1 Earthquake Magnitude Measurements for Puerto Rico Dariush Motazedian and Gail M. Atkinson

2 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. –In Puerto Rico digital database (since 1993) we deal with small to moderate earthquakes as you saw in the previous picture. Graph from PRSN Web

3 Magnitude Measurements Since we deal with small to moderate earthquakes in our Puerto Rico database, the Brune point source model is applicable for investigation of magnitude. The acceleration spectrum for an earthquake at a distance R can be modeled as a point source. –A (f)= A 0 (f) [c 1 /R c2 ] [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, –Thus we get A 0,,the Brune point source model: A 0 (f)=CM 0 (2π f) 2 / [1+(f/ f 0 ) 2 ] D 0 (f)= CM 0 / [1+f/f 0 )2] Usually there are two ways to calculate M 0 or M from these equations.

4 low frequencies (f << fo) approach At low frequencies (f << fo), the displacement spectrum becomes: –D 0 (f) = C M 0 We can use low frequencies approach to calculate seismic moment since A difficulty with this approach is that the frequency content of the recorded time series should extend to enough low frequencies to obtain the displacement spectrum at low frequencies.

5 low frequencies (f << fo) approach But, the available seismographic data are mostly short-period records. Unfortunately, short-period network data do not extend to sufficiently low frequencies. The low frequency approach can be employed to broadband records. The broadband instruments in Puerto Rico have been installed only recently. There has been a single IRIS broadband station in Puerto Rico since 1993.

6 low frequencies (f << fo) approach The low frequency approach is not appropriate for Puerto Rico since; –we have just one IRIS broadband station in Puerto Rico since –Broadband stations in Puerto Rico have been installed only recently.

7 Higher frequencies (f >> fo) If we want to use higher frequencies to calculate seismic moment based on the acceleration spectrum. –A 0 (f)=CM 0 (2π f) 2 / [1+(f/ f 0 ) there are some difficulties. Difficulties with this approach –It is sensitive to stress drop. –It is sensitive to kappa factor. –It is sensitive to anelastic attenuation –It is sensitive to upper limit of instrument response.

8 To get around low and high frequencies difficulties, Chen and Atkinson (2002) proposed an alternative magnitude measure, M 1. 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). 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

9 M 1 is an intermediate-frequency magnitude obtained from the spectral amplitude at 1 Hz. M 1 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 instrument response problem at lower frequencies. –1Hz frequency is low enough to avoid high frequency difficulties.

10 Advantages of M 1 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 M 1 is not sensitive to behavior of spectrum at higher frequencies.

11 Advantages of M 1 Since the value of M 1 is not sensitive to behavior of spectrum at higher frequencies it is not sensitive to Kappa as well. It is applicable to all broadband and short period seismometers. Instrument response is the worst seismologist nightmare in seismic data proceeding of most of seismic networks in the world ! –But, The instrument response of almost all types of seismometer is flat at 1 Hz. –But, Instrument response at 1Hz is the most accurate instrument response since the calibration of almost all types of seismometer is done at 1Hz –Thus, less headache with M 1 It is applicable to recorded time series with low sampling rates as long as the Nyquist frequency is more than 1Hz!

12 Advantages of M 1 M 1 is very sensitive to the energy underlying 1Hz frequency

13 Disadvantages of M 1 It is applicable just to small and moderate earthquakes (M<5.0). What happens if we apply M 1 to larger earthquakes?

14 M 1 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 to cover all of possible directivity effects. Then, we calculated M1 for all of 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.

15 M 1 for Puerto Rico We calculated M 1 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.

16 M 1 for Puerto Rico (M1=0.71mb+0.92) (M1=0.76Md+0.43) There is a systematic difference between M 1 and catalogue magnitudes mb or Md. Catalogue magnitude exceeding moment magnitude by about 0.4 units on average.

17 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 is just based on a single station recording. Because M is calculated from a single station, M is not reliable. But there is a systematic difference between M and M cat, the same as we had between M 1 and M cat.

18 M 1 versus M If we plot M 1, 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 M 1 versus M based o the low frequency application is the same as the trend that we had for simulated earthquakes.

19 The reported CMT moment magnitude in catalogue (Mw) and the estimated M (this study) for earthquakes in Puerto Rico. DateDistance (km)Mw (catalogue)M (this study) 1996,05, ,10, ,01, ,08,

20 Summary and Conclusion M 1 is applicable to all short period and broad band data. M 1 is not sensitive to stress drop. M 1 closely 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 M 1 are in close agreement with each other for small to moderate earthquakes. There is a systematic difference between M 1 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 M 1 be used as a regional magnitude scale for Puerto Rico earthquakes, and as an estimate of M for events of M<5.