractures in the second part (when dealing with multiple fractures). In this case, please revise the meaningfulness of the elastic models implemented when assessing the importance of FPD effects (see "Specific comments").
Specific comments:
 Section 2.1 The lowfrequency limits elastic linear slip model (LFLSM)
This model is not valid for single fractures and it should not be used in that context. In the second part of the work, it is used to approximate the effective properties of a set of conjugate fractures but the authors should understand and explain in which scenarios this model makes sense first. The authors should also explain how this model is adapted for the case of conjugate fractures as it has been presented for "a single set of rotationally invariant fractures".
 2.2 The highfrequency limit elastic linear slip model (HFLSM)
Same as in Section 2.1.
 3 Nakagawa's poroelastic LSM
Please explain why this model is required (i.e., validation only) and the main assumptions of a LSM.
 5.1 Viscoelastic modeling based on VLSM: "In order to assess the FPD effects on seismic response, the similar procedure was adopted in the implementation of elastic modeling by replacing the VLSM with the LFLSM (assuming fluid pressure is equilibrium) or the HFLSM (assuming fluid pressure is nonequilibrium)."
The use of the LFLSM and HFLSM models from Sections 2.1 and 2.2, respectively, is incorrect for individual fractures. To assess the importance of FPD effects, the authors could utilize the low and highfrequency limits of the VLSM model by Barbosa et al. (2016), which is valid for a single fracture and provides the desired elastic limits.
Comment on Figure 2.
Since the traces are recorded sufficiently away from the fracture, the slow wave is not present (it gets completely attenuated close to the fracture). This should be mentioned as Nakagawa's model provides the slow wave solution and Barbosa's does not. Nevertheless, this comparison shows that the effects on P and S waves are properly accounted for.
6.1 Single horizontal fracture model
 a) The authors should compute the characteristic frequency of FPD effects or present Zn plots to confirm that FPD effects are indeed important at 35Hz. Based on the values given in Table 1, I got that the maximum FPD effects occur around 45Hz, which is close to the frequency considered by the authors.
 b) The model should also be validated for oblique incidence (or inclined fractures) before moving on to multiple fractures.
 From Section 6.2 onwards, the approach is not suitable for the analyzed cases. The VLSM cannot accurately represent the seismic response of connected fractures as it does not account for pressure relaxation effects between them. The assumption that the VLSMbased modeling is "accurate" for assessing FPD effects is incorrect.
Additionally, the authors need to describe how the models LFLSM and HFLSM, presented in Sections 2.1 and 2.2, respectively, apply to cases of conjugate fractures (e.g., how are the dry compliance matrices computed for a set of conjugate fractures). The assumptions underlying this approximation, as they correspond to effective medium models, should also be explained.
In Section 6.3, the authors attribute the observed differing results to scattering caused by the presence of fractures, but it is uncertain whether the scattering is accurately modeled.
I have also made some minor technical corrections, which are annotated in the attached PDF. Please note that these corrections are not exhaustive, given the major concerns expressed above.
Best regards,
Nicolas Barbosa

AC1: 'Reply on RC1', Yingkai Qi, 26 Jan 2024
Dear reviewer
Thank you for your professional comments and advice on our manuscript entitled “Seismic wave modeling of fluidsaturated fractured porous rock Including fluid pressure diffusion effects of discrete distributed largescale fractures” (ID 675243). Those comments and advice are valuable and helpful for revising and improving our paper. According to your nice suggestions, we have made extensive corrections to our previous manuscript, the detailed corrections are listed below.
Reviewer’s report
 Section 2.1 The lowfrequency limits elastic linear slip model (LFLSM). This model is not valid for single fractures and it should not be used in that context. In the second part of the work, it is used to approximate the effective properties of a set of conjugate fractures but the authors should understand and explain in which scenarios this model makes sense first. The authors should also explain how this model is adapted for the case of conjugate fractures as it has been presented for "a single set of rotationally invariant fractures".
 Section 2.2 The highfrequency limit elastic linear slip model (HFLSM). Same as in Section 2.1.
 Section 3 Nakagawa's poroelastic LSM. Please explain why this model is required (i.e., validation only) and the main assumptions of a LSM.
