Fault-plane solution using P-wave first motionpolarity

Author: Sonia ZehsazSupervisor: Dr. K. Moghtased-Azar

Advisor: Dr. A. Rastbood

University of Tabriz

September 24, 2017

Source mechanism theory

The focal mechanisms or "seismic beach balls" describe:

I Geometry of the fault

I Slip of the fault

I Stress field in the region

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Double-Couples

..Force or Forces?.

.Displacement

Forces!

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Methods?

1. Forward:Polarity of P-Wave first motion

2. Inverse:Waveform inversion

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Polarity of P-Wave first motion

Body wave radiation pattern in far-field

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Polarity of P-Wave first motion

P-wave motion

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Polarity of P-Wave first motion

The regions of compresional and dilatational first motions bytwo nodal planes

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Polarity of P-Wave first motion

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Forward methodology

Inputs:

1. Source Location2. Stations Location3. Velocity Model4. Seismograms

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Methodology

Compute:

1. Ray azimuths and Take-off angles

I The angle of incidence at the earthquake source is the angle fromthe vertical at which the ray leaves the source.

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Methodology (Cont.)

2. On a sphere: projection on the lower ” focal sphere”

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Methodology (Cont.)

2. On a sphere: projection on the lower ” focal sphere”

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Methodology (Cont.)

3. Find the number of misfit polarities

4. Use grid search to find all acceptable solutions:

Solutions in which the number of misfit polarities ≤ maximumnumber of allowed misfits

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Methodology (Cont.)

5. Average to find the preferred solutions

The preferred solution, or the most probable solution, is the averageof the acceptable fault plane solutions.

6. Remove solutions which are more than 30◦ (user specified angledefining ”close”) of average solution

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Methodology (Cont.)

7. Compute quality of focal mechanism

I Compute variance (RMS) or fault plane uncertainly:The RMS difference of the acceptable nodal planes from the preferredplanes.

I Compute mechanism probability:The probability that the real mechanism is close to the preferred mecha-nism, with a user specified angle defining ”close”.

I Compute station distribution ratio.

I Select the best possible solution.

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Quality of focal mechanism

Validation

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Questions

1. Which method (forwar or inverse) does estimate focalmechanisms of a small earthquake?

2. Earthquake models can be divided into two categories:single couple and double couple.Which one is routinely used to approximate the source ofearthquakes?

3. When a reliable estimate for a focal mechanism can beobtainable and Which factors can affect the estimation of thefocal mechanism? observerd p-wave first motion polarities orvelocity models or stations coverage?

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Refrences

I Aki, K. and P. Richards, 1980. Quantitative Seismology, Theory and Methods, Vol.1, W. H. Freeman and Co., San Francisco, California.

I Stein, S. and Wysession, M., 2003. Introduction to seismology, earthquakes andearth structure, Blackwell Publishing, Oxford, 498 pp.

I Hardebeck, J. L., and P. M. Shearer (2002). A new method for determining first-motion focal mechanisms, Bull. Seism. Soc. Am.92,2264-2276.

I Hardebeck, J. L., and P. M. Shearer (2003). Using S/P Amplitude Ratiosto Constrain the Focal Mechanisms of Small Eartquakes, Bull. Seism. Soc.Am.93,2434-2444.

I Reasenberg, P., and D. Oppenheimer (1985). FPFIT, FPPLOT, and FPPAGE:FORTRAN computer programs for calculating and displaying earthquake fault-plane solutions,U.S. Geol. Surv. Open-File Rept. 85-739, 109 pp.

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Thanks for your attention!

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