The ANSS event ID is pr2020001008 and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/pr2020001008/executive.
2020/01/01 10:59:48 17.939 -66.843 7.0 3.64 Puerto Rico
USGS/SLU Moment Tensor Solution ENS 2020/01/01 10:59:48:0 17.94 -66.84 7.0 3.6 Puerto Rico Stations used: IU.SJG PR.AGPR PR.AOPR PR.CELP PR.CRPR PR.ECPR PR.EMPR PR.GCPR PR.HUMP PR.OBIP PR.PRSN PR.UUPR Filtering commands used: cut o DIST/3.3 -40 o DIST/3.3 +50 rtr taper w 0.1 hp c 0.03 n 3 lp c 0.10 n 3 Best Fitting Double Couple Mo = 4.79e+21 dyne-cm Mw = 3.72 Z = 7 km Plane Strike Dip Rake NP1 295 90 -40 NP2 25 50 -180 Principal Axes: Axis Value Plunge Azimuth T 4.79e+21 27 348 N 0.00e+00 50 115 P -4.79e+21 27 242 Moment Tensor: (dyne-cm) Component Value Mxx 2.81e+21 Mxy -2.36e+21 Mxz 2.79e+21 Myy -2.81e+21 Myz 1.30e+21 Mzz 2.69e+14 ############## ###### ############- ######### T ############---- ########## #############---- #############################----- ##############################------ -##############################------- ------##########################-------- ----------######################-------- ---------------#################---------- -------------------#############---------- -----------------------########----------- ---------------------------####----------- ----- ---------------------#---------- ----- P --------------------######------ ---- -------------------###########- -----------------------############# ---------------------############# -----------------############# --------------############## -------############### ############## Global CMT Convention Moment Tensor: R T P 2.69e+14 2.79e+21 -1.30e+21 2.79e+21 2.81e+21 2.36e+21 -1.30e+21 2.36e+21 -2.81e+21 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20200101105948/index.html |
STK = 295 DIP = 90 RAKE = -40 MW = 3.72 HS = 7.0
The NDK file is 20200101105948.ndk The waveform inversion is preferred.
Given the availability of digital waveforms for determination of the moment tensor, this section documents the added processing leading to mLg, if appropriate to the region, and ML by application of the respective IASPEI formulae. As a research study, the linear distance term of the IASPEI formula for ML is adjusted to remove a linear distance trend in residuals to give a regionally defined ML. The defined ML uses horizontal component recordings, but the same procedure is applied to the vertical components since there may be some interest in vertical component ground motions. Residual plots versus distance may indicate interesting features of ground motion scaling in some distance ranges. A residual plot of the regionalized magnitude is given as a function of distance and azimuth, since data sets may transcend different wave propagation provinces.
Left: ML computed using the IASPEI formula for Horizontal components. Center: ML residuals computed using a modified IASPEI formula that accounts for path specific attenuation; the values used for the trimmed mean are indicated. The ML relation used for each figure is given at the bottom of each plot.
Right: Residuals from new relation as a function of distance and azimuth.
Left: ML computed using the IASPEI formula for Vertical components (research). Center: ML residuals computed using a modified IASPEI formula that accounts for path specific attenuation; the values used for the trimmed mean are indicated. The ML relation used for each figure is given at the bottom of each plot.
Right: Residuals from new relation as a function of distance and azimuth.
![]() |
The focal mechanism was determined using broadband seismic waveforms. The location of the event (star) and the stations used for (red) the waveform inversion are shown in the next figure.
![]() |
|
The program wvfgrd96 was used with good traces observed at short distance to determine the focal mechanism, depth and seismic moment. This technique requires a high quality signal and well determined velocity model for the Green's functions. To the extent that these are the quality data, this type of mechanism should be preferred over the radiation pattern technique which requires the separate step of defining the pressure and tension quadrants and the correct strike.