 Section 5.1 Viscoelastic modeling based on VLSM. The use of the LFLSM and HFLSM models from Sections 2.1 and 2.2, respectively, is incorrect for individual fractures. To assess the importance of FPD effects, the authors could utilize the low and highfrequency limits of the VLSM model by Barbosa et al. (2016), which is valid for a single fracture and provides the desired elastic limits.
 Comment on Figure 2. Since the traces are recorded sufficiently away from the fracture, the slow wave is not present (it gets completely attenuated close to the fracture). This should be mentioned as Nakagawa's model provides the slow wave solution and Barbosa's does not. Nevertheless, this comparison shows that the effects on P and S waves are properly accounted for.
 Section 6.1 Single horizontal fracture model. (a) The authors should compute the characteristic frequency of FPD effects or present Zn plots to confirm that FPD effects are indeed important at 35Hz. Based on the values given in Table 1, I got that the maximum FPD effects occur around 45Hz, which is close to the frequency considered by the authors. (b) The model should also be validated for oblique incidence (or inclined fractures) before moving on to multiple fractures.
 From Section 6.2 onwards, the approach is not suitable for the analyzed cases. The VLSM cannot accurately represent the seismic response of connected fractures as it does not account for pressure relaxation effects between them. The assumption that the VLSMbased modeling is "accurate" for assessing FPD effects is incorrect. Additionally, the authors need to describe how the models LFLSM and HFLSM, presented in Sections 2.1 and 2.2, respectively, apply to cases of conjugate fractures (e.g., how are the dry compliance matrices computed for a set of conjugate fractures). The assumptions underlying this approximation, as they correspond to effective medium models, should also be explained. In Section 6.3, the authors attribute the observed differing results to scattering caused by the presence of fractures, but it is uncertain whether the scattering is accurately modeled.
 I have also made some minor technical corrections, which are annotated in the attached PDF.
The author’s answer:
 The LFLSM in the previous draft is not appropriate for individual fractures. We have replaced it with the lowfrequency limit of Barbosa’s VLSM (LVLSM) in section 2.3 to model the elastic properties of individual fractures in which the fluid pressure is in complete equilibrium.
 The HFLSM in the previous draft is not appropriate for individual fractures. We have replaced it with the highfrequency limit of Barbosa’s VLSM (HVLSM) in section 2.3 to model the elastic properties of individual fractures in which the fluid pressure is nonequilibrium.
 We explain the reason for using Nakagawa's poroelastic LSM in Section 3.2, lines 266~268, which is marked in green. The main assumptions of PLSM are described in Section 2.2, lines 115~118, which are marked in green.
 We replace the LFLSM and HFLSMbased modeling scheme with LVLSMbased or HVLSMbased modeling scheme to simulate wave scattering of individual fractures in Section 3.2, lines 259~260, which is marked in green.
 The slow Pwaves are invisible in the poroelastic modeling. According to the reviewer’s suggestion, we mention it in Section 4.1, 328~329, which is marked in green.
 (a) According to the reviewer’s suggestion, we calculated the characteristic frequency to be 46Hz and plotted Zn and Zx in Section 4.1, lines 317~322, which is marked in green. The central frequency (35Hz) of the Ricker wavelet used for numerical simulation is close to the characteristic frequency (46Hz), which ensures that the impact of the FDP effects on seismic scattering is significant in the seismic frequency band. (b) We have shown the numerical simulation results for a single inclined fracture in Section 4.1.
 We are very sorry for our negligence in the critical assumption of Barbosa’s VLSM, so we have changed the multiple conjugate fractures with a set of aligned fractures in Section 4.2.
 We thank the reviewer for all of these nice suggestions, we have made corrections.
We have restructured the manuscript to better address the problems.
Thank you very much for your attention and time. Look forward to hearing from you.
