Regional spectral decay model for the Sichuan, China: Application in ground motion simulation of the Ms 6.0 Changning earthquake

Dang, Pengfei; Zhao, Bingyan; Liu, Qifang; Cui, Jie; Jia, Xinjian

doi:10.5194/egusphere-2026-5413

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https://doi.org/10.5194/egusphere-2026-5413

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21 Sep 2026

| 21 Sep 2026

Regional spectral decay model for the Sichuan, China: Application in ground motion simulation of the Ms 6.0 Changning earthquake

Pengfei Dang, Bingyan Zhao, Qifang Liu, Jie Cui, and Xinjian Jia

Abstract. 4260 recordings of 165 events by 168 stations were used to calculate the spectral decay kappa parameter. The kappa values of the two horizontal components were similar and generally larger than those of the vertical component. The impact of magnitude and site condition on the κ₀ value was also investigated, which showed that κ₀ increased with magnitude, indicating that κ₀ is influenced by source effects. In addition, the results showed that softer sites have higher κ₀ values, indicating that site conditions significantly affect κ₀ estimates. The single-station κ₀ values showed little difference between the two horizontal components, both of which were significantly greater than the κ₀value of the UD component. Furthermore, the relationships between κ₀ and Vs30 were derived, which indicates that κ₀ value decreases with increasing parameter Vs30. Moreover, the logκ₀-logf₀ correlations estimate the κ₀ better than the lnVs30-κ₀ correlation does. Finally, we performed ground motion simulations at 16 stations to validate the derived site-based kappa model. Ground motion simulations at 16 stations demonstrate that both site- and event-related κ₀ mainly affect high-frequency amplitudes. These findings provide a basis for seismic attenuation study and refined ground motion simulation in the study region.

Received: 07 Sep 2026 – Discussion started: 21 Sep 2026

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Pengfei Dang, Bingyan Zhao, Qifang Liu, Jie Cui, and Xinjian Jia

Status: final response (author comments only)

RC1:
'Comment on egusphere-2026-5413', Anonymous Referee #1, 21 Oct 2026
Major comments
Selection of the frequency range for κ estimation - Section 3

The estimation of κ can be sensitive to the frequency interval selected for fitting the high-frequency Fourier-amplitude spectral decay. The authors state that the lower limit is determined as f_E = 1.5f0, where f₀ is obtained from H/V, but subsequently report fixed f_E values of 12 and 9 Hz for Class C and D sites. It is unclear how f_E and f_X were selected in these cases. Please also clarify whether SNR > 3 was required throughout the fitted interval, how source-corner-frequency effects were considered, and whether the estimated κ values are stable under reasonable changes in the fitting bounds.
Separation of source, path, and site contributions - Lines 193–200; 213–243

The authors derive κ₀ by extrapolating κ = κ₀ + mR to zero epicentral distance. While conventional, this procedure does not in itself establish that the intercept is attributable exclusively to near-surface attenuation. The measured high-frequency spectral decay may also reflect source-spectral properties and path effects inadequately represented by a single regional distance slope. Please clarify how the source corner frequency and source spectral shape were controlled, and discuss whether spatial variations in path attenuation could influence the derived intercepts. In particular, please specify whether m was held fixed for station-specific regressions or estimated separately at each station. A sensitivity assessment of regional-slope assumptions and the propagated uncertainty in station-specific zero-distance intercepts, particularly where few recordings are available, would strengthen their interpretation as site-related parameters.
Statistical evidence for magnitude dependence - Lines 213–268

The conclusion that κ₀ increases with earthquake magnitude is not adequately supported by the presented results. Although the estimated intercepts increase across the three magnitude ranges, the differences are relatively small compared with their associated uncertainties. For example, the EW-component κ₀ increases from 0.0296 ± 0.0029 s for 3.0 ≤ M < 4.0 to 0.0326 ± 0.0041 s for 5.0 ≤ M ≤ 6.0. The authors should therefore provide statistical evidence supporting the significance of this trend, either through appropriate comparisons between magnitude groups or by explicitly modelling magnitude dependence. Moreover, the observed variations should be interpreted with caution, since the estimated zero-distance intercepts may also be affected by source-related spectral characteristics, frequency-band selection, and differences in the distance and station distributions among magnitude groups. The authors should clarify to what extent these effects have been accounted for before attributing the observed variations to a systematic magnitude dependence of κ₀.
Influence of site conditions and inconsistencies in Table 1 - Lines 224–243

