Location

2007/05/08 15:46:49 45.39N 112.13W 13.5 4.7 Montana

Arrival Times (from USGS)

Arrival time list

Felt Map

USGS Felt map for this earthquake

USGS Felt reports page for Intermountain Western US

Focal Mechanism

 SLU Moment Tensor Solution
 2007/05/08 15:46:49 45.39N 112.13W 13.5 4.7 Montana
 
 Best Fitting Double Couple
    Mo = 4.37e+22 dyne-cm
    Mw = 4.36 
    Z  = 10 km
     Plane   Strike  Dip  Rake
      NP1      345    55   -85
      NP2      156    35   -97
 Principal Axes:
   Axis    Value   Plunge  Azimuth
     T   4.37e+22     10      71
     N   0.00e+00      4     162
     P  -4.37e+22     79     274



 Moment Tensor: (dyne-cm)
    Component  Value
       Mxx     4.30e+21
       Mxy     1.29e+22
       Mxz     1.74e+21
       Myy     3.66e+22
       Myz     1.49e+22
       Mzz    -4.09e+22
                                                     
                                                     
                                                     
                                                     
                     ---###########                  
                 #---------############              
              ###------------#############           
             ###---------------############          
           ####-----------------#############        
          ####-------------------#############       
         #####--------------------##########         
        ######---------------------######### T #     
        ######----------------------########   #     
       #######---------   ----------#############    
       #######--------- P -----------############    
       #######---------   -----------############    
       ########----------------------############    
        #######-----------------------##########     
        ########----------------------##########     
         ########---------------------#########      
          ########-------------------#########       
           #########-----------------########        
             #########---------------######          
              ##########------------######           
                 ###########-------####              
                     #############-                  
                                                     
                                                     
                                                     

 Harvard Convention
 Moment Tensor:
      R          T          F
 -4.09e+22   1.74e+21  -1.49e+22 
  1.74e+21   4.30e+21  -1.29e+22 
 -1.49e+22  -1.29e+22   3.66e+22 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20070508154649/index.html
        

      STK = 345
      DIP = 55
     RAKE = -85
       MW = 4.36
       HS = 10

The solutions from the two techniques are equivalent. Note that the waveform inversion down weighted the obervation at BOZ, the shortest distance, because subtle changes in location affect the separation into radial and vertical components and since the larger amplitudes here would dominate the solution. The additon of the TA data did not change the waveforms fit, except that the 0.02 - 0.05 band had to be sued instead of the 0.02 - 0.06 Hz band, perhaps because the current model coutl not fit both the PnL and the Surface wave. This requires more model studies for this area, which is slightly faster than the UTAH-Pechmann model. The surface wave amplitude data give about the soame solution.

Waveform Inversion

The focal mechanism was determined using broadband seismic waveforms. The location of the event and the and stations used for the waveform inversion are shown in the next figure.
Location of broadband stations used for waveform inversion

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 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 0.05 n 3
The results of this grid search from 0.5 to 19 km depth are as follow:

           DEPTH  STK   DIP  RAKE   MW    FIT
WVFGRD96    0.5   180    40   -65   4.02 0.3526
WVFGRD96    1.0   195    50   -30   4.03 0.3395
WVFGRD96    2.0    10    65   -55   4.13 0.4057
WVFGRD96    3.0     5    70   -65   4.22 0.4505
WVFGRD96    4.0     0    65   -70   4.25 0.4991
WVFGRD96    5.0   360    65   -70   4.27 0.5402
WVFGRD96    6.0   355    60   -70   4.30 0.5697
WVFGRD96    7.0   350    60   -80   4.32 0.5967
WVFGRD96    8.0   350    60   -80   4.35 0.6293
WVFGRD96    9.0   345    55   -85   4.36 0.6319
WVFGRD96   10.0   350    55   -80   4.35 0.6205
WVFGRD96   11.0   -10    55   -80   4.34 0.5980
WVFGRD96   12.0     0    60   -65   4.32 0.5757
WVFGRD96   13.0   200    95    30   4.30 0.5672
WVFGRD96   14.0   200    95    30   4.30 0.5649
WVFGRD96   15.0    25    95   -25   4.30 0.5615
WVFGRD96   16.0   205    85    25   4.31 0.5580
WVFGRD96   17.0    25    95   -25   4.31 0.5526
WVFGRD96   18.0   205    85    25   4.32 0.5461
WVFGRD96   19.0   205    85    25   4.32 0.5392
WVFGRD96   20.0   205    85    20   4.33 0.5327
WVFGRD96   21.0   205    85    25   4.35 0.5212
WVFGRD96   22.0   205    85    25   4.35 0.5127
WVFGRD96   23.0    25    95   -25   4.36 0.5040
WVFGRD96   24.0   205    85    25   4.36 0.4949
WVFGRD96   25.0    25    95   -25   4.37 0.4858
WVFGRD96   26.0   205    85    25   4.37 0.4762
WVFGRD96   27.0    25    95   -25   4.37 0.4667
WVFGRD96   28.0    25    95   -25   4.38 0.4573
WVFGRD96   29.0   205    80    25   4.38 0.4483

