Physically Based and Empirical Ground Motion Prediction Equations for Multiple Intensity Measures (PGA, PGV, I_a, FIV3, CII, and Maximum Fourier Acceleration Spectra) on Sakhalin Island

Round 1

Reviewer 1 Report

COMMENTS ON THE REVIEW COPY

GEOSCIENCES_2342132_2023_13, x.  https://doi.org/10.3390/xxxxx

            The paper entitled “Physical based and empirical ground motion prediction equations for multiple intensity measures (PGA, PGV, Ia, FIV3, CII and Maximum Fourier Acceleration spectra) in Sakhalin Island” by A. Konovalov, I.Orlin, A. Stepnov and Y. Stepnova  is a very good and useful research, concerning the critical issue of the regional predictive models of a variety of ground shaking measures combining various characteristics of the source to site distances. Additionally suitable mathematical formulation is developed, being proposed ground motion empirical equations in statistical, physical and geometrical representation giving appropriate empirical constants. Some very new and useful empirical parameters have been adopted and some source parameters as the stress drop were considered and estimated.

The paper is in a good format with adequate formulations, figures and tables. Some minor comments/corrections are included in this review, in order to improve the final presentation of the paper. Taking into account the general presentation of the paper, the data used and the applied approach I would like to recommend this paper for publication in the Geosciences journal with some minor revisions.

Some minor comments/corrections are incorporated improving the final version of the manuscript.

1.            Page 1, line 13: You mention at the end of the line that the Hypocentral distance was used as a basic distance metric. Although in the manuscript and other distance metrics have been applied (e.g. Repi, Rjb etc). Clarify and give some more analytical description regarding the adopted distance metrics.

2.            Page 2, line 91: You mention a parameter CII but not any description / information is given in the introduction regarding this parameter. Include some detailed description.

3.            Page 3, line 131: Replace the cubic type to cubic type equation.

4.            Page 5, line 166-170: Explain what are the αLP1, αHP1 and αHP3. Give explanations

5.            Page 6, line 181: You have used Repi=3.9 km. Why do you not apply a Hypocentral distance??? Comment.

6.            Page 8, line 206: Replace the word – parameters to regression parameters.

7.            Page 8, line 208. You adopted a point-source approximation and comment that this approach … seems to be reasonable for a M=6.0. Usually since the beginning of 90’s, the point source model is used for seismic sources with M<5.2-5.5. For magnitudes M5.5 or greater adopted finite fault model. Comment your selection.

8.            Page 8, line 234-236. Document your choice of the stress drop ~ 3MPa. Usually, the stress parameter for crustal earthquakes is around 5-7 MPa. Is there any particular reason for this low stress drop parameter????

9.            Page 11, line 300: the Ref.37 has an incomplete writing in the Reference List. Correct it.

10.        Page 12, line 340-347. Explain how you adopted all the physical representation parameters in your calculations. Did you utilize bibliographical references or you made suitable computations???

11.        Page 19, line 474-475. In your conclusions you mentioned that the stress drop of the asperities was about 16 MPa, but in previous pages you mentioned that the stress drop = 3 MPa. Clarify or give extra info regarding the stress drop computations.

12.        General Comment:  Always publications which propose GMPEs for various strong motion parameters present suitable correlations of the proposed-new GMPE with others from different seismotectonic environments or different strong motion data etc. In present case, except for Fig 8, where A (spectral level) versus Mw for various tectonic regions, no any other GMPE comparison is given in the paper. It would be noteworthy to present a such correlation of your GMPEs with other of different tectonic regimes.   

Author Response

Response to Reviewer 1 Comments

Thank you very much for the careful reviewing!

Point 1: Page 1, line 13: You mention at the end of the line that the Hypocentral distance was used as a basic distance metric. Although in the manuscript and other distance metrics have been applied (e.g. Repi, Rjb etc). Clarify and give some more analytical description regarding the adopted distance metrics.

Response 1: We have added a brief description of the most commonly used distance metrics (see Introduction):

In addition to a variety of ground shaking measures, there are also various characteristics of the distance between the source and the site. Hypocentral distance (Rhyp) is quite suitable for point source models, while measures such as Rrup (the closest distance between the site and the three dimensional rupture plane) and Rjb (shortest distance from a site to the surface projection of the rupture plane) are most commonly used for finite sources. The role of high-frequency radiation is also reflected in modified distance metrics (e.g., [19]).

