the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 26 Jan 2022
Angle-domain common-image gathers from Fresnel volume migration
Abstract. In complex geological settings, such as in hard-rock environments, Fresnel volume migration (FVM) has been successfully applied and found to deliver superior image quality compared to conventional imaging techniques. However, previous studies on FVM have mainly focused on obtaining kinematic seismic images, and the analysis of the migrated amplitudes has not received major attention. Therefore this study presents a method for constructing angle-domain common-image gathers (ADCIGs) and common-angle stacks from FVM, which can facilitate prestack amplitude analysis from the migrated seismic data in the angle-domain. These ADCIGs were constructed inside the migration loops using phase slowness vectors derived from traveltime gradient fields. We then tested this method on synthetic and field seismic data and investigated the reliability of the output for amplitude versus angle (AVA) analysis. The test results obtained showed that the AVA responses from the common-angle stacks resemble that of the input synthetic shot gather of migration relatively well, indicating the promising feasibility of AVA analysis from common-angle stacks. When implemented on field data acquired from a hard-rock environment, the proposed method can provide common-angle stacks with a higher signal-to-noise ratio and better reflection coherency compared to the common-angle stacks from the standard Kirchhoff prestack depth migration. This study extends the implementation of FVM toward amplitude analysis, which can help improve the feasibility of hard-rock characterization.
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Interactive discussion
Status: closed
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RC1: 'Comment on se-2021-143', Anonymous Referee #1, 24 Feb 2022
The paper presents a method to generate angle-domain common-image gathers using Fresnel volume migration (FVM) and phase-slowness vectors obtained from traveltime gradient field, the latter used to bin the migrated data with the correct angles. The two methods are not new and have been published previously, but the combination of the two is new to the best of my knowledge. The paper is well-written and organized, and the figures are of good quality and support the text. Unfortunately, the real benefits and advantages of the proposed method over the classic Kirchhoff prestack depth migration (KPSDM) remain to be demonstrated. The synthetic and real data examples selected to illustrate the usefulness of the method to generate AVA-compliant gathers and thus AVA analysis are not convincing.
The synthetic model comprising only two layers is extremely simple. Obviously, there are merits in using simple models. They allow for a better understanding of the method and easier comparison with theoretical results (i.e. analytical AVA results). Unfortunately, the results and comparison with KPSDM results for such a simple model lead to the following question: why should anyone use FVM to generate angle-domain common-image gathers if results are almost identical to that of KPSDM (see figure 8 g, h, and i)? Whereas figure 8 might re-assure readers that the method provides as good results as KSPDM, it fails to demonstrate any advantages. The problem is not the method but the simplistic model, which excludes the potential interference of smeared migration artifacts on AVA data. The impact of such interference on AVA curves (which should be more significant for KSPDM) can only be demonstrated by using a slightly more complex model with several geological layers. Such an example is necessary to show how FVM can help and improve AVA analysis.
The application of AVA analysis to hard rock environments is certainly interesting but also very challenging. The common-angle stacks shown in Figure 11 confirm this. As a reader, I wonder what useful AVA information can be extracted from those gathers. Assessing the added value of FVM over KPSDM for such data remains highly subjective. The FVM common-angle stack shown in the zoomed-in area of figure 8 looks more coherent but only over a limited range of angles. No reliable AVA analysis can be performed with this data. So, how does it help demonstrate the usefulness of FVM for AVA analysis? Why even show it? A field example from a less complex geological environment with supporting petrophysics (i.e. wireline logs for quantitative analysis) is needed. The authors propose this as future work. I would argue that this is needed in this paper.
I recommend a major revision. This should provide enough time to include examples that can effectively help support the promising methodology presented in this paper.
Minor question: The weights in equation 2 are a function of zeta and tau, but only tau is found on the term on the right-hand side. Am I missing something?
Citation: https://doi.org/10.5194/se-2021-143-RC1 - AC1: 'Author response to Referee 1', Tomi Jusri, 08 Apr 2022
-
AC3: 'Additional information: references', Tomi Jusri, 08 Apr 2022
References cited in our response document:
Connolly, P. (1999). Elastic impedance. The leading edge, 18(4):438–452.
Resnick, J. R., Ng, P., and Larner, K. (1987). Amplitude versus offset analysis in the presence of dip. In SEG Technical Program Expanded Abstracts 1987, pages 617–620. Society of Exploration Geophysicists.