The claim that softer sites have higher κ₀ needs stronger statistical support. For the EW component, the reported rock-site estimate (0.0330 s) is slightly higher than the soil-site estimate (0.0309 s); the Class C–Class D differences are also modest relative to their standard errors. Please report the numbers of stations and recordings in each group, the classification criteria, and direct tests of the relevant contrasts rather than inferring differences from individual estimates. There is also a numerical inconsistency: the Class C EW/NS/UD values stated at lines 225 (0.0313/0.0326/0.0218 s) differ from Table 1 (0.0329/0.0343/0.0174 s).
Reliability of station-specific κ₀ estimates - Lines 270–278; Table S1

The authors estimate station-specific κ₀ values for stations having at least four earthquake recordings. Although this selection increases the spatial coverage of the analysis, I am concerned about the reliability of κ₀ estimates obtained from such small samples. This issue is particularly relevant when the recordings cover a limited distance range, because the resulting zero-distance intercept may be strongly influenced by individual observations. Furthermore, the supplementary table shows considerable variability among station-specific κ₀ values, including several negative estimates that are subsequently replaced with zero. While replacing physically implausible negative values may be acceptable for some engineering applications, doing so also modifies the statistical distribution of κ₀ and potentially affects the subsequent empirical regressions. I recommend that the authors consider restricting the development of predictive relationships to stations with sufficiently well-constrained κ₀ estimates, or adopt a regression approach that explicitly accounts for the varying uncertainty of individual station estimates.
Statistical treatment of repeated observations - Section 4

The authors employ robust regression and Huber–White standard errors to quantify regression uncertainties; however, the hierarchical structure of the dataset suggests that correlations may exist among recordings associated with the same earthquake or recording station. This introduces potential correlations associated with both event-specific and station-specific effects. The standard Huber–White heteroscedasticity-consistent estimator does not, by itself, account for arbitrary dependence among observations sharing the same event or station. The authors should explain how these dependencies have been treated. I recommend revising the uncertainty analysis to account for the hierarchical structure of the dataset and distinguishing tests of individual coefficients from tests of differences between groups.
Consistency and reproducibility of stochastic ground-motion simulations - Lines 337–355; Table S2

The main text states that a stress drop of 8 MPa was selected through a trial-and-error procedure, whereas Table S2 reports 0.8 MPa. The authors must identify the correct value and clarify whether this parameter was calibrated using the same recordings subsequently employed for model validation. More importantly, the authors adopt earthquake H/V spectral ratios as local site-amplification factors and combine them with crustal amplification functions for NEHRP classes C/D. However, earthquake H/V amplitudes are not equivalent, in general, to absolute horizontal S-wave site amplification because the vertical component may be amplified itself. Comparisons with site/reference approaches indicate that H/V peak amplitudes often represent an approximate lower bound, not a guaranteed lower bound at every site and frequency (Duval et al., 2001). Methods explicitly correcting earthquake H/V for vertical amplification have been proposed (e.g., Zhu et al., 2020). Please justify the use of uncorrected H/V in EXSIM, clarify the reference conditions and potential overlap between the two amplification factors, and evaluate sensitivity to plausible alternative amplification functions.
Validation of the proposed κ₀ model - Lines 356–399

The authors compare observed ground motions with simulations obtained using station-related and event-related κ₀ values. However, the evidence presented does not adequately demonstrate that the station-related model provides a statistically significant improvement in predictive performance. Although period-dependent mean biases and standard deviations are reported in Figure 7, a more comprehensive quantitative comparison of the predictive performance of the two approaches would be helpful. For instance, the authors could compare the residual dispersion and RMSE of the two models as functions of spectral period, using paired station-by-station residuals. The independence of the validation procedure should also be clarified. The authors state that the event-related κ₀ was estimated from recordings of the Changning earthquake (lines 344–346), which is also the earthquake considered in the ground-motion simulations. However, it is unclear whether the specific recordings used to estimate the event-related κ₀ overlap with those subsequently employed for evaluating the simulations. Similarly, the authors should specify whether recordings of the Changning earthquake were included in the dataset used to derive the station-related κ₀ values, and which observations were used in the trial-and-error calibration of the stress drop. Finally, the authors should explain how the reported statistical results demonstrate the superiority of the station-related κ₀ model over the event-related approach, rather than simply indicating that both models exhibit limited average bias. Without these clarifications, the conclusion that the proposed station-related κ₀ model improves ground-motion simulations may remain insufficiently supported.
Numerical inconsistencies in the supplementary material - Tables S1 and S3

