Ground‐Motion Prediction Models for Arias Intensity and Cumulative Absolute Velocity for Japanese Earthquakes Considering Single‐Station Sigma and Within‐Event Spatial Correlation

Abstract

Arias intensity (I A ) and cumulative absolute velocity (CAV) are groundmotion measures that have been found to be well suited to application in a number of problems in earthquake engineering. Both measures reflect multiple characteristics of the ground motion (e.g., amplitude and duration), despite being scalar measures. In this study, new ground-motion prediction models for the average horizontal component of I A and CAV are developed, using an extended database of strong-motion records from Japan, including the 2011 Tohoku event. The models are valid for magnitude greater than 5.0, rupture distance less than 300 km, and focal depth less than 150 km. The models are novel because they take account of ground-motion data from the 2011 Tohoku earthquake while incorporating other important features such as event type and regional anelastic attenuation. The residuals from the ground-motion modeling are analyzed in detail to gain further insights into the uncertainties related to the developed median prediction equations for I A and CAV. The site-to-site standard deviations are computed and spatial correlation analysis is carried out for I A and CAV, considering both within-event residuals and within-event single-site residuals for individual events as well as for the combined dataset.

Ground motion models for Arias intensity, cumulative absolute velocity, peak incremental ground velocity, and significant duration in New Zealand

“…Previous models for predicting have in some cases depended on this formulation [11,15] to guide functional form selection. Other models [8,10] have calculated according to Equation 1 and disregarded the frequency domain. This study will do the latter.…”

“…Table 4 shows the candidate forms for the depth term. Functions of either or are considered, and reflect the variety of depth terms seen in the literature (e.g., [2,8,10,11,33]). For this and all subsequent terms, the possibility of excluding the term completely is also considered.…”

“…Many GMMs have been developed to predict the spectral acceleration ( ) at a given site in a given earthquake (e.g., [2][3][4][5][6]). Relatively fewer GMMs have been developed to predict evolutionary IMs and significant durations (e.g., [7][8][9][10]). Stafford et al [11] was developed specifically for predicting an evolutionary IM in New Zealand, and it included foreign records in its regression database to address data availability.…”

Regional ground‐motion prediction equations for amplitude‐, frequency response‐, and duration‐based parameters for Greece

“…Among them, Campbell and Bozorgnia and Du and Wang used the next generation attenuation strong‐motion database and proposed models on the basis of 8 and 4 input parameters, respectively. Sandıkkaya and Akkar presented a CAV predictive model using a database compiled from the broader European region, while Foulser‐Piggott and Goda used Japanese data to develop linear and nonlinear site response models accounting for linear magnitude scaling, fault mechanism, event type, and region‐specific anelastic attenuation. As far as Greece is concerned, the only available GMPE for CAV is the one developed by Danciu and Tselentis with the abovementioned dataset of Greek earthquakes that occurred up to 1999.…”

The Predictive Power of Ground‐Motion Prediction Equations

“…When complex functional forms are implemented, the obtained models are often overfitting; that is, the models fit details in the data, which are specific features of the analyzed sample, not of the population generating the sample. Because the overfitting limits the predictive power (e.g., Hagerty and Srinivasan, 1991;Forster and Sober, 1994;Shmueli, 2010), some predictive metrics that introduce a penalty term over the model complexities to handle the bias-variance trade-off must be introduced to evaluate the model performance (e.g., Foulser-Pigott and Goda, 2015). Examples are the BIC (Schwartz, 1978) and the AIC (Akaike, 1973).…”