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Earthquake Magnitude Measurements for Puerto Rico

Dariush Motazedian and Gail M. AtkinsonCarleton University

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Seismicity of Puerto Rico

• Puerto Rico has a high level of seismic activity due to its location on the boundary between the North American and the Caribbean plates. Many big earthquakes have occurred in the past centuries.

• But, the seismicity catalogue for Puerto Rico since 1993, when Puerto Rico Seismic Network started digital recording, is dominated by small earthquakes (M<5), mostly – Md (a local magnitude based on duration) and – mb (body wave magnitude). – Ideally, a regional magnitude scale should be closely correlated with moment

magnitude. What is really needed is a moment-magnitude-based catalogue.

Graph from PRSN Web

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Magnitude Measurements• Since we deal with small to moderate earthquakes in our Puerto Rico database,

the Brune point source model is applicable.

• The acceleration spectrum for an earthquake at a distance R can be modeled as a point source.

– A (f)= A0 (f) [c1/Rc2] [exp-f] [exp(-π f R/Q)] S(f)• If we calculate the Fourier spectrum of a recorded acceleration time series and

play back the attenuation effects: Geometric spreading ,Anelastic attenuation ,Kappa factor, Site effect,– Then we get A0,for the Brune point source model:

• A0 (f)=CM0(2π f) 2/ [1+(f/ f0) 2]• D0 (f)= CM0 / [1+f/f0)2]

• In principle we can calculate M0 from displacement spectrum at low frequencies

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Seismic moment from D(f) (f << fo)• At low frequencies (f <<

fo), the displacement spectrum becomes:– D0 (f) = C M0

• We can thus calculate

seismic moment from spectrum

• But note that the frequency content of the recorded time series must extend to sufficiently low frequencies.

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Problem with calculating moment magnitude from spectrum (f << fo)

• the available seismographic data are mostly short-period records that do not extend to sufficiently low frequencies.

• The low frequency approach can be employed for broadband records, but these have been installed only recently in Puerto Rico.

Normalized Instrument Response of Short Period and Broadband seismometers in Puerto Rico

0.001

0.01

0.1

1

10

0.001 0.01 0.1 1 10 100

f(Hz)

Vol

t/met

er/s

econ

dPuerto Rico SP(S13) IRIS BB (STS-1)

Puerto Rico BB (40T)

• There has been a single IRIS broadband station in Puerto Rico since 1993.

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• Can determine the intermediate frequency magnitude M1 (Chen and Atkinson, 2002)

• We apply a band pass filter to the acceleration spectrum, centered at 1 Hz (a Butterworth filter with the order of 8 from 0.7Hz to 1.3 Hz) to obtain 1-Hz near-source amplitude.

• Calculate the total area under the filtered acceleration spectrum.

• Iterate over magnitude to find a Brune model which, after the application of the same band pass filter, has the same area under its spectrum.

Chen and Atkinson (2002) applied this approach to a large number of worldwide earthquakes (more than 3000 earthquakes).

Use of intermediate frequencies (f =1Hz)

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Intermediate frequencies (f =1Hz) approach

• M1 is an intermediate-frequency magnitude obtained from the spectral amplitude at 1 Hz.

• M1 is defined such that it will equal moment magnitude for

earthquakes following a Brune point-source model at f = 1Hz.

• Why 1 Hz?

– 1Hz frequency is high enough to avoid bandwidth problem at lower frequencies.

– 1Hz frequency is low enough to avoid high frequency

difficulties such as dependence on stress drop and kappa.

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Advantages of M1

• The source spectrum amplitude at f=1Hz is independent of stress drop as long as corner frequency is bigger than 1Hz, which is true for small to moderate earthquakes.

• The value of M1 is not sensitive to behavior of spectrum at higher frequencies.

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Advantages of M1• M1 is very sensitive to the energy underlying 1Hz frequency

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Disadvantages of M1

• It is applicable just to small and moderate earthquakes (M<5.0).

• What happens if we apply M1 to larger earthquakes?

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M1 versus moment magnitude (M)

• Using Stochastic Finite Fault modeling, we simulated 650 acceleration time series for magnitudes from M2.0 to M8.0, distances from 10 km to 500 km and a good coverage on azimuth.

• Then, we calculated M1 for all simulated times series.

•M1 is a good representative of M for small to moderate magnitude up to M5.0.

•For larger magnitudes the deviation becomes large due to the effect of the fault length.

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2 3 4 5 6 7 8M(Moment Magnitude)

M 1

M=M1

M1

M1 as a function of moment magnitude , M.

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M1 for Puerto Rico• We calculated M1 for about 300 Puerto Rico earthquakes recorded

from 1993-through 2002 with M>=3.0.

• Data base

– PRSN Short period time series ; More than 2000 time series.

– IRIS Broadband time series; more than 1200 time series.

– PRSMN Strong Motion data ; More than 30 acceleration time series from 4 events.

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M1 for Puerto Rico• (M1=0.71mb+0.92)• (M1=0.76Md+0.43)

• There is a systematic difference between M1 and catalogue magnitudes mb or Md.

• Catalogue magnitude exceeding moment magnitude by about 0.4 units on average.

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M for Puerto Rico• Although we have just one IRIS

broadband station in Puerto Rico since 1993, but we applied the low frequency approach to calculate moment magnitude ,M.

• We calculated M for about 300 Puerto Rico earthquakes recorded from 1993-through 2002 with M>=3.0.

• These M based on single station recording (not reliable).

• But there is a systematic difference

between M and Mcat, the same as we had between M1 and M cat.

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M1 versus M• we plot M1, which is based on the

amplitude of acceleration source spectra at 1 Hz versus M, which is moment magnitude based on the displacement spectra at lower frequencies.

• Both magnitudes are almost the same for earthquakes with magnitude less than M5.0.

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2 3 4 5 6 7 8

M

M1

M1=M M1(PR data)

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2 3 4 5 6 7 8M

M 1

M=M1

M1

• The trend of M1 versus M from observations is the same as the trend that we had for simulated earthquakes.

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The reported CMT moment magnitude in catalogue (Mw) and the estimated M (this study) for earthquakes in Puerto Rico.

Date Distance (km) Mw (catalogue) M (this study)

1996,05,11 186 5.1 5.2

2001,10,17 191 6.0 5.9

1999,01,18 144 5.0 4.8

1998,08,10 470 5.2 4.6

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Summary and Conclusion

• M1 is applicable to all short period and broad band data.

• M1 is not sensitive to stress drop.

• M1closely tracks moment magnitude for small to moderate events.

• Our estimates of M agree reasonably well with independent values for the few earthquakes that are large enough to have global moment estimates.

• Our values of M and M1 are in close agreement with each other for small to moderate earthquakes.

• There is a systematic difference between M1 or M and catalogue magnitudes mb or Md, with the catalogue magnitude exceeding moment magnitude by about 0.4 units on average.

• It is recommended that M1 be used as a regional magnitude scale for Puerto Rico earthquakes, and as an estimate of M for events of M<5.