The authors should check the consistency of all station-specific parameters and numerical results in the supplementary material, since several numerical inconsistencies can be identified in the tables. For Table S3, which reports the observed geometric-mean PGA, simulated PGA, and their relative difference, I found appreciable discrepancies in 13 of the 16 rows, using the definition printed in the table. For example, station 51GXT yields (599.37 − 535.37)/599.37 = +0.107 rather than +0.02, while station 51YBY yields (16.94 − 19.264)/16.94 = −0.137 rather than −0.41. There are also inconsistencies between the station-specific κ₀ values reported in Tables S1 and S3. For example, station 51ZG2 has EW and NS estimates of approximately 0.0585 and 0.0626 s in Table S1, whereas Table S3 reports 0.0200 s.
Minor comments
Lines 114–143. The filtering procedure should be described in greater detail, including whether the 60 Hz upper corner could affect the fitted spectral decay below 50 Hz.

Lines 126–133. The definition of the S-wave window should be clarified. In particular, the criterion based on the cumulative root-mean-square function is not sufficiently described to ensure reproducibility.

Lines 175–179. The manuscript repeatedly refers to fE when describing both the lower and upper limits of the fitting interval. The notation should be corrected.

Line 152. Equation (1) should explicitly define the logarithmic base, the units used for Vs30, and the applicability limits of the empirical relationship.

Lines 273–276. Negative κ₀ intercepts do not necessarily imply that the observed high-frequency spectral amplitude increases with frequency. The physical interpretation should be revised.

Lines 287–296. Equations (5) and (6) should report the uncertainty associated with both the intercept and the regression slope.

Lines 307–315. The assertion that the κ0–f0 relationship is independent of region is stronger than can be established from a single study region, and conflicts with the statement that regional site conditions affect the relationship.

Line 344. The notation f0 is used both for the site fundamental frequency and for the source corner frequency in different sections. Different symbols should be adopted to avoid ambiguity.

Line 371. The sentence “event-related and event-related κ₀ values” appears to contain a repetition; one instance should presumably read “site-related”.

Figure S5. The caption refers to PSA although the figure displays Fourier amplitude spectra.

Table S1. The table contains entries marked with “&”, whereas the note describes “*” as the identifier for PEER-derived values.

The manuscript would benefit from a thorough revision of the English language, as several grammatical errors, typographical mistakes, and awkward expressions occur throughout the text. A non-exhaustive list of errors and suggested corrections is provided below:
Lines 44–45: relationships were derived, which indicates → indicate

Line 124: the record recorded by Station 015JYC → the recording from station 015JYC

Line 143: After the above screening steps were completely → After the screening steps were completed

Line 154: valid for f_peak > 1 Hz , In addition → valid for f_peak > 1 Hz. In addition,

Line 160: the H/V curve provide → the H/V curve provides

Line 185: was basically ranged from 35–50 Hz → generally ranged from 35 to 50 Hz

Line 192: are differ → differ

Line 209: Ktendiou et al. → Ktenidou et al.

Lines 210–211: divided into soft and rock → classified as soft-soil or rock sites

Lines 214–215: four site condition → four site conditions

Line 236: κ₀ values were refit → κ₀ regression models were refitted

Lines 270–271: values, which indicate that the near-surface spectral attenuation at the station, depend → rephrase

Line 280: around the word → around the world

Line 289: in which function ln() indicates the natural logarithm → where ln denotes the natural logarithm

Lines 307–310: The results showed ... , the results show … → consider splitting in two sentences

Line 310: the κ₀–f₀ correlations is independent → the κ₀–f₀ correlation is independent

Line 342–343: trial-and error tool → trial-and-error procedure

Line 356: pseudospectra acceleration → pseudo-spectral acceleration

Line 361: the simulated PSA → the simulated PSA values

Line 377: which may be resulted from → which may result from

Line 385: at most selected stations → at most of the selected stations (or, preferably, for most selected stations)

Line 426: a negative correlation was derived, this is largely due to a → negative correlation was observed. This may be partly attributable to

Line 430: A more stable relationships requires more records → More stable relationships require more recordings