Point 2: Page 2, line 91: You mention a parameter CII but not any description / information is given in the introduction regarding this parameter. Include some detailed description.

Response 2: A brief description of CII has been included to the Section 2.2.1 Intensity Measures.

Point 3: Page 3, line 131: Replace the cubic type to cubic type equation.

Response 3: Revised.

Point 4: Page 5, line 166-170: Explain what are the αLP1, αHP1 and αHP3. Give explanations

Response 4: Notation has been added to the text.

Point 5: Page 6, line 181: You have used Repi=3.9 km. Why do you not apply a Hypocentral distance??? Comment.

Response 5: Revised: The hypocentral distance is 9.5 km.

Point 6: Page 8, line 206: Replace the word – parameters to regression parameters.

Response 6: Revised.

Point 7: Page 8, line 208. You adopted a point-source approximation and comment that this approach … seems to be reasonable for a M=6.0. Usually since the beginning of 90’s, the point source model is used for seismic sources with M<5.2-5.5. For magnitudes M5.5 or greater adopted finite fault model. Comment your selection.

Response 7: You are quite right! The maximum moment magnitude in our dataset is Mw=5.8. The nearest instrumental site for the Mw=5.8 earthquake is located at the hypocentral distance of 21.5 km. So, we are proposing that the finite-fault effects for the distances above 21.5 km are negligible.

We have revised the corresponding text.

Point 8: Page 8, line 234-236. Document your choice of the stress drop ~ 3MPa. Usually, the stress parameter for crustal earthquakes is around 5-7 MPa. Is there any particular reason for this low stress drop parameter????

Response 8: According to [Allmann, B. P., and Shearer, P. M. (2009), Global variations of stress drop for moderate to large earthquakes, J. Geophys. Res., 114, B01310, doi:10.1029/2008JB005821] the average stress drop for crustal earthquakes in the collision boundaries varies from 2.6 MPa (continental) to 3.4 MPa (oceanic). Sakhalin Island is considered as transition zone form ocean to continent with predominantly collision tectonic regime. So, the mean value of stress drop between continental and oceanic tectonic regimes seems to be reasonable. To the other hand, regional stress drops estimated from Fourier spectra on the average is close to 3 MPa [Konovalov, A.V; Sychev, A.S.; Solov’ev, V.N. Mass estimates of the scalar seismic moments of small earthquake foci on southern Sakhalin. Russ. J. Pacific. Geol. 2011, 5, 225-233. https://doi.org/10.1134/S1819714011030055].

We have citied the corresponding paper.

Point 9: Page 11, line 300: the Ref.37 has an incomplete writing in the Reference List. Correct it.

Response 9: The completed reference has been revised: Kostrov, B. V. Mechanics of Tectonic Earthquake Source. Nauka, Moscow. 1975, 176.

Point 10: Page 12, line 340-347. Explain how you adopted all the physical representation parameters in your calculations. Did you utilize bibliographical references or you made suitable computations???

Response 10: We have utilized the bibliographical reference. It is given in the text: Table 2 contains a list of material parameters and physical constants that are further used in the calculations; they are mainly taken from [35].

Point 11:  Page 19, line 474-475. In your conclusions you mentioned that the stress drop of the asperities was about 16 MPa, but in previous pages you mentioned that the stress drop = 3 MPa. Clarify or give extra info regarding the stress drop computations.

Response 11:

From recent studies of the earthquake source and rupture process it is known that strong ground motion is related to the slip heterogeneity. Asperities recognized as regions on the fault that have large slip relative to the average slip of the rupture area. The asperity areas, as well as the entire rupture areas, scale with the total seismic moment. So, we are considering the multi-asperity source model. The size and stress drop of asperity are significant parameters for predicting strong ground motion. The average stress drop of the circular-crack considered in the current study is the 3 MPa. The stress drop on asperities for the examined earthquakes was about 16 MPa.

