# Use of Macroseismic Intensity Data to Validate a Regionally Adjustable Ground Motion Prediction Model

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Component Attenuation Model (CAM) of PGV

#### 2.1. Generic Source Factor

#### 2.2. Regional Whole Path Anelastic Attenuation Factor

#### 2.3. Crustal Modification Factor

#### 2.3.1. Upper-Crustal Amplification

_{S30}to characterise upper crustal conditions has been demonstrated in reference [42]. The reliability (ability) of Equation (7) to reproduce results of stochastic simulations of the upper crustal amplification phenomenon reasonably accurately is demonstrated in Section 3.

#### 2.3.2. Upper Crustal Attenuation

#### 2.3.3. Mid-Crustal Modification

^{3}, both of which are characteristics of hard rock conditions in the shield regions of Eastern North America, are used as the “benchmark” conditions, for which the amplification factor is set as unity. These benchmark parameters for shear wave velocity and crustal density are denoted as ${\mathsf{\beta}}_{0\mathrm{sim}}$ and ${\mathsf{\rho}}_{\mathrm{sim},}$ respectively.

^{3}, ${\mathsf{\beta}}_{0\mathrm{sim}}$ = 3.8 km/s, and ${\mathsf{\rho}}_{\mathrm{S}}$ and ${\mathsf{\beta}}_{0\mathrm{S}}$ are the density and shear wave velocity of the earth crust at the depth of the source (i.e., the mid-crust).

#### 2.4. Verification of CAM Using Various Seismological Models

#### 2.5. Validation of CAM Using MMI Data

_{L}). The conversion between M (moment magnitude, same as M

_{W}) and M

_{L}would need to be undertaken in the first place to obtain correct estimates of the event magnitude. In this study, the bilinear conversion relationship developed for Australian conditions [50] as defined by Equation (13) was adopted.

_{S}(depth of the upper sedimentary crustal layer) and Z

_{C}(combined thickness of the soft and hard sedimentary crustal rock layers) for each region were obtained from the average estimates of the thickness of soft sediment layer and total sediment layers, respectively, in CRUST1.0 database (https://igppweb.ucsd.edu/~gabi/crust1.html, last accessed in January 2019). V

_{S0.03}(shear-wave velocity values at the depth of 0.03 km) values were identified by curve-fitting to minimise discrepancies (defined as sum of squares errors) between the modelled and recorded SWV values. The SWV value at 8 km depth (V

_{S8}), representing conditions at the source of the earthquake, has also been determined for the two study regions based on information of the regional crustal structure. The detailed information about the recorded SWV value can be found the references [54,55,56,57,58,59]. The velocity profile showing the upper bound of 2.78 km/s in Figure 2 is the shear wave velocity profile for generic hard rock conditions, as recommended in reference [38]. The velocity profile showing the lower bound of 0.76 km/s in Figure 2 was derived from interpolation between the shear wave velocity profiles for generic rock and generic hard rock conditions, as recommended in reference [38]. The modelling approach introduced in reference [39] has been adopted. The frequency-dependent modification factors for the study regions are shown in Figure 3.

## 3. Results of Verification Analyses

#### 3.1. PGV Modelling

_{S30}. Figure 7 shows the upper crustal attenuation factor (${\mathsf{\gamma}}_{an}$) as a function of M and ${\mathsf{\kappa}}_{0}$. Figure 8 shows the overall PGV obtained both from stochastic simulations and CAM predictions. The regression coefficients together with the regression goodness (R

^{2}) values for different component factors demonstrating excellent agreement between the two sets of results are summarised in Table 5.

#### 3.2. Translating Seismological Models into GMPEs in Terms of PGV

_{S30}= 0.76 km/s and ${\mathsf{\kappa}}_{0}$ = 0.025 s) have been input into the seismological models for defining the Fourier amplitude spectrum (FAS) and for making predictions of PGV through stochastic simulations. All the selected seismological models have been translated into PGV predictive models with a reasonable level of accuracy (as shown in Figure 9).