Yours sincerely,
Yingkai Qi
28 Jan., 2024
Chengdu University of Technology
Citation: https://doi.org/10.5194/egusphere20221388AC1

RC2: 'Comment on egusphere20221388', Anonymous Referee #2, 19 Dec 2023
Review for “Seismic wave modeling of fluidsaturated fractured porous rock: Including fluid pressure diffusion effects of discrete distributed largescale fractures”
The main contribution of this study is a numerical method for modeling seismic wave scattering in fractured porous rock including the fluid pressure diffusion effects between the fractures and poroelastic background. The idea of replacing poroelastic modeling with viscoelastic modeling based on VLSM to account for the FPD effects is good. My main questions and suggestions are as follows:
 There are errors in equations (28b) and equations (29b) in section 3.2.
 The poroelastic finitedifference modeling based on the PLSM in section 3.2 is an effective one, I suggest the authors use the PLSM explicitly in the numerical simulation to capture the FPD effect on scattered waves when validating the VLSMbased modeling.
 Why the slow Pwave is invisible in the snapshot of poroelastic modeling?
 The calculation of local effective moduli based on VLSM in section 4 belongs to seismic modeling. It is better to combine the context of section 4 and section 5.1.
Citation: https://doi.org/10.5194/egusphere20221388RC2 
AC2: 'Reply on RC2', Yingkai Qi, 26 Jan 2024
Dear reviewer
Thank you for your professional comments and advice on our manuscript “Seismic wave modeling of fluidsaturated fractured porous rock Including fluid pressure diffusion effects of discrete distributed largescale fractures” (ID 675243). Those comments and advice are valuable and helpful for revising and improving our paper. According to your nice suggestions, we have made extensive corrections to our previous manuscript, the detailed corrections are listed below.
Reviewer’s report
 There are errors in equations (28b) and equations (29b) in section 3.2.
 The poroelastic finitedifference modeling based on the PLSM in section 3.2 is an effective one, I suggest the authors use the PLSM explicitly in the numerical simulation to capture the FPD effect on scattered waves when validating the VLSMbased modeling.
 Why the slow Pwave is invisible in the snapshot of poroelastic modeling?
 The calculation of local effective moduli based on VLSM in section 4 belongs to seismic modeling. It is better to combine the context of section 4 and section 5.1.
The author’s answer:
 We have corrected all the errors in the equations of the manuscript.
 We have presented the PLSM explicitly in the numerical poroelastic modeling scheme in Section 3.2 and given the numerical result in Section 4.1.
 Due to the high diffusion and attenuation of slow Pwaves in the background media, them are invisible in the poroelastic modeling result.
 We thank the reviewer for all of these nice suggestions, we have restructured the manuscript
Thank you very much for your attention and time. Look forward to hearing from you.
Yours sincerely,
Yingkai Qi
28 Jan., 2024
Chengdu University of Technology
Citation: https://doi.org/10.5194/egusphere20221388AC2
Interactive discussion
Status: closed

RC1: 'Comment on egusphere20221388', Nicolas Barbosa, 11 Jul 2023
Review on:
Qi et al: Seismic wave modeling of fluidsaturated fractured porous rock: Including fluid pressure diffusion effects of discrete distributed largescale fractures
General comment:
Dear Editor and Authors,
I have completed the review of the abovementioned manuscript and would like to provide my feedback and suggestions for improvement.
The authors employ a numerical approach based on Coates and Schoenberg's "local effective medium theory" (1995) and Barbosa et al (2106) linear slip model (VLSM) to model seismic wave scattering in fluidsaturated fractured porous rock. The VLSM allows to account for waveinduced fluid pressure diffusion effects between individual fractures and the embedding background rock by considering complexvalued and frequencydependent fracture properties (i.e., compliances). The rest of the domain can be modeled using an elastic solid, which is the main advantage of the method compared to, for example, poroelastic ones.
The authors validate the approach for normal incidence (both P and S wave incidence) by comparing results with those of a fully poroelastic model in which fractures are represented using the interface model of Nakagawa and Schoenberg (2007). While the comparison with the fully poroelastic model is valid, the comparison with the elastic models described as LFLSM and HFLSM is not appropriate, as they do not model individual fractures. Nevertheless, I found this first part of the manuscript interesting as it aims at quantifying the importance of waveinduced fluid pressure diffusion (FPD) effects and is worth further development (e.g., inclined fracture case, see Specific comments).