Citation: https://doi.org/10.5194/se-2021-143-AC3
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RC2: 'Comment on se-2021-143', Anonymous Referee #2, 04 Mar 2022
Dear authors,
This manuscript considers the method of extracting the angle domain common image gather (ADCIG) and common angle stack (CAS) from Fresnel volume migration (FVM), where beside the kinematic properties of the migration image the focus is on improving the accuracy of the dynamic properties. The performance of the proposed method is investigated in amplitude versus angle (AVA) analysis. The manuscript is well written, organized satisfactorily and the idea is promising.
Main comments:
- Fresnel volume migration is a well-developed method to modify the Kirchhoff pre-stack depth migration to eliminate the artifacts. On the other hand, the ADCIGs are the most precise gathers suggested as a solution for multi pathing, which are used for velocity and AVA analysis. There are some nice studies which show the superior performance of ADCIGs in imaging where the velocity model has complex structure. Actually in front of complex geology, the single ray path assumption is violated and the multi-pathing occurs. In these situations the role of ADCIGs which uniquely define ray path based on their opening angle not their offset, becomes important. Therefore to show the predominance of ADCIG, authors need to use some geologically complex synthetic model, for example a model with some low velocity inclusion, or some benchmark model likes Marmousi to verify the dominant performance of ADCIGs constructed during FVM.
- To augment the manuscript to become easier to follow for the reader, I advise to add more explanation about the theory and the performance of FVM and ADCIG with some supporting figures in the theory section.
- In figures 1 and 4, and in all basemaps the horizontal label Y is meaning less and is introduced after using. Also in figure 11, it changed to X. So I advise to unify them and change it to distance, maybe become more sensible.
Minor comments:
Increase the X and Y axis ticks and labels in figures 6, 7, 11. It is difficult to read them now.
Line 68: Introduce the x' after equation 5 too.
Line 78: Using the "noise-free" is an exaggerating phrase here, because beside the KPSDM result, it is a clear image but not generally free of any artifacts.
Line 89 and 91: It is better to change one of the names for scattering azimuth angle or illumination azimuth angle, because their symbols in figure 2 are hardly distinguishable.
Figure 8: There isn't any red circle in the figure which is introduced in the caption.
Based on supplying a synthetic example which the single path is violated on, I recommend a major revision.
Citation: https://doi.org/10.5194/se-2021-143-RC2 - AC2: 'Author response to Referee 2', Tomi Jusri, 08 Apr 2022
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EC1: 'Editor Comment on se-2021-143', Michal Malinowski, 09 May 2022
Dear Authors,
I had now a closer look at your responses to reviewers’ comments. I also went through the manuscript and the reviewers’ comments again. My general observation is that the real data example from a hardrock site is too much of a jump from the synthetic example presented. I don’t agree with your reasoning that since the velocities are not much differentiated in crystalline rocks, therefore your simple 2-layer model is a sufficient justification. There are other challenges, including steeply dipping reflectors, complex wave interference and scattering. A more complex synthetic example can help you in explaining the benefits of FVM vs KPSDM for AVA, as noted by Reviewer 1:
“The problem is not the method but the simplistic model, which excludes the potential interference of smeared migration artifacts on AVA data. The impact of such interference on AVA curves (which should be more significant for KSPDM) can only be demonstrated by using a slightly more complex model with several geological layers. Such an example is necessary to show how FVM can help and improve AVA analysis”.
In other words, the synthetic data need to have some degree of migration noise from layers interfering with the amplitudes of reflections from the shallower layer(s). Therefore, I insist on making another synthetic example with more layers and/or complex structure (dipping reflector, wedge) to better illustrate the above issue.
Another thing is the real data example. It is not very meaningful as it stands right now. It is just illustrating that the common-angle stacks from FVM are less noisy as compared to KPSDM (Isn’t it a general property of FVM as compared to KPSDM, something you will observe also for offset gathers). Getting from there to the quantitative interpretation is a long way ahead (primarily because of the amplitude handling during processing and scarcity of the wireline logs).
Reviewer 1 was also advocating for “A field example from a less complex geological environment with supporting petrophysics (i.e. wireline logs for quantitative analysis)”. I agree with this comment – if only you can have such an example, it would be much more beneficial for demonstrating the perspectives of your method for QI (which is the ultimate goal of developing your method, anyway). Going one step further from your AVA gathers / stacks to either reflectivity inversion or impedance inversion would be a great benchmark for your method (confronted and calibrated with the borehole data). And you can use standard industry tools for this step.
