Orientation-Independent Measures of Ground Motion

Abstract

The geometric mean of the response spectra for two orthogonal horizontal components of motion, commonly used as the response variable in predictions of strong ground motion, depends on the orientation of the sensors as installed in the field. This means that the measure of ground-motion intensity could differ for the same actual ground motion. This dependence on sensor orientation is most pronounced for strongly correlated motion (the extreme example being linearly polarized motion), such as often occurs at periods of 1 sec or longer. We propose two new measures of the geometric mean, GMRotDpp, and GMRotIpp, that are independent of the sensor orientations. Both are based on a set of geometric means computed from the as-recorded orthogonal horizontal motions rotated through all possible nonredundant rotation angles. GMRotDpp is determined as the ppth percentile of the set of geometric means for a given oscillator period. For example, GMRotD00, GMRotD50, and GMRotD100 correspond to the minimum, median, and maximum values, respectively. The rotations that lead to GMRotDpp depend on period, whereas a single-period-independent rotation is used for GMRotIpp, the angle being chosen to minimize the spread of the rotation-dependent geometric mean (normalized by GMRotDpp) over the usable range of oscillator periods. GMRotI50 is the groundmotion intensity measure being used in the development of new ground-motion prediction equations by the Pacific Earthquake Engineering Center Next Generation Attenuation project.Comparisons with as-recorded geometric means for a large dataset show that the new measures are systematically larger than the geometric-mean response spectra using the as-recorded values of ground acceleration, but only by a small amount (less than 3%). The theoretical advantage of the new measures is that they remove sensor orientation as a contributor to aleatory uncertainty. Whether the reduction is of practical significance awaits detailed studies of large datasets. A preliminary analysis contained in a companion article by Beyer and Bommer finds that the reduction is small-to-nonexistent for equations based on a wide range of magnitudes and distances. The results of Beyer and Bommer do suggest, however, that there is an increasing reduction as period increases. Whether the reduction increases with other subdivisions of the dataset for which strongly correlated motions might be expected (e.g., pulselike motions close to faults) awaits further analysis.

Is Ground‐Motion Variability Distance Dependent? Insight from Finite‐Source Rupture Simulations

“…We computed the PGV values as proposed by Boore et al (2006), using the GMRotD50 definition. GMRotD50 is an orientation-independent geometric mean using period-dependent rotation angles.…”

The use of post-earthquake residual displacements as a performance indicator in seismic assessment

“…In this study, the pseudospectral acceleration (PSA) of a single-degree-of-freedom system with a period equal to the fundamental period T 1 of the structure and a damping ratio of 5% is adopted to measure the intensity of the ground motion experienced at the site. More specifically, the GMRotI50 value as defined by Boore et al (2006) is used to measure the ground motion intensity at the site.…”

New predictive equations for Arias intensity from crustal earthquakes in New Zealand

“…I xx + I yy = const; Travasarou et al 2003). This point is worth emphasizing, as it implies that the use of the arithmetic mean of the two recorded horizontal components results in an orientation-independent measure of the Arias Intensity (Boore et al 2006). The most common representation of the Arias Intensity is recovered for the case of zero damping in the SDOF oscillators.…”

“…The significance of ensuring that appropriate component definitions are used has recently been reinforced in various studies (Bommer et al 2005;Baker and Cornell 2006;Beyer and Bommer 2006;Boore et al 2006). Each of these studies suggests methods for moving between different component definitions used in predictive equations.…”