#### 3.3. Comparing with Historical MMI Data and Existing GMPEs

## 4. Discussion

_{n}< 1.0 s, and ${\mathrm{Q}}_{0}$ = 1000 for all T

_{n}≥ 1.0 s has been adopted in predicting response spectral values. According to Bommer and Alarcon [25], the ratio between response spectral acceleration (RSA) and PGV (RSA/PGV) is nearly constant at T

_{n}= 0.5 s, thus, ${\mathrm{Q}}_{0}$ = 893 was adopted in CAM for predicting the value of PGV in this study.

^{−1.33}, as per recommendations by A12 [18], at short distance as opposed to the conventional factor of R

^{−1}is controversial, whilst good match between the model predictions and field recorded data has been demonstrated in references [18,19]. It is noted that when calibrating seismological parameters (to achieve agreement between predictions from a seismological model and field recorded data) there are trade-offs of the assumed stress drop values with the assumed rate of geometrical attenuation. Stress drop behaviour of earthquakes, as assumed by different groups of investigators (based on calibration), can be very inconsistent. The geometrical factors adopted by the two study groups can accordingly be very inconsistent too (R

^{−1.33}versus R

^{−1}), whilst achieving good agreement between predictions and recorded data in their respective studies.

- Uncertainties with the relationship for conversion from MMI to PGV: Although the adopted MMI–PGV conversion function is recommended by many studies, there are still significant variances when applying the function to a diversity of regions, which is demonstrated by the discrepancies between not using residual corrections (Equation (11)) and using residual corrections (Equation (12)) in the relationship functions shown in Figure 10 and Figure 11.
- Uncertainties with the modification factor for conversion from MMI on a soil site to MMI on a rock site: a factor of 1.5 was adopted for both SEA (recommended by AS1170.4-2007 [64]) and SEC region (recommended by Tsang et al. [16]). CAM can only give predictions on rock sites and thus the conversion between soil sites and rock sites is essential.Uncertainties with magnitude conversion: in SEA, local magnitude (M
_{L}) has been converted into moment magnitude (M) based on studies conducted by Geoscience Australia [50]. However, the magnitude of ancient recordings in SEC has not been assured (the magnitude identified with individual recordings is assumed to be in moment magnitude). - Uncertainties with shear wave velocity profiling: a geology-based approach for constructing SWV profile was adopted. This approach can make the best use of local recording data, thereby minimising inter-regional variability when calculating the upper crustal modification factor. For SEA region, the proposed SWV profile resulted in a V
_{S30}value that is the same as previous study (0.76 km/s) [68]. However, for SEC region, the SWV profile obtained from this study (V_{S30}= 1.45 km/s) is different from that presented by Tsang et al. [16] (V_{S30}= 1.1 km/s, which is different from V_{S0.03}). More local data for accurate SWV profile modelling is required in future studies. - Uncertainties with the seismological parameters: no complete seismological model has been developed specifically for the SEC region. The parameter values (including stress drop value and geometric attenuation factor) used in CAM are mainly default values that are expected for a typical intraplate region.
- Another intrinsic limitation of CAM is that it has not taken earthquake duration effects into account in a comprehensive manner. Incorporating an adjustment factor for earthquake duration effects into CAM is recommended for its future development.

## 5. Conclusions

## Supplementary Materials

**MMI**recordings for the SEA region can be found online at: https://www.dropbox.com/s/v3eqh3w686ho97j/MMI%20events%20SEA.xlsx?dl=0. The

**MMI**recordings for the SEC region can be found online at: https://www.dropbox.com/s/8vr4wq9mbsee5c0/MMI%20Events%20SEC.xlsx?dl=0. The vs. data can be found online at: https://www.dropbox.com/s/u3v127wjt10cwwk/Shear%20wave%20velocity%20data.xlsx?dl=0. The link to access

**CAM**for response spectrum modelling: https://www.dropbox.com/s/jjfbfc8cm2srub3/CAM-Response-spectral-acceleration.pdf?dl=0.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**M-R combinations for selected regions. (

**a**) South-Eastern Australia (SEA); (

**b**) South-Eastern China (SEC).

**Figure 2.**Shear-wave velocity profile: (

**a**) SEA; (

**b**) SEC, in which CRUST1.0 is a global crustal database (https://igppweb.ucsd.edu/~gabi/crust1.html, last accessed in January 2019), the shear wave velocity data can be found in the “Supplementary Materials”.