Point 12: General Comment: Always publications which propose GMPEs for various strong motion parameters present suitable correlations of the proposed-new GMPE with others from different seismotectonic environments or different strong motion data etc. In present case, except for Fig 8, where A (spectral level) versus Mw for various tectonic regions, no any other GMPE comparison is given in the paper. It would be noteworthy to present a such correlation of your GMPEs with other of different tectonic regimes.

Response 12:

We compared the resulting equation for PGA with several global and regional models for crustal seismicity (see Figure 10). These four GMPEs are: AS1997 [46], ASB2013 [44], JSGGA2022 [47] and MF2013_1 [29]. The comparisons are shown on each panel corresponding to the earthquake magnitude M 4, M 5.0 and M 6. Attenuation equations were reduced to the VS30=350 m/s and reverse faulting mechanism. Models JSGGA2022 and ASB2013 were developed using Rhyp metric whereas other GMPEs used Rrup and Rjb. Although GMPEs are guided with different uses in distance metrics, it does not significantly affect the results due to the point-source approximation for the considered magnitude range.

Figure 10 indicates the model-to-model variability caused by regional differences. As it can be seen in these figures, the simple point-source model developed in the current study does not extrapolate well to magnitudes M>=5 at short distances that often control seismic hazard. To be useful for seismic hazard applications, the GMPE needs to extrapolate in a reasonable manner. The finite-fault term added to the distance metric in (4) is one way to get the point-source model to extrapolate properly. We are importing this term from the model MF2013_1. The MF2013_1 model for crustal seismicity in Japan was developed in the form of geometric representation of GMPE. It means that geometrical spreading term in (4) is taken =1. So, we are adding additional term to equation (4). The hybrid model is now getting the form

where  and  are the constants: =0.006875, =0.5.

The parameters of the developed attenuation model in the geometric representation are given in Table 3c. The corresponding illustration is given in the Figure 10.

The lineament-domain source model is used in seismic hazard assessments on Sakhalin Island. The maximum magnitude for area sources does not exceed Mw 6. For such seismic sources, one can use the regional attenuation equation (41), while for extended line sources the global models should be applied.

We have revised the corresponding text.

Author Response File: Author Response.docx

Reviewer 2 Report

comments attached

Comments for author File: Comments.pdf

Author Response

Response to Reviewer 2 Comments

We would like to thank anonymous reviewer for the constructive criticism and valuable remarks which have significantly improved the manuscript.

General Comments

Point 1: What is the reason for not constraining both the a and k terms to their physical values?

Response 1:

The parameter a shows the scaling between the seismic moment and the rupture area, which, according to the circular-crack model (Kostrov, Das, et al.), is given as: M₀ ~ S^3/2. The coefficient a in this case takes the value 0.5. It is difficult to describe the statistical scattering from the given law in terms of the stress drop of the circular-crack. Therefore, within the framework of the physical model, the coefficient a is fixed at the value of 0.5.

Point 2: I think that fitting 12 different ground-motion metrics using either Mw or ML is a distraction that does not add much to understanding the key issue of defining the high-frequency amplitude. If MFAS is the best parameter for estimating the stress drop, then it would be better to focus the regression for this parameter. If there is a need to show the fits to all of these ground-motion metric, the reason should be clearly explained.

Response 2:

Different metrics of strong ground motion are used in various applied issues. For example, PGA/PGV are most commonly used in the seismic hazard assessments. The Arias intensity (Ia) is most commonly used in seismic risk assessments, including geotechnical and structural applications. The FIV3 metric has been proposed recently. It is consisted with the potential damage assessment. Although this metric is not as popular as PGA, PGV or Ia, we use FIV3 for empirical testing and comparison of ground motion equations with most commonly used strong ground motion metrics.

Additionally we proposed the high-frequency spectral measurements such as high-frequency Arias intensity and maximum Fourier acceleration spectra. From recent studies of the earthquake source and rupture process it is known that high-frequency incoherent radiation is related to the slip heterogeneity. Asperities are recognized as regions on the fault that have large slip relative to the average slip of the rupture area. The asperity areas, as well as the entire rupture areas, scale with the total seismic moment. The size and stress drop of asperity are significant parameters for predicting strong ground motion. So, the spectral metrics are the best parameters for estimating stress drop on the asperities.