I understand that the new real data example might be more challenging, as it depends on the data you have. Therefore, to sum up: in my opinion, a more complex synthetic model example is a must. New real data example – depending on whether you can find a suitable target for your analysis. Definitely, it will strengthen your manuscript.
Best regards,
Editor
Citation: https://doi.org/10.5194/se-2021-143-EC1 -
AC4: 'Reply on EC1', Tomi Jusri, 11 May 2022
Dear Editor,
Thank you for your patience. We have discussed your comments thoroughly.
The proposed approach is based on a homogeneous medium assumption, and therefore, it is valid for amplitude calculation only from a single reflector. Using a complex geologic model, for example, a two-reflector model, the proposed approach will not calculate the AVA curve for the deeper reflector correctly because it does not consider factors affecting the wave propagation through the heterogeneous media, such as amplitude losses and ray bending. If we want to consider heterogeneous media, we will have to incorporate another sophisticated method to allow estimating the amplitudes correctly, for example, the transport equation (e.g., Buske S., Finite-difference solution of the transport equation: First results, Pure and Applied Geophysics, 148, 565–581,1996). The inclusion of such a method is beyond the scope of our manuscript.
On the other hand, our manuscript offers a novel approach to obtaining angle domain common image gathers (ADCIGs) from Fresnel volume migration (FVM) for a simple two-layer geologic model. While we understand that the test on a more complex geologic model is essential for establishing a technique for QI in hard rocks, we strive to reach intermediate progress and a new milestone in this very challenging topic. We doubt that we can provide a more established technique soon enough for the current submission. Nevertheless, for the current submission, we can offer the following:
1) A synthetic test using a single dipping reflector, as you also mentioned, as one of the possibilities for a more complex geologic model :
"Therefore, I insist on making another synthetic example with more layers and/or complex structure (dipping reflector, wedge) to better illustrate the above issue."
2) Editing the premise of the manuscript to make it clearer to the readers from the beginning that the current experiment is limited to a simple two-layer geologic model. We will change the title, abstract, introduction, discussion, and conclusions of the manuscript for this.
Regarding the field seismic data set, we do not have proper borehole data for the AVA analysis for the geothermal area in Italy. Furthermore, since the approach is not yet valid for a multi-reflector model, we doubt that performing AVA inversion from field seismic data controlled by borehole data will be meaningful. However, what we can offer for the current submission is:
3) Prestack analysis from the migrated field seismic data, made possible now by the proposed approach.
In conclusion, we hope you can consider the three points mentioned above sufficient for the revised manuscript. Should you be willing to consider this revision, we would like to ask for more time to submit the revised manuscript, i.e., until 31 July, when possible.
We look forward to hearing from you.Sincerely,
Authors
Citation: https://doi.org/10.5194/se-2021-143-AC4
-
AC4: 'Reply on EC1', Tomi Jusri, 11 May 2022
Interactive discussion
Status: closed
-
RC1: 'Comment on se-2021-143', Anonymous Referee #1, 24 Feb 2022
The paper presents a method to generate angle-domain common-image gathers using Fresnel volume migration (FVM) and phase-slowness vectors obtained from traveltime gradient field, the latter used to bin the migrated data with the correct angles. The two methods are not new and have been published previously, but the combination of the two is new to the best of my knowledge. The paper is well-written and organized, and the figures are of good quality and support the text. Unfortunately, the real benefits and advantages of the proposed method over the classic Kirchhoff prestack depth migration (KPSDM) remain to be demonstrated. The synthetic and real data examples selected to illustrate the usefulness of the method to generate AVA-compliant gathers and thus AVA analysis are not convincing.
The synthetic model comprising only two layers is extremely simple. Obviously, there are merits in using simple models. They allow for a better understanding of the method and easier comparison with theoretical results (i.e. analytical AVA results). Unfortunately, the results and comparison with KPSDM results for such a simple model lead to the following question: why should anyone use FVM to generate angle-domain common-image gathers if results are almost identical to that of KPSDM (see figure 8 g, h, and i)? Whereas figure 8 might re-assure readers that the method provides as good results as KSPDM, it fails to demonstrate any advantages. The problem is not the method but the simplistic model, which excludes the potential interference of smeared migration artifacts on AVA data. The impact of such interference on AVA curves (which should be more significant for KSPDM) can only be demonstrated by using a slightly more complex model with several geological layers. Such an example is necessary to show how FVM can help and improve AVA analysis.