**Figure 4.**Simulated values of peak ground velocity (PGV) (symbols) alongside predictions by CAM (lines) for varying moment magnitudes (M4.5–M7.5) and stress drops (30–300 bar), at R = 30 km.

**Figure 5.**Anelastic attenuation factor (β). (

**a**) Simulated PGV values normalised at ${\mathrm{Q}}_{0}$ = 680 for varying M values (M4.5–M7.5) and distances (4–800 km) shown alongside predictions by CAM (lines); (

**b**) simulated PGV values normalised at M = 6 for varying ${\mathrm{Q}}_{0}$ values (150–800) and distances (4–800 km) shown alongside predictions by CAM (lines).

**Figure 6.**Regression analysis results of upper crustal amplification factor (${\mathsf{\gamma}}_{am}$).

**Figure 7.**Regression analysis results of upper crustal attenuation factor (${\mathsf{\gamma}}_{an}$).

**Figure 8.**Simulated PGV values (symbols) for varying M values (M4.5–M7.5) and distances (4–800 km) shown alongside predictions by CAM (lines) for ∆σ = 200 bar, V

_{S30}= 0.76 km/s, and ${\mathsf{\kappa}}_{0}$ = 0.025 s.

**Figure 9.**Comparison between predictions by CAM (lines) and simulations of seismological models (symbols). (

**a**) AB95 model, with trilinear geometric spreading and ${\mathrm{Q}}_{0}$ = 680; (

**b**) SGD02 model, with magnitude-dependent geometric spreading and ${\mathrm{Q}}_{0}$ = 351; (

**c**) A04 model, with trilinear geometric spreading and ${\mathrm{Q}}_{0}$ = 893; (

**d**) BS11 model, with bilinear geometric spreading and ${\mathrm{Q}}_{0}$ = 410.

**Figure 10.**Comparison between historical recorded and model-predicted modified Mercalli intensity (MMI) for SEA.

**Table 1.**Parameter values used in stochastic simulations for component attenuation model (CAM) modelling.

Parameter | Input Value |
---|---|

Ref. source shear wave velocity for hard rock (of Eastern North America) | ${\beta}_{0sim}$ = 3.8 km/s [1] |

Ref. source density for hard rock | ${\rho}_{sim}$ = 2.8 g/cm^{3} [1] |

Source model | Generalised additive double-corner frequency model [35] |

Spectral sag | $\mathsf{\epsilon}\text{}={10}^{0.605\text{}-\text{}0.255\mathrm{M}}$ |

Distance | R = Hypocentral distance |

Geometrical attenuation | Variable function (refer Table 2) |

Stress drop, $\Delta \mathsf{\sigma}$ | $\Delta \mathsf{\sigma}$ = 200 bars (default for intraplate regions) |

Wave transmission quality factor | ${Q}_{0}$ = 120, 150, 200, 300, 400, 500, 600, 680, 800. |

Exponential factor | $n=0.0000008{Q}_{0}^{2}-0.0014{Q}_{0}+0.93$^{1} [36] |

Time-averaged shear wave velocity for the top 30 m depth, ${\mathrm{V}}_{\mathrm{S}30}$ | ${\mathrm{V}}_{\mathrm{S}30}$ = 0.618, 0.76, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.78 km/s |

Kappa factor | κ_{0} = 0.001, 0.0025, 0.005, 0.0075, 0.01, 0.015, 0.02, 0.025, 0.03, 0.035, 0.04, 0.045, 0.05, 0.055, 0.06, 0.065, 0.07, 0.075, 0.08, 0.085, 0.09, 0.095, 0.1 s |

Source duration | $0.5/{f}_{a}+0.5/{f}_{b}$, where ${f}_{a}$ and ${f}_{b}$ are corner frequencies [35] |

Path duration | 0.05 × R, where R is the hypocentral distance [1] |

Time step | $\mathrm{dt}$ = 0.002 s |

^{1}The equation is only used when the exponent value is unknown.