The results show that the attenuation relations based on the MFAS spectral metric are characterized by the smallest scattering among the considered ground motion measures.

The MFAS metric has one significant disadvantage. Peak amplitude of the spectrum can be caused not only by the asperity radiation, but also by soil amplification. In practice, it is rather problematic to discriminate the contribution of these phenomena. It requires the geotechnical studies or/and the investigation of H/V spectral ratios at the site.

At the same time, the modified Arias intensity is an integral characteristic (averaged over the corresponding frequency range in the spectral domain). We expect that the soil amplification factor does not affect significantly the Ia-based GMPEs.

The attenuation equations for the multiple intensity measures are developed for the first time for the target area. So, it is the main reason to show all of these ground-motion metrics and corresponding attenuation equations.

Corresponding revision have been made (see Introduction and Discussion).

Point 3: The physical model is based on moment magnitude. What is the reason for using ML with the physical model? If the ML is a better magnitude scale to use with the physical model, the technical basis for this should be explained.

Response 3: Yes. Using magnitude ML for a physical model doesn't make sense. The corresponding data in the tables and the text have been removed.

Point 4: The simple point-source model does not extrapolate well to large magnitudes at short distances that often control seismic hazard. For the Sakhalin Island, large events occur (e.g., M6.8 to M7.3 shown in Fig 1). To be useful for seismic hazard applications, the GMM needs to extrapolate in a reasonable manner. The finite-fault term (d exp(eM)) added to the distance in eq (2) is one way to get the point-source model to extrapolate properly. In this study, the finite- fault term is set to zero because there are insufficient data to constrain the d and e coefficients. Ignoring the finite-fault term limits the applicability of the results model. The standard approach for developing regionalized GMMs with sparse data is to constrain the finite-fault term based on coefficients from global models that have enough data to constrain the finite- fault coefficients or to use finite-fault simulations (e.g., ExSIM) to constrain the coefficients.

Response 4:

We compared the resulting equation for PGA with several global and regional models for crustal seismicity (see Figure 10). These four GMPEs are: AS1997 [46], ASB2013 [44], JSGGA2022 [47] and MF2013_1 [29]. The comparisons are shown on each panel corresponding to the earthquake magnitude M 4, M 5.0 and M 6. Attenuation equations were reduced to the VS30=350 m/s and reverse faulting mechanism. Models JSGGA2022 and ASB2013 were developed using Rhyp metric whereas other GMPEs used Rrup and Rjb. Although GMPEs are guided with different uses in distance metrics, it does not significantly affect the results due to the point-source approximation for the considered magnitude range.

Figure 10 indicates the model-to-model variability caused by regional differences. As it can be seen in these figures, the simple point-source model developed in the current study does not extrapolate well to magnitudes M>=5 at short distances that often control seismic hazard. To be useful for seismic hazard applications, the GMPE needs to extrapolate in a reasonable manner. The finite-fault term added to the distance metric in (4) is one way to get the point-source model to extrapolate properly. We are importing this term from the model MF2013_1. The MF2013_1 model for crustal seismicity in Japan was developed in the form of geometric representation of GMPE. It means that geometrical spreading term in (4) is taken =1. So, we are adding additional term to equation (4). The hybrid model is now getting the form

where  and  are the constants: =0.006875, =0.5.

The parameters of the developed attenuation model in the geometric representation are given in Table 3c. The corresponding illustration is given in the Figure 10.

The lineament-domain source model is used in seismic hazard assessments on Sakhalin Island. The maximum magnitude for area sources does not exceed Mw 6. For such seismic sources, one can use the regional attenuation equation (41), while for extended line sources the global models should be applied.

Figure 10. Distance attenuation of PGA for comparison of the developed GMPEs with the global and regional attenuation equations . The description of the models is given in the text.

We added a new Section: 4.2. Comparison of GMPEs and Finite-Fault Effects

Point 5: The paper shows that the asperity stress drop is proportional to the MFAS. Some discussion of the resulting stress drops would be useful. For example, is the average asperity stress drop for the Sakhalin Island region different from other regions? If the stress drop is not different from a global average, then global ground-motion models can be applied to the Sakhalin Island region.

Response 5: We agree with the comment.