Line 444: supporting the fundings of this study → supporting the findings of this study
Citation: https://doi.org/10.5194/egusphere-2026-5413-RC1
RC2:
'Comment on egusphere-2026-5413', Anonymous Referee #2, 23 Oct 2026
The manuscript investigates the spectral decay parameter (k) using strong-motion recordings from western-central Sichuan, China, and develops a regional model for k0, which is subsequently applied to stochastic ground-motion simulations of the 2019 Changning earthquake. The study draws on a substantial dataset comprising recordings from 165 earthquakes at 168 stations. It examines the effects of earthquake magnitude and site conditions on k, estimates station-specific k0 values, investigates their relationships with VS30, and performs ground motion simulations to validate the derived the k0 estimations.
The topic is relevant to engineering seismology and regional ground-motion modelling. The dataset is potentially valuable, and the integration of empirical spectral decay estimates with stochastic finite-fault simulations is of practical interest. However, several methodological and interpretative issues need to be addressed to strengthen the analysis and support the main conclusions. I therefore recommend major revision, with particular attention to the following issues:
The description of previous studies on k0 estimation in the Introduction is insufficient and should be expanded to provide a more comprehensive overview of the state of the art. The authors should explicitly compare their approach with existing regional k models and previous studies addressing the separation of source, path, and site contributions. Futhermore, recent relevant studies should be included. For example, Ktenidou et al. (2021) discussed key challenges in estimating k0, particularly those associated with uncertainties in source and site characteristics. Moratto et al. (2025) proposed estimating station-specific k0 from ambient seismic noise, thereby reducing the trade-off between high-frequency attenuation and earthquake stress drop. Pandel et al. (2026) investigated the relationship between site amplification and k0estimates, highlighting the importance of distinguishing these effects. The methodological novelty of the present study should also be established more clearly in relation to previous investigations of regional attenuation in Sichuan and other tectonic settings. The Introduction should conclude with a concise statement identifying the specific knowledge gap addressed by the study and explaining how the proposed approach advances beyond existing methods.

Although the authors acknowledge in the Introduction that k may be influenced by source, path, and site effects, the subsequent analysis appears to attribute several of the observed relationships primarily to site conditions, without adequately considering the potential contributions of other mechanisms. In particular, the trade-off between high-frequency attenuation and earthquake source stress drop should be discussed. Furthermore, although k0 is generally interpreted as a site-related parameter, source contributions cannot necessarily be excluded (see Ktenidou et al., 2015). A more comprehensive discussion of these potential contributions, even if they are commonly neglected in practice, would provide a more balanced physical interpretation of the results.

The paper reports slightly higher k0 values at stations classified as rock sites than at those classified as soil sites. The authors acknowledge that this trend differs from expectations and suggest that the initial site classification may explain the result. They subsequently distinguish between site classes C and D and find higher k0 values for class D. Although this explanation is plausible, it is not sufficient. Site classification appears to be one of the main factors used to interpret k0, yet the manuscript also acknowledges that the initial site categories are not homogeneous. This limitation should be addressed more thoroughly, and its implications for the interpretation of the results should be discussed.

The paper would benefit from a comparison of the estimated k0 values with those previously reported for the study area and for regions with similar seismological and geological characteristics. Such a comparison would help place the results in a broader context and assess their consistency with existing estimates. In addition, the differences in k0 estimated from different ground-motion components are not sufficiently discussed. The authors should consider the potential influence of sensor orientation and the implications for the robustness of the estimates. In this regard, Van Houtte et al. (2014) proposed an approach for estimating k0 independently of sensor orientation, which may be relevant to the present analysis.

The manuscript derives a relationship between k0 and Vs30, concluding that k0 decreases with increasing Vs30. However, the reported correlation coefficients are relatively low (approximately 0.124 and 0.164 in absolute magnitude, depending on the relationship considered), indicating a weak linear association. These results therefore provide limited support for a robust predictive relationship between the two parameters. This limitation is particularly relevant because Vs30 is not directly measured at most stations but is instead estimated using an empirical relationship involving the predominant frequency and amplitude of the H/V ratio. These indirect estimates are subject to uncertainty and may be influenced by the same near-surface conditions that affect k0. The authors should discuss these limitations more explicitly and clarify the extent to which the observed relationship can be considered robust, given the uncertainty in the Vs30 estimates and the relatively weak correlations.

The simulation of the 2019 Changning earthquake represents an important component of the manuscript. However, the validation does not yet convincingly demonstrate that the station-specific k0 model is generally more accurate. First, the authors should clarify whether recordings of the Changning earthquake were included in the dataset used to estimate the station-specific parameters. If so, the comparison is not fully independent and may overestimate the predictive performance of the proposed model. Second, the simulation results, and consequently the validation, appear to depend on several modelling assumptions and input parameters, including the source model, the assumed stress drop of 8 MPa, the quality factor Q(f), and site amplification. The authors should discuss the sensitivity of the results to these parameters and clarify to what extent the observed agreement can be attributed specifically to the adopted k0 rather than to compensating effects among the different simulation inputs.

