Left: mLg computed using the IASPEI formula. Center: mLg residuals versus epicentral distance ; the values used for the trimmed mean magnitude estimate are indicated. Right: residuals as a function of distance and azimuth.
The ANSS event ID is nm608509 and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/nm608509/executive.
2011/02/28 05:00:50 35.269 -92.355 3.2 4.7 Arkansas
USGS/SLU Moment Tensor Solution
ENS 2011/02/28 05:00:50:0 35.27 -92.36 3.2 4.7 Arkansas
Stations used:
AG.FCAR AG.HHAR AG.WLAR NM.UALR TA.S40A TA.T38A TA.T39A
TA.T40A TA.U38A TA.U39A TA.U40A TA.V37A TA.V38A TA.V39A
TA.W38A TA.W39A TA.W40A TA.X38A TA.X39A TA.X40A TA.Y38A
TA.Y39A TA.Y40A US.MIAR
Filtering commands used:
hp c 0.02 n 3
lp c 0.0625 n 3
Best Fitting Double Couple
Mo = 1.19e+23 dyne-cm
Mw = 4.65
Z = 4 km
Plane Strike Dip Rake
NP1 26 85 -170
NP2 295 80 -5
Principal Axes:
Axis Value Plunge Azimuth
T 1.19e+23 4 160
N 0.00e+00 79 52
P -1.19e+23 11 251
Moment Tensor: (dyne-cm)
Component Value
Mxx 9.22e+22
Mxy -7.36e+22
Mxz 1.33e+20
Myy -8.87e+22
Myz 2.27e+22
Mzz -3.54e+21
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############ T
Global CMT Convention Moment Tensor:
R T P
-3.54e+21 1.33e+20 -2.27e+22
1.33e+20 9.22e+22 7.36e+22
-2.27e+22 7.36e+22 -8.87e+22
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20110228050050/index.html
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STK = 295
DIP = 80
RAKE = -5
MW = 4.65
HS = 4.0
The NDK file is 20110228050050.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: mLg computed using the IASPEI formula. Center: mLg residuals versus epicentral distance ; the values used for the trimmed mean magnitude estimate are indicated.
Right: residuals as a function of distance and azimuth.
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.
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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.
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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:
hp c 0.02 n 3 lp c 0.0625 n 3The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT
WVFGRD96 0.5 295 80 -5 4.56 0.6149
WVFGRD96 1.0 295 80 -5 4.58 0.6451
WVFGRD96 2.0 115 90 0 4.61 0.6884
WVFGRD96 3.0 295 85 -5 4.64 0.7082
WVFGRD96 4.0 295 80 -5 4.65 0.7114
WVFGRD96 5.0 295 80 -5 4.66 0.7046
WVFGRD96 6.0 295 80 -5 4.67 0.6931
WVFGRD96 7.0 295 80 -5 4.67 0.6792
WVFGRD96 8.0 295 75 5 4.68 0.6699
WVFGRD96 9.0 295 75 5 4.69 0.6635
WVFGRD96 10.0 295 70 5 4.70 0.6573
WVFGRD96 11.0 295 70 5 4.71 0.6496
WVFGRD96 12.0 295 70 5 4.71 0.6421
WVFGRD96 13.0 295 70 5 4.72 0.6353
WVFGRD96 14.0 295 70 5 4.72 0.6287
WVFGRD96 15.0 295 70 5 4.72 0.6223
WVFGRD96 16.0 295 70 5 4.73 0.6161
WVFGRD96 17.0 295 70 5 4.74 0.6098
WVFGRD96 18.0 295 70 5 4.74 0.6033
WVFGRD96 19.0 295 75 5 4.75 0.5970
WVFGRD96 20.0 295 70 5 4.76 0.5911
WVFGRD96 21.0 295 70 5 4.76 0.5834
WVFGRD96 22.0 295 70 5 4.77 0.5756
WVFGRD96 23.0 295 70 5 4.77 0.5677
WVFGRD96 24.0 295 70 5 4.78 0.5603
WVFGRD96 25.0 295 70 5 4.78 0.5530
WVFGRD96 26.0 295 70 5 4.79 0.5455
WVFGRD96 27.0 295 70 5 4.79 0.5379
WVFGRD96 28.0 295 70 0 4.80 0.5303
WVFGRD96 29.0 295 70 0 4.81 0.5233
The best solution is
WVFGRD96 4.0 295 80 -5 4.65 0.7114
The mechanism corresponding to the best fit is
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The best fit as a function of depth is given in the following figure:
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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
hp c 0.02 n 3 lp c 0.0625 n 3
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| 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. |
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| 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 following figure shows the stations used in the grid search for the best focal mechanism to fit the surface-wave spectral amplitudes of the Love and Rayleigh waves.
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The surface-wave determined focal mechanism is shown here.
NODAL PLANES
STK= 28.24
DIP= 80.15
RAKE= 169.85
OR
STK= 119.99
DIP= 80.00
RAKE= 10.00
DEPTH = 5.0 km
Mw = 4.77
Best Fit 0.8549 - P-T axis plot gives solutions with FIT greater than FIT90
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Surface wave analysis was performed using codes from Computer Programs in Seismology, specifically the multiple filter analysis program do_mft and the surface-wave radiation pattern search program srfgrd96.
Digital data were collected, instrument response removed and traces converted
to Z, R an T components. Multiple filter analysis was applied to the Z and T traces to obtain the Rayleigh- and Love-wave spectral amplitudes, respectively.
These were input to the search program which examined all depths between 1 and 25 km
and all possible mechanisms.
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| Pressure-tension axis trends. Since the surface-wave spectra search does not distinguish between P and T axes and since there is a 180 ambiguity in strike, all possible P and T axes are plotted. First motion data and waveforms will be used to select the preferred mechanism. The purpose of this plot is to provide an idea of the possible range of solutions. The P and T-axes for all mechanisms with goodness of fit greater than 0.9 FITMAX (above) are plotted here. |
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| Focal mechanism sensitivity at the preferred depth. The red color indicates a very good fit to the Love and Rayleigh wave radiation patterns. 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. Because of the symmetry of the spectral amplitude rediation patterns, only strikes from 0-180 degrees are sampled. |
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The CUS.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 CUS Model with Q from simple gamma values 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 1.0000 5.0000 2.8900 2.5000 0.172E-02 0.387E-02 0.00 0.00 1.00 1.00 9.0000 6.1000 3.5200 2.7300 0.160E-02 0.363E-02 0.00 0.00 1.00 1.00 10.0000 6.4000 3.7000 2.8200 0.149E-02 0.336E-02 0.00 0.00 1.00 1.00 20.0000 6.7000 3.8700 2.9020 0.000E-04 0.000E-04 0.00 0.00 1.00 1.00 0.0000 8.1500 4.7000 3.3640 0.194E-02 0.431E-02 0.00 0.00 1.00 1.00