The review of this problem regarding the stress drop on asperities showed that the most common estimates were provided for inland crustal earthquakes in Japan. According to [Satoh, T., Okazaki, A. (2016). Relation Between Stress Drops and Depths of Strong Motion Generation Areas Based on Previous Broadband Source Models for Crustal Earthquakes in Japan. In: Kamae, K. (eds) Earthquakes, Tsunamis and Nuclear Risks. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55822-4_6] the average stress drops are 21.2±9.2 MPa, 13.3±5.3 MPa and 18.0±8.6 MPa for reverse, strike-slip and all types of faults, respectively. Taking into account that the source mechanisms of Sakhalin earthquakes are predominantly reverse and strike-slip faults, the value of 18 MPa seems to be reasonable for comparison with the same one in the current study (16 MPa). The comparison clearly showed that the stress drop on asperities for examined earthquakes is generally close to similar estimates for crustal earthquakes in Japan.

So, inland part of Japan may be proposed as a master region for selecting seismic records and further developing of the regional ground motion prediction equations in a wide range of magnitudes.

A brief review of stress drop studies in other regions (in the context of multi-asperity model) has been included to the Section 3.2.

Point 6: The authors propose using a new magnitude measure MIa. To use this new magnitude measure in seismic hazard, you would need to develop the source characterization for MIa. For faults, you would not be able to convert slip rate to earthquake rates by balancing the moment rate on the fault.

The alternative approach is to use Mw for the magnitude and use the stress drop parameter to calibrate the high-frequency amplitude. If there is an advantage of defining a new earthquake magnitude, then the use of this magnitude should be discussed.

Response 6: This is a good idea!

The advantages of a new earthquake magnitude are: 1) it deals both with the asperity size and stress drop on asperity, 2) the size and stress drop of asperity are significant parameters for predicting strong ground motion, 3) the asperity areas, as well as the entire rupture areas, scale with the total seismic moment (e.g., [Irikura, Miyake, 2011]), 4) from log-linear dependence between acceleration source spectral level and moment magnitude it follows that spectral-based magnitude does not saturated in the high value range, 5) the proposed magnitude scale is calibrated in the near-source distance range, 6) calibration equation in terms of point-source distance metrics is considered to be a better metric, not least because studies have shown that the hypocenter is often located close to areas of relatively large slip, which are considered as sub-sources of high-frequency incoherent radiation (e.g., [Akkar S., Sandkkaya M.A., Bommer J.J. Empirical ground-motion models for point- and extended source crustal earthquake scenarios in Europe and the Middle East // Bull. of Earthq. Engineering. 2014. 12(1): 359–387. doi: 10.1007/s10518-013-9461-4]).

The efficient magnitude determination immediately after significant earthquakes is extremely important for the early warning issues. The most commonly used regional and teleseismic magnitudes are saturated. It results in significant underestimation of earthquake size, potential damages and tsunami hazard. USGS reports reliable moment magnitude estimation, based on W-phases inversion, 30-60 min after the origin time of the large earthquake. Some approaches propose a shorter times of order of 10 min (e.g., [Qiang Yao, Dun Wang, Lihua Fang, Jim Mori; Rapid Estimation of Magnitudes of Large Damaging Earthquakes in and around Japan Using Dense Seismic Stations in China. Bulletin of the Seismological Society of America 2019; 109 (6): 2545–2555. doi: https://doi.org/10.1785/0120190107]), meanwhile the efficiency strongly depends on network coverage and other technical details. So, rapid and accurate estimation of earthquake magnitude is still important problem.

In seismic hazard assessments the moment magnitude is more suitable among the other magnitude scales because it directly deals with the rupture size. The alternative approach is to use Mw as a basic measure of the asperity size, while stress drop parameter is used for calibrating the high-frequency amplitudes. This is one of the areas for further research.

Corresponding revision have been made (see Section 3.3).

Point 7: The paper shows that the simple functional forms used in GMMs is consistent with a simple physics-based point-source model. For the last 30 years, GMM developers have relied on the functional form of the point-source model proposed by Boore (1983) and updated over the years to understand and constrain the coefficients for GMMs. For example, the effect of the magnitude dependence of the corner frequency is the basis for the quadratic magnitude scaling in GMMs. The effect of the two site terms (amplification due to the VS profile and attenuation due to kappa) on the spectral shape have been incorporated into the GMM scaling.

