Earthquake Stress Drop Earthquake Stress Drop from Spectral Ratiosfrom Spectral Ratios

Matthew A. d’ALESSIOTokyo University, Earthquake Research Institute

Kazutoshi IMANISHIGeological Survey of Japan, AIST

William L. ELLSWORTHU.S. Geological Survey

Earthquake Stress Drop Earthquake Stress Drop from Spectral Ratiosfrom Spectral Ratios

ダレシオ マシュー

東京大学 地震研究所

今西 和俊

産業技術総合研究所地質情報研究部門

エルスワ-ス ウィリアムU.S. Geological Survey

What are the stress drops of small earthquakes?What are the stress drops of What are the stress drops of small earthquakes?small earthquakes?

How much does stress drop vary?(need estimates of uncertainty)

What are the dimensions ofrupture patches??

StrengthCan we observe higher stress drops at deeper depths?

Dep

th

Spectra contain earthquake source informationSpectra contain earthquake Spectra contain earthquake source informationsource information

(Aki, 1967)

Pow

er S

pect

ral D

ensi

ty

Period

Long period energy →Moment

Corner Frequency → Source Dimensions

Given assumptions about source kinematics…

Path-dependent processes also affect frequency contentPathPath--dependent processes also affect dependent processes also affect frequency contentfrequency content

Frequency dependent attenuation

Scattering/Conversions

Geometric spreading

Mechanism

Directivity

Instrument response

frequency

Nearby earthquakes experience similar pathsNearby earthquakes experience Nearby earthquakes experience similar pathssimilar paths

Ratio of spectragives relative moment of two events with many path-dependent effects eliminated.

÷

Input: Many seismogramsOutput: Moment & Corner FrequencyInput: Many seismogramsInput: Many seismogramsOutput: Moment & Corner FrequencyOutput: Moment & Corner Frequency

Two events recorded on samecomponent of same station

Fourier transform to get frequencydomain representation

Divide the spectral amplitudes by one another.

Fit Boatwright Ω2 curve to spectra: Moment + Corner Frequency

Events fromLast Friday!

Method advanced by Hough, 1997; Ide et al., 2004; Imanishi et al., 2004

Our test case is SAFOD Target areaOur test case is SAFOD Target areaOur test case is SAFOD Target area

http://earthscope.org

~5 km33 eventsWithin 300 m of one another~2.2 km depth2001-last Friday(catalog of R. Nadeau, UC Berkeley)

12 HRSN borehole seismometers65 - 550 m deep (Typically 250) 250 Hz sample rate

Stack data over multiple windows,components, and stationsStack data over multiple windows,Stack data over multiple windows,components, and stationscomponents, and stations

P SP S

scale

scale

More data =more robust spectra

“Multi-window”approach

Results from P and S are similarResults from P and S are similarResults from P and S are similar

Moment (Mo) Corner Frequency (Fc)

Same moment from P and S

S corner lower than P because of different velocities.

Assume static, circular crack to determine source radius and stress drop.

Stress drop is typically 0.5 to 5 MPaStress drop is typically 0.5 to 5 Stress drop is typically 0.5 to 5 MPaMPa

Hickman & Zobackstress estimate

PS

Magnitude21

Bootstrap uncertainties(95% bounds)

Magnitude21

Repeating events have nearly identical stress drop (no surprise)Repeating events have nearly Repeating events have nearly identical stress drop (no surprise)identical stress drop (no surprise)

HRSN(shallow boreholes)

Hickman & Zobackstress estimate

PS

Pilot Hole array results showhigher stress dropsPilot Hole array results showPilot Hole array results showhigher stress dropshigher stress drops

HRSN(shallow boreholes)

SAFOD Pilot Hole Array(deep borehole)

Hickman & Zobackstress estimate

Imanishi &Ellsworth

Magnitude21

Deeper events have higher stress drop(Preliminary results)Deeper events have higher stress dropDeeper events have higher stress drop(Preliminary results)(Preliminary results)

SAFOD Targets

6-8 km deep events

Magnitude21

Plans for future workPlans for future workPlans for future work

Confirm these preliminary results.

Explain difference between HRSN and Pilot Hole observations.

Apply technique to a many more earthquakes

Fits are decent, though data are noisyFits are decent, though data are noisyFits are decent, though data are noisy

Residuals much smaller

than scatter between individualspectral windows.

model

95% bounds

data

Path effects cancel out in spectral ratiosPath effects cancel out Path effects cancel out in spectral ratiosin spectral ratios

Raw Spectra Ratios

1. co-located event

2. similar focal mechanism

3. source model (Ο2 Boatwright model)

Assumption

Simultaneously, relative seismic moments and corner frequencies for events in each cluster are determined.

Method advanced by Hough, 1997; Ide et al., 2004; Imanishi et al., 2004

Stress drop is typically 0.5 to 5 MPaStress drop is typically 0.5 to 5 Stress drop is typically 0.5 to 5 MPaMPa

Events withFc > 100 Hz

PS