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Empirical Specification of Ground Motions. Ground-motion prediction equations Collections of ground-motion values (and time series) for magnitude and distance bins. Developing Equations. When have data (rare for most of the world): Regression analysis of observed data

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## Empirical Specification of Ground Motions

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**Empirical Specification of Ground Motions**• Ground-motion prediction equations • Collections of ground-motion values (and time series) for magnitude and distance bins**Developing Equations**• When have data (rare for most of the world): • Regression analysis of observed data • When adequate data are lacking: • Regression analysis of simulated data (making use of motions from smaller events if available to constrain distance dependence of motions). • Hybrid methods, capturing complex source effects from observed data and modifying for regional differences.**Overview**• Empirical ground-motion prediction equations • What they are and how they are used • The database • Processing of data • Combining horizontal components • Expected dependency on magnitude and distance • What functional form to use • What to use for the explanatory variables**Overview**• Empirical ground-motion prediction equations • Possible biases and how to avoid them • Site characterization • Basin depth • Nonlinear response • Testing the results • Results and comparisons of various prediction equations**Overview**• Empirical ground-motion prediction equations • Scatter • Complications and future directions**Ground-Motion Prediction Equations**Gives mean and standard deviation of response-spectrum ordinate (at a particular frequency) as a function of magnitude distance, site conditions, and perhaps other variables.**Call them “Ground-Motion Prediction Equations” (GMPEs)**• “Attenuation Equations” is a poor term • The equations describe the INCREASE of amplitude with magnitude at a given distance • The equations describe the CHANGE of amplitude with distance for a given magnitude (usually, but not necessarily, a DECREASE of amplitude with increasing distance).**Deriving the Equations**• Regression analysis of observed data if have adequate observations (rare for most of the world). • Regression analysis of simulated data for regions with inadequate data (making use of motions from smaller events if available to constrain distance dependence of motions). • Hybrid methods, capturing complex source effects from observed data and modifying for regional differences.**Observed data adequate for regression except**close to large ‘quakes Observed data not adequate for regression, use simulated data**What Measure of Seismic Intensity to Use?**• PSA (derived from SD) • SD? Need for displacement-based design • Can be derived from PSA, so GMPEs in terms of PSA also give equations for SD • If use SA, then need separate GMPEs for PSA and SD • Usually horizontal component**How to Use Two Horizontal Components**• Use both independently • Use larger component as recorded • Use larger component after rotation to find maximum • Use vector sum • Use geometric mean as recorded • Use orientation-independent geometric mean**The geometric means of these two sets of records differ**by a factor of 2 at T = 1 s**Measure of Ground-Motion Intensity:GMRotI50**Boore, D. M., J. Watson-Lamprey, and N. A. Abrahamson (2006). Orientation-independent measures of ground motion, BSSA 96, 1502-1511.**How does the motion depend on magnitude?**• Source scaling theory predicts a general increase with magnitude for a fixed distance, with more sensitivity to magnitude for long periods and possible nonlinear dependence on magnitude**Shape depends strongly on magnitude; for this reason scaling**spectral shapes by peak acceleration is not advised**How does the motion depend on distance?**• Generally, it will decrease (attenuate) with distance • But wave propagation in a layered earth predicts more complicated behavior (e.g., increase at some distances due to critical angle reflections (“Moho-bounce”) • Equations assume average over various crustal structures**What functional form to use?**• Motivated by waves propagating from a point source • Add more terms to capture effects not included in simple functional form**What to use for the Predictor Variables?**• Moment magnitude • Some distance measure that helps account for the extended fault rupture surface (remember that the functional form is motivated by a point source, yet the equations are used for non-point sources) • Distance must be estimated for future event (leaves out distance to energy center, hypocentral distance)**Moment Magnitude**• Best single measure of overall size of an earthquake • Can be determined from ground deformation or seismic waves • Can be estimated from paleoseismological studies • Can be related to slip rates on faults**May need to convert magnitudes**• Use empirical and/or theoretical relations • Important to use a common magnitude measure • This is essential in comparing ground-motion prediction equations • Moment magnitude is now the standard**Many distance measures are used**• There is no standard, although the closest distance to the rupture surface is probably the distance most commonly used • The distance measure must be something that can be estimated for a future earthquake**Limitations in the dataset can produce biased results**• Data censuring (lack of data from operational non-triggered recorders) can lead to attenuation with distance that is too small • Non-uniform distribution of data on M-D space can lead to tradeoffs in the magnitude scaling and the distance decay**Avoiding the magnitude-distance tradeoff**• Use 2 stage regression • Use weighted least-squares (random effects model)**An Example of a Recent Major Effort to Derive New**Ground-Motion Prediction Equations (GMPEs): Next Generation Attenuation (NGA) Project David M. Boore U. S. Geological Survey**NGA Project**• NGA-E (empirical) • New ground motion models based primarily on empirical data • Use analytical models (seismological and geotechnical) to guide extrapolation outside of empirical data • Results used only in terms of scaling**NGA Project Details**• Five developer teams • Ed Idriss • Brian Chiou and Bob Youngs • Dave Boore and Gail Atkinson • Norm Abrahamson and Walt Silva • Ken Campbell and Yousef Bozorgnia**Supporting Working Groups**• Data Processing • Ground Motion Database • Validation of 1-D Rock Motion Simulation • Source/Path Effects • Site Classification & Site Effects • Statistical Modeling of Data • Parameterization to capture directivity effects**NGA Project Details**• All developers used a common database (175 earthquakes, 3551 recordings) • Metadata (e.g., magnitude, distance, etc.) • Uniformly processed strong-motion recordings • U.S. and foreign earthquakes • Active tectonic regions • The database development took much longer than anticipated, resulting in at least a year delay in the project completion**Some earthquakes not included:**1987 Elmore Ranch, CA (add USGS data) 1992 Cape Mendocino, CA (add USGS data) 1997 Umbria-Marche, Italy, events 2002 Molise, Italy 2003 Zemmouri, Algeria (M 6.8) 2003 San Simeon, CA (M 6.4) 2003 Bam, Iran (M 6.5) 2004 Parkfield, CA (M 6.0) 2004 Chuetsu, Japan (M 6.6 + AS) 2005 Zarand, Iran (M 6.3)**NGA Project Details**• Developers applied their own selection criteria to the common database • Selection criteria explicitly defined • Selection criteria shared with other developers • Defensible reason for excluding data • Other developers notified if metadata modified**Developer Scope**• Ground motion model • Model for median estimate • Model for aleatory standard deviation • Ground motion parameters • Horizontal components (Average, FN and FP) • PGA, PGV and PGD • Spectral acceleration (5% damping, 0-10 sec period) • Applicable moment magnitude range • 5.0 – 8.5 (strike-slip faulting) • 5.0 – 8.0 (reverse faulting)**Developer Scope**• Applicable distance range • 0 – 200 km • Fault types • Strike slip • Reverse • Normal • Site classification scheme • Developers select their preferred classification scheme • Provide a translation scheme to NEHRP categories • Need not include soft soil

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