The text includes several pages on the point-source model and the simplified form used for the regression. I think that this section could be shortened and just reference previous studies that fit ground-motion data to the point-source model (e.g., Atkinson and Silva, 2000 BSSA).

Response 7: We fully agree with reviewer. The text has been shortened.

Point 8: The authors highlight that they showed the relation between the Arias intensity and the physics-based model for the first time, but I don't see what is new here. As noted in the paper, the Arias intensity is related to the FAS(f) through Parseval's theorem. The high-pass filter applied to the AI in the paper just limits the lower frequency range used in the integral. The point-source model defines the FAS(f), so it is directly related to the Arias Intensity. If there is something fundamentally new about relation between the physical model and the Arias intensity, then it should to be clearly identified and explained.

Response 8:

The ideas of a developing of the physically-based GMPEs were proposed in [Hanks, T.C. and McGuire, R.K. The character of high-frequency strong ground motion. Bulletin of the Seismological Society of America. 1981. 71, 2071-2095.]. Hanks and McGuire used the Parseval’s theorem, which states that the integral of the square of a function is equal to the integral of the square of its Fourier transform.

In [Wilson, 1993] source related acceleration spectrum was modeled by the simplified band-limited function. It takes constant value between a lower frequency, related to the source size, and an upper bounding frequency, related to the upper-crustal attenuation. The source spectrum proposed to be zero outside the mentioned frequency range. Geometrical spreading was considered as a major attenuation factor. Anelastic attenuation was neglected. As a result there were derived semi-empirical relations between Arias intensity, moment magnitude, source-to-site distance and static stress drop.

Stafford et al. [2009] considered a more general case, when earthquake acceleration spectrum is given by the multiplication of attenuation and source functions. Authors proposed -Brune spectrum in the framework of single-crack source model. The attenuation was described by the geometrical spreading and frequency independent Q-factor.

We are introducing an improved analytical predictive equation for Arias intensity. We gathered all attenuation functions such as frequency dependent anelastic attenuation, upper crustal attenuation, upper crustal amplification factor and geometrical spreading. The idea of utilization of the Parseval’s theorem for developing the analytical attenuation equations is not new. The novelty of the given approach is that high-frequency radiation is described in terms of multi-asperity source model.

The text has been revised.

Specific Comments

1. Section 2.12 data set

(1a) What is meant by monitoring over the "long duration"?

It means long-term observations. The text has been revised.

(1b) The format of the data does not need to be explained.

The text has been removed.

(1c) What are the number of recordings, number of earthquakes, and number of different stations in the data set?

The total amount of recordings, earthquakes and stations in the dataset are 285, 28 and 22, respectively. The total amount of CII measures is 131. The number of CII with two or more felt reports is 83.

We have added the total amounts of records, earthquakes and stations.

2. Page 6, line 185

The terminology "quadratic acceleration spectrum" is not familiar to me. Combining the two components in this manner is typically called the "vector sum".

The text has been revised.

3. Page 8, lines 195-196

The manuscript says that the variability of site conditions in Japan is very low. What is the basis for this this statement? Comparisons of the site terms in Japan with other regions have shown shows much larger variability or the site terms for a given VS30 in Japan than in California (e.g., Abrahamson and Gulerce, 2022, Earthquake Spectra)

Yes, there is a misinterpretation of the site term. The meaning is that reference soil conditions is similar in both regions.

We have removed the text about variability of site conditions in Japan.

4. Page 8, eq (2)

Eq (2) does not include a site term. Is the implication that there are no differences in the site effects throughout the Sakhalin Island?

Yes, exactly.

5. Page 8, lines 211-212

Using hypocenter distance is not a substitute for the finite-fault effect.

The point source model is most commonly used for seismic sources with Mw<5.5. We considered earthquakes with magnitude up to Mw 5.8. The nearest instrumental site for the Mw 5.8 earthquake is located at the hypocentral distance of 21.5 km. So, we are proposing that the finite-fault effects for distances above 21.5 km are negligible. The point-source approximation seems to be reasonable for a given magnitude and distance ranges.