The application of AVA analysis to hard rock environments is certainly interesting but also very challenging. The common-angle stacks shown in Figure 11 confirm this. As a reader, I wonder what useful AVA information can be extracted from those gathers. Assessing the added value of FVM over KPSDM for such data remains highly subjective. The FVM common-angle stack shown in the zoomed-in area of figure 8 looks more coherent but only over a limited range of angles. No reliable AVA analysis can be performed with this data. So, how does it help demonstrate the usefulness of FVM for AVA analysis? Why even show it? A field example from a less complex geological environment with supporting petrophysics (i.e. wireline logs for quantitative analysis) is needed. The authors propose this as future work. I would argue that this is needed in this paper.
I recommend a major revision. This should provide enough time to include examples that can effectively help support the promising methodology presented in this paper.
Minor question: The weights in equation 2 are a function of zeta and tau, but only tau is found on the term on the right-hand side. Am I missing something?
Citation: https://doi.org/10.5194/se-2021-143-RC1 - AC1: 'Author response to Referee 1', Tomi Jusri, 08 Apr 2022
-
AC3: 'Additional information: references', Tomi Jusri, 08 Apr 2022
References cited in our response document:
Connolly, P. (1999). Elastic impedance. The leading edge, 18(4):438–452.
Resnick, J. R., Ng, P., and Larner, K. (1987). Amplitude versus offset analysis in the presence of dip. In SEG Technical Program Expanded Abstracts 1987, pages 617–620. Society of Exploration Geophysicists.
Citation: https://doi.org/10.5194/se-2021-143-AC3
-
RC2: 'Comment on se-2021-143', Anonymous Referee #2, 04 Mar 2022
Dear authors,
This manuscript considers the method of extracting the angle domain common image gather (ADCIG) and common angle stack (CAS) from Fresnel volume migration (FVM), where beside the kinematic properties of the migration image the focus is on improving the accuracy of the dynamic properties. The performance of the proposed method is investigated in amplitude versus angle (AVA) analysis. The manuscript is well written, organized satisfactorily and the idea is promising.
Main comments:
- Fresnel volume migration is a well-developed method to modify the Kirchhoff pre-stack depth migration to eliminate the artifacts. On the other hand, the ADCIGs are the most precise gathers suggested as a solution for multi pathing, which are used for velocity and AVA analysis. There are some nice studies which show the superior performance of ADCIGs in imaging where the velocity model has complex structure. Actually in front of complex geology, the single ray path assumption is violated and the multi-pathing occurs. In these situations the role of ADCIGs which uniquely define ray path based on their opening angle not their offset, becomes important. Therefore to show the predominance of ADCIG, authors need to use some geologically complex synthetic model, for example a model with some low velocity inclusion, or some benchmark model likes Marmousi to verify the dominant performance of ADCIGs constructed during FVM.
- To augment the manuscript to become easier to follow for the reader, I advise to add more explanation about the theory and the performance of FVM and ADCIG with some supporting figures in the theory section.
- In figures 1 and 4, and in all basemaps the horizontal label Y is meaning less and is introduced after using. Also in figure 11, it changed to X. So I advise to unify them and change it to distance, maybe become more sensible.
Minor comments:
Increase the X and Y axis ticks and labels in figures 6, 7, 11. It is difficult to read them now.
Line 68: Introduce the x' after equation 5 too.
Line 78: Using the "noise-free" is an exaggerating phrase here, because beside the KPSDM result, it is a clear image but not generally free of any artifacts.
Line 89 and 91: It is better to change one of the names for scattering azimuth angle or illumination azimuth angle, because their symbols in figure 2 are hardly distinguishable.
Figure 8: There isn't any red circle in the figure which is introduced in the caption.
Based on supplying a synthetic example which the single path is violated on, I recommend a major revision.
Citation: https://doi.org/10.5194/se-2021-143-RC2 - AC2: 'Author response to Referee 2', Tomi Jusri, 08 Apr 2022
-
EC1: 'Editor Comment on se-2021-143', Michal Malinowski, 09 May 2022
Dear Authors,
I had now a closer look at your responses to reviewers’ comments. I also went through the manuscript and the reviewers’ comments again. My general observation is that the real data example from a hardrock site is too much of a jump from the synthetic example presented. I don’t agree with your reasoning that since the velocities are not much differentiated in crystalline rocks, therefore your simple 2-layer model is a sufficient justification. There are other challenges, including steeply dipping reflectors, complex wave interference and scattering. A more complex synthetic example can help you in explaining the benefits of FVM vs KPSDM for AVA, as noted by Reviewer 1:
“The problem is not the method but the simplistic model, which excludes the potential interference of smeared migration artifacts on AVA data. The impact of such interference on AVA curves (which should be more significant for KSPDM) can only be demonstrated by using a slightly more complex model with several geological layers. Such an example is necessary to show how FVM can help and improve AVA analysis”.