In the second part of the work, the authors extend the application of their modeling approach to cases of multiple intersecting fractures. While this is a pertinent scenario, the VLSM does not allow properly reproducing the seismic response of hydraulically connected fractures. The authors do not seem to be aware of this critical assumption as they assume that this solution is "accurate" when comparing it to elastic models to assess FPD effects.
Overall, I think this work requires a major revision, in particular of the assumptions and models used. As a possible way to go, the authors could expand on the first part of the work related to individual fractures and consider notintersecting fractures in the second part (when dealing with multiple fractures). In this case, please revise the meaningfulness of the elastic models implemented when assessing the importance of FPD effects (see "Specific comments").
Specific comments:
 Section 2.1 The lowfrequency limits elastic linear slip model (LFLSM)
This model is not valid for single fractures and it should not be used in that context. In the second part of the work, it is used to approximate the effective properties of a set of conjugate fractures but the authors should understand and explain in which scenarios this model makes sense first. The authors should also explain how this model is adapted for the case of conjugate fractures as it has been presented for "a single set of rotationally invariant fractures".
 2.2 The highfrequency limit elastic linear slip model (HFLSM)
Same as in Section 2.1.
 3 Nakagawa's poroelastic LSM
Please explain why this model is required (i.e., validation only) and the main assumptions of a LSM.
 5.1 Viscoelastic modeling based on VLSM: "In order to assess the FPD effects on seismic response, the similar procedure was adopted in the implementation of elastic modeling by replacing the VLSM with the LFLSM (assuming fluid pressure is equilibrium) or the HFLSM (assuming fluid pressure is nonequilibrium)."
The use of the LFLSM and HFLSM models from Sections 2.1 and 2.2, respectively, is incorrect for individual fractures. To assess the importance of FPD effects, the authors could utilize the low and highfrequency limits of the VLSM model by Barbosa et al. (2016), which is valid for a single fracture and provides the desired elastic limits.
Comment on Figure 2.
Since the traces are recorded sufficiently away from the fracture, the slow wave is not present (it gets completely attenuated close to the fracture). This should be mentioned as Nakagawa's model provides the slow wave solution and Barbosa's does not. Nevertheless, this comparison shows that the effects on P and S waves are properly accounted for.
6.1 Single horizontal fracture model
 a) The authors should compute the characteristic frequency of FPD effects or present Zn plots to confirm that FPD effects are indeed important at 35Hz. Based on the values given in Table 1, I got that the maximum FPD effects occur around 45Hz, which is close to the frequency considered by the authors.
 b) The model should also be validated for oblique incidence (or inclined fractures) before moving on to multiple fractures.
 From Section 6.2 onwards, the approach is not suitable for the analyzed cases. The VLSM cannot accurately represent the seismic response of connected fractures as it does not account for pressure relaxation effects between them. The assumption that the VLSMbased modeling is "accurate" for assessing FPD effects is incorrect.
Additionally, the authors need to describe how the models LFLSM and HFLSM, presented in Sections 2.1 and 2.2, respectively, apply to cases of conjugate fractures (e.g., how are the dry compliance matrices computed for a set of conjugate fractures). The assumptions underlying this approximation, as they correspond to effective medium models, should also be explained.
In Section 6.3, the authors attribute the observed differing results to scattering caused by the presence of fractures, but it is uncertain whether the scattering is accurately modeled.
I have also made some minor technical corrections, which are annotated in the attached PDF. Please note that these corrections are not exhaustive, given the major concerns expressed above.
Best regards,
Nicolas Barbosa

AC1: 'Reply on RC1', Yingkai Qi, 26 Jan 2024
Dear reviewer
Thank you for your professional comments and advice on our manuscript entitled “Seismic wave modeling of fluidsaturated fractured porous rock Including fluid pressure diffusion effects of discrete distributed largescale fractures” (ID 675243). Those comments and advice are valuable and helpful for revising and improving our paper. According to your nice suggestions, we have made extensive corrections to our previous manuscript, the detailed corrections are listed below.