The abstract is unclear and requires a substantial revision to improve its clarity and coherence. More generally, the manuscript requires careful English-language editing, as some sentences are grammatically awkward or overly long, and terminology is not always used consistently.

References:
Ktenidou , O.J. , Abrahamson, N.A., Drouet, S. & Cotton, F., 2015. Understanding the physics of kappa (k): insights from a downhole array, Geophys. J. Int., 203, 678–691.
Ktenidou , O.-J. , Abrahamson, N.A., Darragh, R.B. & Kishida, T., 2021. The search for hard-rock kappa (k) in NGA-East: a semi-automated method for large, challenging datasets in stable continental regions, Earthq. Spectra, 37, 1391–1419.
Moratto L., Panebianco S., Satriano C., Stabile TA., Priolo E. (2025). Using ambient noise k0 estimation to improve microearthquakes source parameters assessment in the High Agri Valley. Geophys. J. Int. 242, 1-19, doi:10.1093/gji/ggaf191
Pandel, B., Rathje, E. M., Savvaidis, A., & Kottke, A. R. (2026). Partitioning Site Amplification and \(\kappa_0\) in Earthquake Recordings. Earthquake Spectra, 42(3), e70104. https://doi.org/10.1002/esp4.70104
Van Houtte , C. , Ktenidou, O.-J., Larkin, T. & Holden, C., 2014. Hard-site k 0 (kappa) calculations for Christchurch, New Zealand, and comparison with local ground-motion prediction models, Bull. seism. Soc. Am., 104, 1899–1913.
Citation: https://doi.org/10.5194/egusphere-2026-5413-RC2
CC1: 'Comment on egusphere-2026-5413', Dr. Ranjit Das, 31 Oct 2026

The manuscript switches dynamically between surface-wave magnitude (Mₛ), local magnitude (Mₗ), and moment magnitude (M𝑤), creating a severe physical misalignment between the empirical data and the simulation framework. While the authors state that they convert Mₛ values for their regional regression dataset (Line 111), the stochastic finite-fault simulation section (Page 13) abruptly introduces a moment magnitude (M𝑤) value of 5.7 for the Changning event, directly referencing Guo et al. (2022). To resolve this fundamental discrepancy, the authors must explicitly discuss the phenomenon of magnitude scale saturation and clarify why a unified moment magnitude scale (M𝑤), or an optimized scale explicitly tailored for small, medium and large events such as the Das magnitude scale (Mwg) (Das et al, 2019), was not adopted to homogenize the source parameters seamlessly across both components of the study.
Furthermore, a dedicated paragraph should be incorporated into either the Introduction or Discussion section to highlight the physical limitations of the historical Mₛ catalog scale. As fundamentally demonstrated by Gutenberg and Richter (1956), Mₛ is not a robust magnitude scale for high-fidelity engineering applications because its absolute dependence on 20-second surface waves renders it inherently insensitive to focal-depth variations, incapable of adequately capturing high-frequency near-fault source processes, and highly susceptible to early saturation. These well-known limitations directly affect the reliability of source characterization and may consequently influence the accuracy of the high-frequency spectral decay (κ) adjustments derived in this study.
References:
Gutenberg B, Richter CF (1956) Earthquake magnitude, intensity,

energy, and acceleration: (Second paper). Bull Seismol Soc Am 46(2):105–145
Das, R., Sharma, M. L., Wason, H. R., Choudhury, D., & Gonzalez, G. (2019). A seismic moment magnitude scale. Bulletin of the Seismological Society of America, 109(4), 1542-1555.

Citation: https://doi.org/10.5194/egusphere-2026-5413-CC1

Pengfei Dang, Bingyan Zhao, Qifang Liu, Jie Cui, and Xinjian Jia

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Pengfei Dang, Bingyan Zhao, Qifang Liu, Jie Cui, and Xinjian Jia

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Short summary

Spectral amplitude drops at high frequencies beyond a threshold, always modeled by kappa. Using Sichuan ground motion data, we studied event κ vs epicentral distance, magnitude, and site conditions. Conclusions: (1) κ0 increases with magnitude. (2) Vs30 from empirical equation weakly correlates with κ0; however, Vs30-k corrections derived from drilling and PEER agree. (3) κ0 relates to short-period amplitude; at f<1Hz, simulated FAS differ from observed.


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