Mechanics of Earthquakes and Faulting

Transcription

1 Mechanics of Earthquakes and Faulting Lecture 18, 16 Nov Earthquake Magnitude and Moment Brune Stress Drop Seismic Spectra & Earthquake Scaling laws Scaling and Self-Similarity of Earthquake Rupture Implications for Rupture Dynamics and the Mode of Rupture Propagation

2 Thermo-mechanics of faulting San Andreas fault strength, heat flow. Consider: W f = τ v q If τ ~ 100 MPa and v is ~ 30 mm/year, then q is: 1e8 (N /m 2 ) 3e-2 (m/3e7s) = 1e-2 (J/s m 2 ) ~ 100 mw/m2. Problem of finding very low strength materials. Relates to the very broad question of the state of stress in the lithosphere? Byerlee s Law, Rangley experiments, Bore hole stress measurements, bore hole breakouts, earthquake focal mechanisms. Seismic stress drop vs. fault strength.

3 Fault Strength, State of Stress in the Lithosphere, and Earthquake Physics

4 Thermo-mechanics of faulting Fault strength, heat flow. Average Shear Stress Average slip velocity Consider shear heating: W f = τ v q If τ ~ 100 MPa and v is ~ 30 mm/year, then q is: 1e8 (N /m 2 ) 3e-2 (m/3e7s) = 1e-1 (J/s m 2 ) 100 mw/m 2

5 Fault Strength and State of Stress Data from Lachenbruch and Sass, 1980 Heat flow Stress orientations S A F e.g. Townend & Zoback, 2004;; Hickman & Zoback, 2004

6 Data from Lachenbruch and Sass, 1980 Fault Strength and State of Stress Heat flow Stress orientations Have been used to imply that the SAF is weak, µ 0.1. Inferred stress directions S A F σ 1 σ 1 S A F Predicted Observed e.g. Townend & Zoback, 2004;; Hickman & Zoback, 2004

7 SAFOD The San Andreas Fault Observatory at Depth Is the San Andreas anomalously weak?

8 SAF - Geology Based on Zoback et al., EOS, 2010

9 Frictional Strength, SAFOD Phase III Core Carpenter, Marone, and Saffer, Nature Geoscience, 2011 Carpenter, Saffer and Marone, Geology, 2012

10 Weak Fault in a Strong Crust Carpenter, Saffer, and Marone. Geology, 2012

11 Seismic Spectra & Earthquake Scaling laws. Aki, Scaling law of seismic spectrum, JGR, 72, , Hanks, b Values and ω -γ seismic source models: implications for tectonic stress variations along active crustal fault zones and the estimation of high-frequency strong ground motion, JGR, 84, , Scaling and Self-Similarity of Earthquake Rupture: Implications for Rupture Dynamics and the Mode of Rupture Propagation 0 Self-similar: Are small earthquakes the same as large ones? Do small ones become large ones or are large eq s different from the start? 1 Geometric self-similarity: aspect ratio of rupture area 2 Physical self-similarity: stress drop, seismic strain, scaling of slip with rupture dimension 3 Observation of constant b-value over a wide range of inferred source dimension. 4 Same physical processes operate during shear rupture of very small (lab scale, mining induced seismicity) and very large earthquakes? 5 Expectation of scaling break if rupture physics/dynamics change in at a critical size (or slip velocity, etc.). Shimazaki result. (Fig. 4.12). Length-Moment scaling and transition at L 60km (Romanowicz, 1992; Scholz, 1994). 6 Gutenberg-Richter frequency-magnitude scaling, b-values. 7 G-R scaling, b-value data. Single-fault versus fault population. G-R versus characteristic earthquake model. 8 Crack vs. slip-pulse models

12 Earthquake Source Properties, Spectra, Scaling, Self-similarity Displacement and acceleration source spectra. Spectra: zero-frequency intercept (M o ), corner frequency (ω o or f c ), high frequency decay (ω γ ), maximum (observed, emitted) frequency f max ω -n ω-square model, ω -2 ω-cube model, ω -3 log u at R Far-field body-wave spectra and relation to source slip function log freq. (ω) Displacement waveform for P & S waves: In general, very complex. Ω(x, t) and Ω(ω) depend on slip function, azimuth to observer and relative importance of nucleation and stopping phases

13 Scaling and Self-Similarity Are small earthquakes the same as large ones? 1 Geometric self-similarity: rupture aspect ratio 2 Physical self-similarity: stress drop, seismic strain, scaling of slip with rupture dimension Circular ruptures (small) Hanks, 1977 Abercrombie & Leary, 1993

14 Earthquake Source Properties, Spectra, Scaling, Self-similarity ω -3 log u at R log freq. (ω) ω-cube model, ω -3 Similarity condition M o α L 3 ω o α L -1 Ω(0) α ω o -3 This defines a scaling law. Spectral curves differ by a constant factor at a given period (e.g., 20 s), but they have the same high-freq. asymptote This behavior is expected when the nucleation phase is responsible for the high-freq. asymptote --but consider problem of time domain implication for amplitude (M b decreases with M o )

15 Seismic Source Spectra. Saturation occurs for large events, particularly saturation of M s (T=20 s) Corner frequency, Brune Stress drop. Aki, 1967

16 Earthquake Source Properties, Spectra, Scaling, Self-similarity ω -2 log u at R ω-square model, ω -2 Two possible explanations log freq. (ω) 1)!Similarity condition (not-similarity) M o α L 2 ω o α L -1 Ω(0) α ω o -2 2) Have similarity condition in terms of nucleation, but high-freq. asymptote is produced by stopping phase if rupture stops very abruptly

17 Earthquake Source Properties, Spectra, Scaling, Self-similarity Displacement and acceleration source spectra. Spectra: zero-frequency intercept (M o ), corner frequency (ω o or f c ), high frequency decay (ω γ ), maximum (observed, emitted) frequency f max f max log u at R ω -n log a at R log freq. (ω) log freq. (ω) Aki, Scaling law of seismic spectrum, JGR, 72, , Hanks, b Values and ω -γ seismic source models: implications for tectonic stress variations along active crustal fault zones and the estimation of high-frequency strong ground motion, JGR, 84, , 1979.

18 Earthquake Source Properties, Spectra, Scaling, Self-similarity Source spectra for two events of equal stress drop: omega cube model Large and Small Eq L log u at R L ω -3 S S f max log freq. (ω) High-freq. spectral properties: produced by rupture growth, represent nucleation and enlargement log a at R L S log freq. (ω)

19 Source spectra for two events of equal stress drop: omega square model Large and Small Eq L log u at R L ω -2 S S L f max log freq. (ω) High-freq. spectral properties: produced by rupture growth, represent nucleation and enlargement log a at R L S S f max log freq. (ω)

20 Earthquake Source Properties, Spectra, Scaling, Self-similarity Relation between source (a) displacement (b) velocity (c) acceleration history and asymptotic behavior of spectrum