Reviewer’s report
 Section 2.1 The lowfrequency limits elastic linear slip model (LFLSM). This model is not valid for single fractures and it should not be used in that context. In the second part of the work, it is used to approximate the effective properties of a set of conjugate fractures but the authors should understand and explain in which scenarios this model makes sense first. The authors should also explain how this model is adapted for the case of conjugate fractures as it has been presented for "a single set of rotationally invariant fractures".
 Section 2.2 The highfrequency limit elastic linear slip model (HFLSM). Same as in Section 2.1.
 Section 3 Nakagawa's poroelastic LSM. Please explain why this model is required (i.e., validation only) and the main assumptions of a LSM.
 Section 5.1 Viscoelastic modeling based on VLSM. The use of the LFLSM and HFLSM models from Sections 2.1 and 2.2, respectively, is incorrect for individual fractures. To assess the importance of FPD effects, the authors could utilize the low and highfrequency limits of the VLSM model by Barbosa et al. (2016), which is valid for a single fracture and provides the desired elastic limits.
 Comment on Figure 2. Since the traces are recorded sufficiently away from the fracture, the slow wave is not present (it gets completely attenuated close to the fracture). This should be mentioned as Nakagawa's model provides the slow wave solution and Barbosa's does not. Nevertheless, this comparison shows that the effects on P and S waves are properly accounted for.
 Section 6.1 Single horizontal fracture model. (a) The authors should compute the characteristic frequency of FPD effects or present Zn plots to confirm that FPD effects are indeed important at 35Hz. Based on the values given in Table 1, I got that the maximum FPD effects occur around 45Hz, which is close to the frequency considered by the authors. (b) The model should also be validated for oblique incidence (or inclined fractures) before moving on to multiple fractures.
 From Section 6.2 onwards, the approach is not suitable for the analyzed cases. The VLSM cannot accurately represent the seismic response of connected fractures as it does not account for pressure relaxation effects between them. The assumption that the VLSMbased modeling is "accurate" for assessing FPD effects is incorrect. Additionally, the authors need to describe how the models LFLSM and HFLSM, presented in Sections 2.1 and 2.2, respectively, apply to cases of conjugate fractures (e.g., how are the dry compliance matrices computed for a set of conjugate fractures). The assumptions underlying this approximation, as they correspond to effective medium models, should also be explained. In Section 6.3, the authors attribute the observed differing results to scattering caused by the presence of fractures, but it is uncertain whether the scattering is accurately modeled.
 I have also made some minor technical corrections, which are annotated in the attached PDF.
The author’s answer:
 The LFLSM in the previous draft is not appropriate for individual fractures. We have replaced it with the lowfrequency limit of Barbosa’s VLSM (LVLSM) in section 2.3 to model the elastic properties of individual fractures in which the fluid pressure is in complete equilibrium.
 The HFLSM in the previous draft is not appropriate for individual fractures. We have replaced it with the highfrequency limit of Barbosa’s VLSM (HVLSM) in section 2.3 to model the elastic properties of individual fractures in which the fluid pressure is nonequilibrium.
 We explain the reason for using Nakagawa's poroelastic LSM in Section 3.2, lines 266~268, which is marked in green. The main assumptions of PLSM are described in Section 2.2, lines 115~118, which are marked in green.
 We replace the LFLSM and HFLSMbased modeling scheme with LVLSMbased or HVLSMbased modeling scheme to simulate wave scattering of individual fractures in Section 3.2, lines 259~260, which is marked in green.
 The slow Pwaves are invisible in the poroelastic modeling. According to the reviewer’s suggestion, we mention it in Section 4.1, 328~329, which is marked in green.
 (a) According to the reviewer’s suggestion, we calculated the characteristic frequency to be 46Hz and plotted Zn and Zx in Section 4.1, lines 317~322, which is marked in green. The central frequency (35Hz) of the Ricker wavelet used for numerical simulation is close to the characteristic frequency (46Hz), which ensures that the impact of the FDP effects on seismic scattering is significant in the seismic frequency band. (b) We have shown the numerical simulation results for a single inclined fracture in Section 4.1.
 We are very sorry for our negligence in the critical assumption of Barbosa’s VLSM, so we have changed the multiple conjugate fractures with a set of aligned fractures in Section 4.2.
 We thank the reviewer for all of these nice suggestions, we have made corrections.
