Estimating the rupture extent of low frequency 2011-04-03T10:07:28.248001-2011-04-03T10:08:46.998001 earthquakes near Parkfield, CA ground velocity (m/s) 3.0 1.5 1.5 3.0 1e 8 PB.B073..EH1 10:07:39 10:08:09 10:08:39 Jessica Hawthorne (Leeds) Amanda Thomas (Oregon), Pablo Ampuero (Caltech) 6 April 2017
ground velocity (m/s) Tremor 3.0 1.5 1.5 3.0 1e 8 PB.B073..EH1 2011-04-03T10:07:28.248001-2011-04-03T10:08:46.998001 10:07:39 10:08:09 10:08:39 Many small earthquakes On the plate interface below the seismogenic zone Low-frequency: most energy in 1-10 Hz band Constituent earthquakes have long durations?
Low frequency earthquakes have long durations. Why? ground velocity low frequency earthquake stack earthquake 0.5 seconds in Cascadia (Bostock et al., 2015) 0.2 seconds near Parkfield (Thomas et. al., 2016)
Low frequency earthquakes have long durations. Why? ground velocity low frequency earthquake stack They re spatially big, with durations earthquake radius 0.8 shear wave speed 1200 m diameters earthquake 0.5 seconds in Cascadia (Bostock et al., 2015) 0.2 seconds near Parkfield (Thomas et. al., 2016)
Low frequency earthquakes have long durations. Why? ground velocity low frequency earthquake stack They re spatially big, with durations earthquake radius 0.8 shear wave speed 1200 m diameters earthquake 0.5 seconds in Cascadia (Bostock et al., 2015) 0.2 seconds near Parkfield (Thomas et. al., 2016) 8 4 Or LFEs have different rupture dynamics? 0-100 0 100 distance along fault (m) 10 8 10 6 10 4 10 2 1 slip rate / plate rate
LFE families near Parkfield, CA 5 km 36 N SCYB RMNB SMNB LCCB 35.9 N 120.6 W CCRB MMNB B073 B075 VCAB FROB 120.5 W B076 VARB JCSB EADB 4000 and 8000 detections in the catalog of Shelly et al, 2009 HRSN and PBO borehole data, 2006-2016 Do these LFEs have diameters > 1 km, as suggested by 0.2-s durations? B078 GHIB B072 B079
Want to use variation in travel time within the source region to estimate the LFEs spatial extents d d/vrupt d/vp Apparent stfs are 2 1 d d/vrupt Similar at periods longer than the travel time across the earthquake Different at shorter periods d/vrupt + d/vp
apparent source time function 2000 Synthetic 1000 apparent source time functions 0 1000 4000 3000 2000 1000 0 0 1 2 3 4 200 m diameter 1000 0 2 4 6 8 400 m diameter 4000 station direction 3000-1 2000 11 21 Measure 1000 phase similarity: 32 35 0 46 1000R = 1 ŝ a 60 0 N 5 ŝ a 0.10 0.15 72 stations 84 94 coherent phase moveout 0.4 0.2 10 0 10 1 1.0 Similar at periods 0.8 longer than the travel 0.6 time across the 0.4 earthquake 0.2 Different at shorter periods 10 0 10 1 1.0 0.8 0.6 0.4 0.2 diameter 1.3 wavespeed 10 0 10 1 frequency (Hz)
Empirical Green s function phase removal Expect apparent stfs (s tk and s ik ) to vary among stations when wavelength < rupture diameter. But we only have the observations: d tk = s tk g k and d ik = s ik g k
Empirical Green s function phase removal Expect apparent stfs (s tk and s ik ) to vary among stations when wavelength < rupture diameter. But we only have the observations: ˆdtk = ŝ tk ĝ k and ˆd ik = ŝ ik ĝ k
