For regions without enough strong ground motion records, a seismology-based
method is adopted to predict motion PGA (peak ground acceleration) values on
rock sites with parameters from small earthquake data, recorded by regional
broadband digital monitoring networks. Sichuan and Yunnan regions in
southwestern China are selected for this case study. Five regional parameters
of source spectrum and attenuation are acquired from a joint inversion by the
micro-genetic algorithm. PGAs are predicted for earthquakes with moment
magnitude (

Ground motion prediction equation (GMPE) is a vital field in the research of
engineering seismology. A great number of research results have been
published, and most of them are empirical, such as those for the western
United States by the Next Generation Attenuation (NGA) project (Power et al., 2008; Bozorgnia
et al., 2012; Boore et al., 2014) and those for Japan (Si and Midorikawa,
2000; Kanno, 2006). Empirical GMPEs are developed, mainly based on plenty
of strong ground motion records. For the regions without enough observed
data, like the mainland of China and many others, it is difficult to build GMPEs
this way. Obviously, there are more records of small earthquakes from regional
earthquake monitoring networks than those of strong motion in general.
The main goal of this paper is to see if these data could be a
basis to estimate the regional parameters in a seismology-based attenuation
relationship (Hanks and McGuire, 1981; Boore, 1983; Atkinson, 1984; Boore and
Atkinson, 1987). If they are really helpful, the bottleneck restriction of
insufficient strong motion records will be broken completely. Five regional
parameters, stress drop

Seismological stations and small earthquakes in Sichuan and Yunnan regions.

Small earthquake data recorded from January 2001 to December 2007 by Sichuan and Yunnan digital earthquake networks are adopted for the inversion. The period is from the beginning of operations of both networks to the end of the year before the Wenchuan Earthquake. There are 29 digital seismological stations in Sichuan and 26 stations in Yunnan; their locations are shown as triangles in Fig. 1.

A total of 147 records from 82 small earthquakes in Sichuan and 863 records from
154 small earthquakes in Yunnan, with

The distributions of focal depth and hypocentral distance with

The time window of the velocity time history, with time interval 0.02 s, starts from S-wave arrives until that 80 % energy is included.

There are 69 strong ground motion stations in Sichuan and 36 stations in
Yunnan. A total of 1234 records from 118 Sichuan earthquakes and 78 records from
27 Yunnan earthquakes, with

Comparison of the result with strong ground motion data in the Sichuan region and the Yunnan region.

Fourier amplitude spectrum of ground motion from a point source of a given
earthquake can be presented as (Boore, 1983; Atkinson and Boore, 2000;
Boore, 2003)

The constant, proportion factor, is given by

In order to eliminate the dependence of the motion amplitude on source size,
the following source spectrum model (Tao et al., 2008) is adopted rather
than the well-known

Inverse results.

The geometric attenuation term

Residual distribution in the Sichuan region and the Yunnan region.

Ten hybrid source models in the case of Wenchuan Earthquake, redrawn from Liu and Tao (2013).

Acceleration response spectra of motions from 30 hybrid source
models at

Acceleration time histories synthesized and observed at

The mean acceleration response spectra of synthesized and observed
motions at

The energy dissipation along the wave propagation path is very complicated;
the medium energy dissipation term

The above-mentioned five regional parameters,

The five parameter values of the solution, after having searched 2000 generations, are listed in Table 1.

For each given pair of magnitude and distance, the Fourier amplitude spectrum by Eq. (1) with the parameter values in Table 1, combined with a random phase spectrum, is transformed into a time domain. The time history is then enveloped for the amplitude nonstationarity. Then, the enveloped time history is transformed back into frequency domain, and scaled to the amplitudes directly from Eq. (1). The scaled spectrum is transformed back to the time domain again, and PGA for this magnitude distance is read from this final time history. Fifty acceleration time histories are generated and the average PGA is the stable expected PGA.

It is a kind of check, to compare the result with regional limited strong
ground motion data in Sect. 2.2. These data are never adopted in the
inversion. The attenuation curves for

To get a quantitative measure, the residual between the observed value and the
corresponding predicted value is calculated by

In the cases of

The mean value and standard deviation for all distances but the three magnitude intervals are listed in Table 2. The statistic features are stable as a whole and unusual in just a few intervals. It means that there are really not enough observed data in the interval. The values of standard deviation are comparable with those of empirical prediction in the regions with rich strong motion data. The facts show that it is possible to build an attenuation relation by small earthquake data recorded by regional broadband earthquake networks, for regions without enough strong ground motion records.

Mean value and standard deviation of residuals.

Near-fault ground motion of a large earthquake is complicated and governed by
the source mechanism; therefore, it is not possible to be predicted by GMPEs,
but possible by strong motion synthesis from a finite fault source model. In
order to see if the five regional parameters obtained above are helpful in
near-fault ground motion synthesis, two rock-site stations, Maoxian station
(MXT, 31.7

Thirty hybrid source models are built (Liu and Tao, 2013); 10 of them are shown in Fig. 8. The motion from each sub-source is generated in the same way as mentioned above. The motion from the all sub-sources on rupture plane are superposed by the time histories from every sub-source in the time domain, taking into account the time difference between the rupture in the sub-source and the initial rupture and the time difference between wave arrival times at the ground point from the sub-source and from the rupture start point.

For each station, 30 acceleration time histories are synthesized from these 30 models; the mean values of PGAs are listed in Table 3. The PGAs vary around the mean values with some randomness, and those values are close to the observed PGAs. Response spectra of the 30 motions at each station are shown as gray lines in Fig. 9, in which the black dotted line shows the mean spectrum at each station, and the black solid line shows the spectrum closest to the mean from source model 4. The acceleration time histories from this source model are chosen as samples for the two stations, shown as the top couple in Fig. 10. The two couples below are E–W and N–S components of the observed time histories at the stations. The amplitudes are similar, but the durations are different obviously. For Maoxian station, the second and the third sub-shocks are not synthesized.

Synthesized PGA and observed PGA at two rock stations (gal).

The response spectra of motions at the two stations from model 4 are shown with those of the observed time histories in Fig. 11, as the black solid line and dotted lines, respectively. The spectra are close to each other at Maoxian station, but they are different between a period of 0.3 and 0.4 s and longer than 0.7 s at Pixian station.

An approach to predict strong ground motion PGA in southwestern China is
presented in this paper, by means of a seismology-based attenuation
relationship with five regional parameters:

This work was financially supported by National Nature Science Foundation of China 51178435, 51478443 and 51178151 and International Science & Technology Cooperation Program of China 2011DFA21460.Edited by: F. Masci Reviewed by: G. De Luca and one anonymous referee