- Ground-motion model is:
_{1}is in cm∕s2, e_{1}= 0.210, e_{2}= 3.220, e_{3}= 0.036, c_{1}= -2.840, c_{2}= -0.361, c_{3}= 0.021, h_{A}= 13.452 and σ_{t}= 0.968 (total)for basic Phase 1 model; b_{1}= -2.558, b_{2}= 0.912, b_{3}= 0.952 and σ_{t}= 0.896 for directivity model; a_{1}= -0.538, a_{2}= 0.130, a_{3}= 0.957 and σ = 0.852 for borehole damping and fault zone amplification model; e_{1}= -6.822, e_{2}= 2.549, e_{3}= -0.121, c_{1}= -0.953, c_{2}= -0.138, c_{3}= -0.013, d_{1}= 0.892, h_{A}= 3.547 and σ_{t}= 0.924 for Phase 2 model; e_{1}= -7.532, e_{2}= 2.557, e_{3}= -0.105, c_{1}= -1.121, c_{2}= -0.142, c_{3}= -0.008, d_{1}= 1.308, h_{A}= 3.749 and σ_{t}= 0.985 for Phase 2 model using only stations in direction of rupture. In Phase 2 models model for Y_{1}has additional term d_{1}lnI_{Dir}. - Select data from events in 45 × 125km
^{2}rectangular area around the San Jacinto fault zone, a strike-slip fault system, from 02/2010 to 05/2012 plus data from 3 moderate events: 03/2013 (M_{L}5.1), 07/2010 (M_{L}5.9) and 06/2005 (M_{L}5.6), and their aftershocks. - Data from 140 stations, including broadband instruments, from various networks within 90 × 275km rectangle around fault zone. Broadband data converted to acceleration. Bandpass filter data using 1–30Hz 4th-order Butterworth filter. Prefer accelerometric data for M > 3 (to avoid saturation) and velocimetric data for M < 3 (because of higher sensivity). Pick ground-motion parameters automatically using signal-to-noise ratio algorithm.
- Derive two sets of models: Phase 1 (using data up to 05/2012, about 20000 records) and Phase 2 (including 03/2013 earthquake sequence).
- Focal depths between about 0 and 25km with peak between 5 and 20km.
- Vast majority of data from M
_{L}< 3.5 (only a handful of events have higher magnitudes). - Find using r
_{epi}and h_{A}rather than r_{hypo}results in slightly smaller σ. - Derive series of models starting from one including only M and r and then adding site, directivity and fault-zone amplification terms. Examine reduction in σ and residuals as additional terms added.
- Because of lack of V
_{s,30}measurements for stations use various geological and topographical methods to estimate V_{s,30}. Find none of these approaches leads to significant reduction in σ. Hence neglect this factor. - Find strong indication in residuals and reduction in σ of fault zone amplification (characterised by distance normal to fault, D).
- Find strong impact of directivity (characterised by index, I
_{Dir}) in residuals and reduction in σ. - Derive final model by adding directivity and then fault zone amplification to basic model.
- Classify stations into: amplifiers, dampers, and good-fit, based on their average residuals within magnitude bins. Examine residuals geographically and find amplifiers are often close to fault and dampers are often in boreholes or posthole sites buried ≥ 10m below surface.
- Initial regression of Phase 2 dataset did not converge. Attempt various regressions of subsets and obtain large σs. Conclude that additional directivity factor needs to be included in basic model.
- In Phase 2 exclude data from r
_{epi}> 80km for M < 3, r_{epi}> 100km for 3 ≤ M < 5 and r_{epi}> 150km for M ≥ 5 to decrease weight of small events at large distances. - Examine σ for various subsets of Phase 1 and 2 data (e.g. only mainshocks or specific sequences).
- Examine geographical distribution of variance of total residuals per event binned into various magnitude ranges. Find very high variances for 03/2013 dataset, which relate to combination of source characteristics and new fault-zone stations.