Removing the Green s functions phases Have the observations: ˆd tk = ŝ tk ĝ k and ˆd ik = ŝ ik ĝ k Cross-correlate at each station ˆx k = ˆd ik ˆd tk = zero phase {}}{ ŝ ik ŝ }{{ tk ĝ } k ĝk same across stations? ˆd phase ψ
Removing the Green s functions phases cro energy 10 1 cross-correlation phases Have the observations: ˆd tk = ŝ tk ĝ k and ˆd ik = ŝ ik ĝ k 10 1 0 1 2 3 4 5 6 2 1 0 1 2 0 2 diameter (m) Cross-correlate diameter (m) at each station 1000 500 300 1000 500 300 180 1.2 90 0 90 180 2 5 10 frequency (Hz) coherent energy fraction ˆx k = ˆd ik ˆd tk 1.0 0.8 0.6 0.4 inter-station zero phase {}}{ = ŝ ik ŝ }{{ tk ĝ } k ĝk same across stations? 0.2when x k phases are the same, wavelength is larger than LFE 2 5 10 frequency (Hz)
00 energy / template energy Template-normalized LFE energies 10 3 10 2 10 1 diameter (m) 1000 500 inter-station coherent LFE 2 10 0 2 5 10 frequency (Hz) 300 cross-correlation phases 1 0 1 2 3 4 5 6 diameter (m) 1000 500 300 180 90 0 90 180 2 5 10 frequency (Hz) total LFE energy: observed minus noise LFE energy coherent across stations: E c = ˆx k ˆx l ˆd tk ˆdtl 2 coherent energy fraction 1.2 1.0 0.8 0.6 0.4 0.2 2
Template-normalized LFE energies 10 0 6 2 1 0 1 2 diameter (m) 300 1000 500 300 1.2 inter-station coherent energy fraction 1.0 0.8 0.6 0.4 0.2 2 5 10 frequency (Hz) 2 5 10 1 0 1 2 3 4 5 6 frequency (Hz) cross-correlation phases 180 90 0 90 diameter (m) 1000 500 180 2 5 10 frequency (Hz) 300 total LFE energy: observed minus noise LFE energy coherent across stations: E c = ˆx k ˆx l ˆd tk ˆdtl 2 coherent energy fraction 1.2 1.0 0.8 0.6 0.4 0.2 2
Averaging over 2600 LFEs: Family 37140 template-normalized energy coherent energy / LFE energy 10 3 10 2 10 1 10 0 1.0 0.8 0.6 0.4 0.2 1000 inter-station coherent LFE diameter (m) 500 300 inter-station coherent 2 5 frequency (Hz) 10 15 Coherent fraction high out to 10 Hz Diameter around 300-400 m Factor 3-4 smaller than 1.2 km expected for 3 km/s rupture velocity
Averaging over 3800 LFEs: Family 37102 template-normalized energy coherent energy / total 10 3 10 2 10 1 10 0 10-1 10-2 1.0 0.8 0.6 0.4 0.2 1000 inter-station coherent LFE diameter (m) 500 300 inter-station coherent point source adjusted for noise 2 5 frequency (Hz) 10 15 Coherent fraction high out to > 5 Hz Diameter < 700 m Decoherence could be due to timing, tapering, nearby LFEs Factor > 2 smaller than 1200 m expected for 3 km/s rupture velocity
So why are the rupture durations long? 8 4 short normal rupture propagation minimum earthquake size 0-100 0 100 distance along fault (m) 10 8 10 6 10 4 10 2 1 slip rate / plate rate Long rise time from nucleation? Slow propagation? Complex rupture patterns? Attenuation?
Conclusions ground velocity (m/s) 3.0 1.5 1.5 3.0 1e 8 PB.B073..EH1 2011-04-03T10:07:28.248001-2011-04-03T10:08:46.998001 10:07:39 10:08:09 10:08:39 Low-frequency nature of tremor does not arise because the asperities are big. High inter-station coherence out to 10 Hz implies average diameters < 400 m and < 700 m Rupture extents are a factor of >2-4 smaller than expected for 0.2-s durations and near-shear-wave rupture velocities Suggest different rupture dynamics or a role for attenuation