Seismological Model | AB95 [1] | SGD02 [47] | A04 [48] | BS11 [49] |
---|---|---|---|---|

Source model ^{1} | $\frac{1-\mathsf{\epsilon}}{1+{\left(f/{f}_{a}\right)}^{2}}+\frac{\mathsf{\epsilon}}{1+{\left(f/{f}_{b}\right)}^{2}}\mathrm{log}\mathsf{\epsilon}=2.52-0.637\mathrm{Mlog}{f}_{a}=2.41-0.533\mathrm{M}\text{}{f}_{b}=\sqrt{\left({f}_{c}^{2}-\left(1-\mathsf{\epsilon}\right){f}_{a}^{2}\right)/\mathsf{\epsilon}}{f}_{\mathrm{c}}=4.9\times {10}^{6}{\mathsf{\beta}}_{0}{\left(\frac{\Delta \mathsf{\sigma}}{{\mathrm{M}}_{0}}\right)}^{1/3}\Delta \mathsf{\sigma}=200\text{}\mathrm{bar}$ | |||

Shear Wave Velocity at Source βos (km/s) | 3.8 | 3.52 | 3.7 | 3.5 |

Geometrical Factor G (R in km) ^{2} | R ≤ 70: R^{−1} 70 < R ≤ 130: R^{0} 130 < R: R^{−0.5} | R ≤ 80: R^{-(1.0296−0.0422(M−6.5))} 80 < R: R^{−0.5(1.0296 + 0.0422(M − 6.5))} | R ≤ 70: R^{−1.3} 70 < R ≤ 140: R^{0.2} 140 < R: R^{−0.5} | R ≤ 50: R^{−1} 50 < R: R^{−0.5} |

Quality Factor Q | 680 f ^{0.36} | 351 f ^{0.84} | max (1000, 893 f ^{0.32}) | 410 f ^{0.5} |

Upper Crustal Amplification Parameter | V_{S30} = 0.76 km/s | V_{S30} = 0.76 km/s | V_{S30} = 0.76 km/s | V_{S30} = 0.76 km/s |

Upper Crustal Attenuation Parameter | κ_{0} = 0.025 s | κ_{0} = 0.025 s | κ_{0} = 0.025 s | κ_{0} = 0.025 s |

^{1}source models presented in the original references have been replaced by the more updated source model presented in the table based on recommendations in reference [35].

^{2}R is hypocentral distance in km.

**Table 3.**Parameter values for modelling shear wave velocity (SWV) profiles for South-Eastern Australia (SEA) and South-Eastern China (SEC).

Parameter | SEA | SEC |
---|---|---|

Z_{S} (km) | 1.0 | 0.01 |

Z_{C} (km) | 4.0 | 2.0 |

V_{S0.03} (km/s) ^{1} | 1.1 | 1.81 |

V_{S8} (km/s) ^{2} | 3.5 | 3.6 [60] |

n | 0.141 | 0.136 |

function form | Z ≤ 0.2, V_{SZ} = V_{S0.03}(Z/0.03)^{0.3297};0.2 < Z ≤ Z _{S} ^{4}, V_{SZ} = V_{S0.2}(Z/0.2)^{0.1732 3};Z _{S} < Z ≤ Z_{C} ^{5}, V_{SZ} = V_{SZC}(Z/Z_{C})^{n};Z _{C} < Z, V_{SZ} = V_{S8}(Z/8)^{0.0833}. | 0 < Z ≤ Z_{S}, V_{SZ} = V_{SZI}(Z/Z_{I})^{0.3297} (Z_{I} = min (Z_{S}, 0.03));Z _{S} < Z ≤ Z_{C}, V_{SZ} = V_{SZC}(Z/Z_{C})^{n};Z _{C} < Z, V_{SZ} = V_{S8}(Z/8)^{0.0833}. |

