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Earthquake Magnitude Measurements for Puerto Rico Dariush Motazedian and Gail M. Atkinson Carleton University. Seismicity of Puerto Rico.

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## Seismicity of Puerto Rico

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**Earthquake Magnitude Measurements for Puerto RicoDariush**Motazedian and Gail M. AtkinsonCarleton University**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**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**Seismic moment from D(f) (f << fo)**• At low frequencies (f << fo), the displacement spectrum becomes: • D0 (f) = CM0 • 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.**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. • There has been a single IRIS broadband station in Puerto Rico since 1993.**Use of intermediate frequencies (f =1Hz)**• 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).**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.**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.**Advantages of M1**• M1 is very sensitive to the energy underlying 1Hz frequency**Disadvantages of M1**• It is applicable just to small and moderate earthquakes (M<5.0). • What happens if we apply M1 to larger earthquakes?**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.**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.**M1 for Puerto Rico**• (M1=0.71mb+0.92) • (M1=0.76Md+0.43) • There is a systematic difference between M1and catalogue magnitudes mb or Md. • Catalogue magnitude exceeding moment magnitude by about 0.4 units on average.**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.**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. • The trend of M1 versus M from observations is the same as the trend that we had for simulated earthquakes.**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 M1or 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.

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