We have revised text. The discussion of finite-fault effects is given in Discussion Section.

6. Page 12, lines 323-328

Does the analytical expression for MFAS consider the large variability in the frequency dependence of the FAS or is it based on an idealized smooth spectrum?

Figure 9 shows the distribution of the frequencies corresponding to the maximum of FAS. The median value is about 1.6 Hz. It is closely related to the value of 2.4 Hz proposed in [Gusev, 1989]. The variability in the frequency dependance is caused by source and attenuation factors. So, upper crustal attenuation and amplification factor should be determined before spectral fitting.

We have included this answer to the text (see Discussion, Sect. 4.1).

7. Tables 3a,b,c

List the units of the standard deviation. Is this log10 or natural log for the ground-motion measures? It looks like log10.

Yes, log10. It follows from equation (4) and Tables 3a-c.

8. Page 15, lines 364-365

The lower standard deviation for the MFAS compared to the FAS(f) is expected from simple statistics. The distribution of the maximum of a set of random numbers has a smaller standard deviation than the standard deviation of the random values themselves. The text should indicate that this lower standard deviation is an expected result.

Yes! We have included this statement to the text (see Discussion).

9. Page 15 lines 373-377

The small increase in the standard deviation for constraining either the magnitude coeff (a) or the geometrical spreading coeff (k) just shows that these two are strongly correlated in the data set. If one is constrained, there is a tradeoff with the other. To test the physical model, both a and k should be fixed at their physical values. I expect that the standard deviation would increase significantly in this case.

Yes. The statistical scattering increases in this case. We have included this recommendation to the Results Section.

10. Page 15, lines 383-384

Wouldn't it be much easier to just invert the FAS(f) for the point-source parameters rather than going through MFAS?

It lies in our research interest. The next step of our study is to select the seismic records from active crustal regions and to improve GMPEs, including inverting FAS(f).

11. Page 18, lines 449-456

This paragraph says that the models developed in this study can be used for accurate prediction of ground motion in active crustal regions. I don't see the basis for this statement. You would need to test the models against a larger data set. Figure 8 is not enough to demonstrate that the model based on the very sparse data set is a good global model that can be used in any active crustal region.

We agree. We have revised the text and mentioned the target area only.

12. Figure 8

Figure 8 shows that there are regional differences in the average high-frequency amplitude. For example, the Japan intraplate events have systematically larger values than other regions. A good use of the local data would be to estimate the region-specific high-frequency amplitude to develop an improved model over use of a global average model for stress drop.

It is a good idea. We have included this recommendation to the Discussion Section.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

The authors addressed my comments, but some were not adequately addressed as noted below.

1. My main concern with this study remains the development of ground-motion models (GMMs) based on sparse local data (M4-M6). Fig 1 shows that there have been 3 events with M6.8-7.3 since 1971.  Any GMM for this region needs to be applicable to M7 events.  The point-source model may be appropriate for the events in the data set, but it is not appropriate for the events that will control the hazard in the region without adding a finite-fault term (effective distance)

The model based on hypocentral distance will not scale properly to M7 earthquakes at short distances. The comparison of the proposed model with other models in Fig 10 is only for M4, 5, 6.  This does not show that the proposed model is appropriate for the larger magnitude events that will control the hazard in this region. Even for M6, it is clear the distance slope at short distances is too strong. This will become a larger issue for M7. 

To show this limitation of the model, add a plot of the model comparison for M7. I expect this will show a large difference between the proposed model and the other models.

2. The limitation of the range of applicability of the proposed model (mag and distance) should be clearly stated in the conclusions.

3. I remain surprised that there is no site term in the model. Is this due to lack of information about site conditions or did the data show that there are not differences in the site effects throughout the region?  It is hard to believe that there are no differences in the site effects for this entire region.

Add text to Section 2.2.2 to clearly state why site effects are not included in the model.  

4. The statistical model for the regression is ordinary least squares (OLS). For the last 25 years, mixed-effects regressions are the standard approach used for GMMs to account for correlations in the data.  Add a sentence to section 2.2.2 to explain why OLS is appropriate for this data.