^{1.}V

_{S0.03}is the shear wave velocity value at the depth of 0.03 km;

^{2.}V

_{S8}is the shear wave velocity value at the depth of 8 km;

^{3.}V

_{S0.2}is the shear wave velocity value at the depth of 200 m;

^{4.}Z

_{S}is the depth of the upper sedimentary crustal layer;

^{5.}Z

_{C}is the combined thickness of the soft and hard sedimentary crustal rock layers.

Parameter | SEA | SEC |
---|---|---|

Source Shear Wave Velocity (km/s) | 3.5 | 3.6 [60] |

Source Density (g/cm^{3}) | 2.8 [18] | 2.9 [61,62] |

Stress Drop (bar) | 200 | 200 |

$\Delta $ (cm/s) | 3.9 ^{1} | 3.9 ^{1} |

Geometric Attenuation Factor (G) [1] | $0\le \mathrm{R}\le 70,{\text{}\mathrm{R}}^{-1}70\mathrm{R}\le 130,{\text{}\mathrm{R}}^{0}130\mathrm{R},{\text{}\mathrm{R}}^{-0.5}$ | $0\le \mathrm{R}\le 70,{\text{}\mathrm{R}}^{-1}70\mathrm{R}\le 130,{\text{}\mathrm{R}}^{0}\text{}130\mathrm{R},{\text{}\mathrm{R}}^{-0.5}$ |

Quality Factor (${Q}_{0}$) | 200 (New South Wales) [15] 100 (Victoria) [15] 300 (South Australia) [15] | 320 [16] |

V_{S30} (km/s) | 0.76 ^{2} | 1.45 ^{2} |

κ_{0} (s) | 0.03 [42] | 0.02 [42] |

Conversion Factor (PGV_{S}/PGV_{R}) | 1.5 [63,64]^{3} | 1.5 [16] |

Source Factor ($\mathsf{\alpha}$) at M6R30 | 1.00 | 1.00 |

Anelastic Attenuation Factor (β) at M6R30 | 0.95 | 0.95 |

Path Adjustment Factor (${\mathsf{\beta}}_{\mathrm{adjustment}\_\mathrm{factor}}$) at M6R30 | 0.98 | 0.98 |

Upper Crustal Amplification Factor (${\mathsf{\gamma}}_{am}$) at M6R30 | 2.22 | 1.52 |

Upper Crustal Attenuation Factor (${\mathsf{\gamma}}_{an}$) at M6R30 | 0.48 | 0.6 |

Crustal Adjustment Factor (${\mathsf{\gamma}}_{\mathrm{adjustment}\_\mathrm{factor}}$) at M6R30 | 1.16 | 1.16 |

Mid-crustal Modification Factor (${\mathsf{\gamma}}_{mc}$) at M6R30 | 1.1 | 1.06 |

Selected GMPEs | SGC09 [65] ^{4} A12 [18] ^{5} | CB08 [66] ^{6} CY08 [2] ^{7} |

^{1}Both $\Delta $ values for SEA and SEC were determined from the calculated PGV at M6R30 from program GENQKE for hard rock conditions [9,15];

^{2}Vs

_{30}values are based on Figure 2.