The observed and predicted traces are filtered using the following gsac commands:
cut o DIST/3.3 -40 o DIST/3.3 +50 rtr taper w 0.1 hp c 0.03 n 3 lp c 0.10 n 3The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT WVFGRD96 1.0 300 80 -10 3.33 0.3584 WVFGRD96 2.0 300 80 -20 3.49 0.4674 WVFGRD96 3.0 120 90 50 3.63 0.5651 WVFGRD96 4.0 115 90 50 3.66 0.6547 WVFGRD96 5.0 295 90 -45 3.68 0.7106 WVFGRD96 6.0 115 90 40 3.70 0.7380 WVFGRD96 7.0 295 90 -40 3.72 0.7490 WVFGRD96 8.0 115 90 45 3.78 0.7464 WVFGRD96 9.0 115 90 40 3.79 0.7311 WVFGRD96 10.0 295 90 -40 3.80 0.7089 WVFGRD96 11.0 115 90 35 3.81 0.6838 WVFGRD96 12.0 295 90 -35 3.82 0.6556 WVFGRD96 13.0 295 90 -35 3.82 0.6267 WVFGRD96 14.0 115 90 35 3.83 0.5992 WVFGRD96 15.0 110 85 30 3.85 0.5759 WVFGRD96 16.0 110 85 30 3.86 0.5576 WVFGRD96 17.0 110 80 30 3.87 0.5430 WVFGRD96 18.0 110 80 30 3.88 0.5298 WVFGRD96 19.0 110 80 30 3.89 0.5163 WVFGRD96 20.0 115 80 30 3.90 0.5067 WVFGRD96 21.0 115 80 30 3.91 0.4966 WVFGRD96 22.0 115 80 30 3.92 0.4861 WVFGRD96 23.0 110 85 30 3.92 0.4780 WVFGRD96 24.0 110 85 25 3.93 0.4699 WVFGRD96 25.0 110 85 25 3.94 0.4638 WVFGRD96 26.0 110 85 25 3.95 0.4569 WVFGRD96 27.0 110 85 25 3.96 0.4510 WVFGRD96 28.0 290 90 -25 3.96 0.4436 WVFGRD96 29.0 290 90 -25 3.96 0.4394
The best solution is
WVFGRD96 7.0 295 90 -40 3.72 0.7490
The mechanism corresponding to the best fit is
![]() |
|
The best fit as a function of depth is given in the following figure:
![]() |
|
The comparison of the observed and predicted waveforms is given in the next figure. The red traces are the observed and the blue are the predicted. Each observed-predicted component is plotted to the same scale and peak amplitudes are indicated by the numbers to the left of each trace. A pair of numbers is given in black at the right of each predicted traces. The upper number it the time shift required for maximum correlation between the observed and predicted traces. This time shift is required because the synthetics are not computed at exactly the same distance as the observed, the velocity model used in the predictions may not be perfect and the epicentral parameters may be be off. A positive time shift indicates that the prediction is too fast and should be delayed to match the observed trace (shift to the right in this figure). A negative value indicates that the prediction is too slow. The lower number gives the percentage of variance reduction to characterize the individual goodness of fit (100% indicates a perfect fit).
The bandpass filter used in the processing and for the display was
cut o DIST/3.3 -40 o DIST/3.3 +50 rtr taper w 0.1 hp c 0.03 n 3 lp c 0.10 n 3
![]() |
Figure 3. Waveform comparison for selected depth. Red: observed; Blue - predicted. The time shift with respect to the model prediction is indicated. The percent of fit is also indicated. The time scale is relative to the first trace sample. |
![]() |
Focal mechanism sensitivity at the preferred depth. The red color indicates a very good fit to the waveforms. Each solution is plotted as a vector at a given value of strike and dip with the angle of the vector representing the rake angle, measured, with respect to the upward vertical (N) in the figure. |
A check on the assumed source location is possible by looking at the time shifts between the observed and predicted traces. The time shifts for waveform matching arise for several reasons:
Time_shift = A + B cos Azimuth + C Sin Azimuth
The time shifts for this inversion lead to the next figure:
The derived shift in origin time and epicentral coordinates are given at the bottom of the figure.
The WUS.model used for the waveform synthetic seismograms and for the surface wave eigenfunctions and dispersion is as follows (The format is in the model96 format of Computer Programs in Seismology).
MODEL.01 Model after 8 iterations ISOTROPIC KGS FLAT EARTH 1-D CONSTANT VELOCITY LINE08 LINE09 LINE10 LINE11 H(KM) VP(KM/S) VS(KM/S) RHO(GM/CC) QP QS ETAP ETAS FREFP FREFS 1.9000 3.4065 2.0089 2.2150 0.302E-02 0.679E-02 0.00 0.00 1.00 1.00 6.1000 5.5445 3.2953 2.6089 0.349E-02 0.784E-02 0.00 0.00 1.00 1.00 13.0000 6.2708 3.7396 2.7812 0.212E-02 0.476E-02 0.00 0.00 1.00 1.00 19.0000 6.4075 3.7680 2.8223 0.111E-02 0.249E-02 0.00 0.00 1.00 1.00 0.0000 7.9000 4.6200 3.2760 0.164E-10 0.370E-10 0.00 0.00 1.00 1.00