5. The revised text needs to be reviewed for English grammar and style.

Author Response

Response to Reviewer 2 Comments

Point 1: My main concern with this study remains the development of ground-motion models (GMMs) based on sparse local data (M4-M6). Fig 1 shows that there have been 3 events with M6.8-7.3 since 1971.  Any GMM for this region needs to be applicable to M7 events.  The point-source model may be appropriate for the events in the data set, but it is not appropriate for the events that will control the hazard in the region without adding a finite-fault term (effective distance)

The model based on hypocentral distance will not scale properly to M7 earthquakes at short distances. The comparison of the proposed model with other models in Fig 10 is only for M4, 5, 6.  This does not show that the proposed model is appropriate for the larger magnitude events that will control the hazard in this region. Even for M6, it is clear the distance slope at short distances is too strong. This will become a larger issue for M7. 

To show this limitation of the model, add a plot of the model comparison for M7. I expect this will show a large difference between the proposed model and the other models.

Response 1:

We have added a plot of the model comparison for M7 (see Fig. 10).

We have prepared additional Figure that show the normalized data for M=7 and corresponding attenuation model.

Figure 11 shows a comparison of attenuation curves with data normalized to Mw 7.0. The observed data were normalized as follows:

lg obs’ = log obs + log pre(Mw=7) - log pre(M),

where obs’ is the normalized data, obs is the observed data, pre(M) is the predicted value by (40) for identical parameters with observed data and pre(Mw=7) is the predicted value of Mw 7.

The PGA values at the near-source distances are close to the flat level around 800 cm/sec/sec. The PGA values converted from macroseismic intensity of the catastrophic 1995 Neftegorsk earthquake (Mw 7.1) are fitted well the prediction model.

Point 2: The limitation of the range of applicability of the proposed model (mag and distance) should be clearly stated in the conclusions.

Response 2:

Recorded strong motion dataset was used, making GMPEs applicable to the earthquake magnitude range of 4 to 6 and distance range up to 150 km.

We proposed the GMPE corresponding to the simple point source model with the physical value of geometrical spreading for the prediction of PGA in Sakhalin Island and surrounding shelf. The applicability of the given model is strictly bounded in the magnitude range from 4 to 6. Site and finite-fault terms describing the PGA model in Japan, are preferred for using in the present GMPE.

Corresponding revision is given in the Conclusion.

Point 3: remain surprised that there is no site term in the model. Is this due to lack of information about site conditions or did the data show that there are not differences in the site effects throughout the region?  It is hard to believe that there are no differences in the site effects for this entire region.

Add text to Section 2.2.2 to clearly state why site effects are not included in the model.

Response 3: Almost all of the instrumental sites are classified as soil category D according to the NEHRP classification. The average measured S-wave velocity in the upper 30 m ground layer (V_S30) was 300-400 m/s (see Section Data Availability Statement). We propose to import the site term from Japanese GMPE [Morikawa, Fujiwara, 2013] that is characterized by the similar reference V_S30.

The text has been revised (see Section 2.1.2).

Point 4: The statistical model for the regression is ordinary least squares (OLS). For the last 25 years, mixed-effects regressions are the standard approach used for GMMs to account for correlations in the data.  Add a sentence to section 2.2.2 to explain why OLS is appropriate for this data.

Response 4: We have added to the Section 2.2.2 the following sentences:

For the last 25 years, mixed-effects regressions are the standard approach used for GMPEs to account for correlations in the data. The alternative approach that is widely used in Japan is the two-step stratified regression analysis method (e.g. [Fukushima and Tanaka, 1990; Kanno et al., 2006]). This method was proposed by Joyner and Boore [1981] to avoid the interaction between the coefficients a and k. In the other words, errors in measuring magnitude would affect the distance coefficient obtained from the ordinary least squares. Over last decades the accuracy of moment magnitude determination has significantly increased. Ordinary least squares seems to be appropriate for this dataset. So, the best coefficients of the model (4) were fitted by multiple linear regression. We analyzed the interaction between magnitude and distance terms by fixing of the coefficients a or/and k at their physical values (see Section 3.1).

Point 5: The revised text needs to be reviewed for English grammar and style.

Response 5: The text is revised by MDPI language service. The proofreading is provided.

Author Response File: Author Response.pdf