We have restructured the manuscript to better address the problems.
Thank you very much for your attention and time. Look forward to hearing from you.
Yours sincerely,
Yingkai Qi
28 Jan., 2024
Chengdu University of Technology
Citation: https://doi.org/10.5194/egusphere20221388AC1

RC2: 'Comment on egusphere20221388', Anonymous Referee #2, 19 Dec 2023
Review for “Seismic wave modeling of fluidsaturated fractured porous rock: Including fluid pressure diffusion effects of discrete distributed largescale fractures”
The main contribution of this study is a numerical method for modeling seismic wave scattering in fractured porous rock including the fluid pressure diffusion effects between the fractures and poroelastic background. The idea of replacing poroelastic modeling with viscoelastic modeling based on VLSM to account for the FPD effects is good. My main questions and suggestions are as follows:
 There are errors in equations (28b) and equations (29b) in section 3.2.
 The poroelastic finitedifference modeling based on the PLSM in section 3.2 is an effective one, I suggest the authors use the PLSM explicitly in the numerical simulation to capture the FPD effect on scattered waves when validating the VLSMbased modeling.
 Why the slow Pwave is invisible in the snapshot of poroelastic modeling?
 The calculation of local effective moduli based on VLSM in section 4 belongs to seismic modeling. It is better to combine the context of section 4 and section 5.1.
Citation: https://doi.org/10.5194/egusphere20221388RC2 
AC2: 'Reply on RC2', Yingkai Qi, 26 Jan 2024
Dear reviewer
Thank you for your professional comments and advice on our manuscript “Seismic wave modeling of fluidsaturated fractured porous rock Including fluid pressure diffusion effects of discrete distributed largescale fractures” (ID 675243). Those comments and advice are valuable and helpful for revising and improving our paper. According to your nice suggestions, we have made extensive corrections to our previous manuscript, the detailed corrections are listed below.
Reviewer’s report
 There are errors in equations (28b) and equations (29b) in section 3.2.
 The poroelastic finitedifference modeling based on the PLSM in section 3.2 is an effective one, I suggest the authors use the PLSM explicitly in the numerical simulation to capture the FPD effect on scattered waves when validating the VLSMbased modeling.
 Why the slow Pwave is invisible in the snapshot of poroelastic modeling?
 The calculation of local effective moduli based on VLSM in section 4 belongs to seismic modeling. It is better to combine the context of section 4 and section 5.1.
The author’s answer:
 We have corrected all the errors in the equations of the manuscript.
 We have presented the PLSM explicitly in the numerical poroelastic modeling scheme in Section 3.2 and given the numerical result in Section 4.1.
 Due to the high diffusion and attenuation of slow Pwaves in the background media, them are invisible in the poroelastic modeling result.
 We thank the reviewer for all of these nice suggestions, we have restructured the manuscript
Thank you very much for your attention and time. Look forward to hearing from you.
Yours sincerely,
Yingkai Qi
28 Jan., 2024
Chengdu University of Technology
Citation: https://doi.org/10.5194/egusphere20221388AC2
Peer review completion
Journal article(s) based on this preprint
Viewed
HTML  XML  Total  BibTeX  EndNote  

386  127  19  532  7  10 
 HTML: 386
 PDF: 127
 XML: 19
 Total: 532
 BibTeX: 7
 EndNote: 10
Viewed (geographical distribution)
Country  #  Views  % 

Total:  0 
HTML:  0 
PDF:  0 
XML:  0 
 1
Cited
2 citations as recorded by crossref.
 Simulation of Propagation of Dynamic Perturbations in Porous Media by the GridCharacteristic Method with Explicit Description of Heterogeneities I. Mitskovets & N. Khokhlov 10.1134/S0965542523100093
 Simulation of Propagation of Dynamic Perturbations in Porous Media by the GridCharacteristic Method with Explicit Description of Heterogeneities I. Mitskovets & N. Khokhlov 10.31857/S0044466923100125
Yingkai Qi
Qingwei Zhao
Chunqiang Feng
The requested preprint has a corresponding peerreviewed final revised paper. You are encouraged to refer to the final revised version.
 Preprint
(2508 KB)  Metadata XML