^{3}PGV

_{S}and PGV

_{R}refer to PGV value on an average soil site and rock site, respectively, the value of 1.5 for the rock to the soil site conversion is based on stipulations by the earthquake loading standard for sites on shallow soil sediments [63] as explained in reference [64];

^{4}SGC refers to Somerville et al. (2009) [65];

^{5}A12 refers to Allen (2012) [18];

^{6}CB08 refers to Campbell and Bozorgnia (2008) [66];

^{7}CY08 refers to Chiou and Youngs (2008) [2].

logα | $\Delta $ | ${\mathit{a}}_{\mathbf{1}}$ | ${\mathit{a}}_{\mathbf{2}}$ | ${\mathit{a}}_{\mathbf{3}}$ | ${\mathit{a}}_{\mathbf{4}}$ | R^{2} |

2.952 | 27.797 | 0.0841 | 0.0059 | −33.35 | 0.9994 | |

logβ | ${\mathit{b}}_{\mathbf{1}}$ | ${\mathit{b}}_{\mathbf{2}}$ | ${\mathit{b}}_{\mathbf{3}}$ | ${\mathit{b}}_{\mathbf{4}}$ | ${\mathit{b}}_{\mathbf{5}}$ | ${R}^{\mathbf{2}}$ |

0.06287 | −0.6326 | −0.4963 | 4.431 | 0.06135 | 0.9807 | |

logβ_{adjustment} | ${\mathit{b}}_{\mathbf{6}}$ | ${\mathit{b}}_{\mathbf{7}}$ | ${\mathit{b}}_{\mathbf{8}}$ | ${\mathit{b}}_{\mathbf{9}}$ | ${\mathit{b}}_{\mathbf{10}}$ | ${R}^{\mathbf{2}}$ |

0.01714 | −0.06931 | 0.08404 | −0.09224 | 0.1389 | 0.9975 | |

$\mathrm{log}{\mathsf{\gamma}}_{\mathit{am}}$ | ${\mathit{\gamma}}_{\mathbf{1}}$ | ${\mathit{\gamma}}_{\mathbf{2}}$ | ${\mathit{\gamma}}_{\mathbf{3}}$ | ${\mathit{\gamma}}_{\mathbf{4}}$ | ${R}^{\mathbf{2}}$ | |

0.7334 | −0.5251 | −0.8479 | −0.019 | 0.9953 | ||

$\mathbf{log}{\mathsf{\gamma}}_{\mathit{an}}$ | ${\mathit{\gamma}}_{\mathbf{5}}$ | ${\mathit{\gamma}}_{\mathbf{6}}$ | ${\mathit{\gamma}}_{\mathbf{7}}$ | ${\mathit{\gamma}}_{\mathbf{8}}$ | ${R}^{\mathbf{2}}$ | |

−21.35 | −1.351 | 0.5584 | −0.03336 | 0.9978 | ||

$\mathrm{log}{\mathsf{\gamma}}_{\mathit{adjustment}}$ | ${\mathit{\gamma}}_{\mathbf{9}}$ | ${\mathit{\gamma}}_{\mathbf{10}}$ | ${\mathit{\gamma}}_{\mathbf{11}}$ | ${\mathit{\gamma}}_{\mathbf{12}}$ | ${\mathit{\gamma}}_{\mathbf{13}}$ | ${R}^{\mathbf{2}}$ |

−0.01333 | 0.07378 | −0.1294 | 0.1046 | 0.01838 | 0.9948 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tang, Y.; Lam, N.; Tsang, H.-H.; Lumantarna, E.
Use of Macroseismic Intensity Data to Validate a Regionally Adjustable Ground Motion Prediction Model. *Geosciences* **2019**, *9*, 422.
https://doi.org/10.3390/geosciences9100422

**AMA Style**

Tang Y, Lam N, Tsang H-H, Lumantarna E.
Use of Macroseismic Intensity Data to Validate a Regionally Adjustable Ground Motion Prediction Model. *Geosciences*. 2019; 9(10):422.
https://doi.org/10.3390/geosciences9100422

**Chicago/Turabian Style**

Tang, Yuxiang, Nelson Lam, Hing-Ho Tsang, and Elisa Lumantarna.
2019. "Use of Macroseismic Intensity Data to Validate a Regionally Adjustable Ground Motion Prediction Model" *Geosciences* 9, no. 10: 422.
https://doi.org/10.3390/geosciences9100422