In other words, the synthetic data need to have some degree of migration noise from layers interfering with the amplitudes of reflections from the shallower layer(s). Therefore, I insist on making another synthetic example with more layers and/or complex structure (dipping reflector, wedge) to better illustrate the above issue.
Another thing is the real data example. It is not very meaningful as it stands right now. It is just illustrating that the common-angle stacks from FVM are less noisy as compared to KPSDM (Isn’t it a general property of FVM as compared to KPSDM, something you will observe also for offset gathers). Getting from there to the quantitative interpretation is a long way ahead (primarily because of the amplitude handling during processing and scarcity of the wireline logs).
Reviewer 1 was also advocating for “A field example from a less complex geological environment with supporting petrophysics (i.e. wireline logs for quantitative analysis)”. I agree with this comment – if only you can have such an example, it would be much more beneficial for demonstrating the perspectives of your method for QI (which is the ultimate goal of developing your method, anyway). Going one step further from your AVA gathers / stacks to either reflectivity inversion or impedance inversion would be a great benchmark for your method (confronted and calibrated with the borehole data). And you can use standard industry tools for this step.
I understand that the new real data example might be more challenging, as it depends on the data you have. Therefore, to sum up: in my opinion, a more complex synthetic model example is a must. New real data example – depending on whether you can find a suitable target for your analysis. Definitely, it will strengthen your manuscript.
Best regards,
Editor
Citation: https://doi.org/10.5194/se-2021-143-EC1 -
AC4: 'Reply on EC1', Tomi Jusri, 11 May 2022
Dear Editor,
Thank you for your patience. We have discussed your comments thoroughly.
The proposed approach is based on a homogeneous medium assumption, and therefore, it is valid for amplitude calculation only from a single reflector. Using a complex geologic model, for example, a two-reflector model, the proposed approach will not calculate the AVA curve for the deeper reflector correctly because it does not consider factors affecting the wave propagation through the heterogeneous media, such as amplitude losses and ray bending. If we want to consider heterogeneous media, we will have to incorporate another sophisticated method to allow estimating the amplitudes correctly, for example, the transport equation (e.g., Buske S., Finite-difference solution of the transport equation: First results, Pure and Applied Geophysics, 148, 565–581,1996). The inclusion of such a method is beyond the scope of our manuscript.
On the other hand, our manuscript offers a novel approach to obtaining angle domain common image gathers (ADCIGs) from Fresnel volume migration (FVM) for a simple two-layer geologic model. While we understand that the test on a more complex geologic model is essential for establishing a technique for QI in hard rocks, we strive to reach intermediate progress and a new milestone in this very challenging topic. We doubt that we can provide a more established technique soon enough for the current submission. Nevertheless, for the current submission, we can offer the following:
1) A synthetic test using a single dipping reflector, as you also mentioned, as one of the possibilities for a more complex geologic model :
"Therefore, I insist on making another synthetic example with more layers and/or complex structure (dipping reflector, wedge) to better illustrate the above issue."
2) Editing the premise of the manuscript to make it clearer to the readers from the beginning that the current experiment is limited to a simple two-layer geologic model. We will change the title, abstract, introduction, discussion, and conclusions of the manuscript for this.
Regarding the field seismic data set, we do not have proper borehole data for the AVA analysis for the geothermal area in Italy. Furthermore, since the approach is not yet valid for a multi-reflector model, we doubt that performing AVA inversion from field seismic data controlled by borehole data will be meaningful. However, what we can offer for the current submission is:
3) Prestack analysis from the migrated field seismic data, made possible now by the proposed approach.
In conclusion, we hope you can consider the three points mentioned above sufficient for the revised manuscript. Should you be willing to consider this revision, we would like to ask for more time to submit the revised manuscript, i.e., until 31 July, when possible.
We look forward to hearing from you.Sincerely,
Authors
Citation: https://doi.org/10.5194/se-2021-143-AC4
-
AC4: 'Reply on EC1', Tomi Jusri, 11 May 2022
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