The best solution is

WVFGRD96    9.0   345    55   -85   4.36 0.6319

The mechanism correspond to the best fit is
Figure 1. Waveform inversion focal mechanism

The best fit as a function of depth is given in the following figure:

Figure 2. Depth sensitivity for waveform mechanism

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 componnet is plotted to the same scale and peak amplitudes are indicated by the numbers to the left of each trace. The number in black at the rightr of each predicted traces 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 and because the velocity model used in the predictions may not be perfect. 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 bandpass filter used in the processing and for the display was

hp c 0.02 n 3
lp c 0.05 n 3
Figure 3. Waveform comparison for depth of 8 km
Focal mechanism sensitivity at the preferred depth. The red color indicates a very good fit to thewavefroms. 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.

Surface-Wave Focal Mechanism

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.
Location of broadband stations used to obtain focal mechanism from surface-wave spectral amplitudes

The surface-wave determined focal mechanism is shown here.


  NODAL PLANES 

  
  STK=       4.87
  DIP=      57.20
 RAKE=     -57.27
  
             OR
  
  STK=     134.99
  DIP=      45.00
 RAKE=    -129.99
 
 
DEPTH = 10.0 km
 
Mw = 4.40
Best Fit 0.8673 - P-T axis plot gives solutions with FIT greater than FIT90

First motion data

The P-wave first motion data for focal mechanism studies are as follow:

Sta Az(deg)    Dist(km)   First motion
G15A      228   38 -12345
BOZ        45   55 -12345
F15A      330   57 -12345
G14A      261  106 -12345
F14A      296  107 -12345
E15A      341  121 -12345
E14A      318  155 -12345
G13A      259  168 -12345
F13A      285  177 -12345
D15A      351  186 -12345
H13A      242  191 -12345
E13A      307  198 -12345
D14A      331  216 -12345
MSO       321  220 -12345
TPAW      155  222 -12345
LOHW      147  223 -12345
RLMT       94  226 -12345
I13A      224  228 -12345
H12A      247  235 -12345
F12A      280  247 -12345
D13A      317  261 -12345
HLID      224  265 -12345
J13A      217  275 -12345
C14A      335  292 -12345
D12A      308  309 -12345
H11A      257  315 -12345
C13A      324  316 -12345
F11A      281  319 -12345
G11A      272  324 -12345
K14A      195  327 -12345
E11A      290  334 -12345
J12A      226  336 -12345
K13A      208  343 -12345
I11A      243  345 -12345
BW06      143  349 -12345
EGMT       30  353 -12345
J11A      235  368 -12345
D11A      301  373 -12345
H10A      258  375 -12345
B13A      333  376 -12345
K12A      217  379 -12345
G10A      270  391 -12345
L13A      202  395 -12345
I10A      250  398 -12345
BMO       265  411 -12345
WALA      343  439 -12345
LAO        69  483 -12345
NEW       313  504 -12345

Surface-wave analysis

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.

The velocity model used for the search is a modified Utah model .

Data preparation

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.

Search over depth. The best fit corresponds to the largest value in the last column.

SRFGRD96    1.0  125.   35.   15. 0.876 0.893   4.25   4.25 0.7818
SRFGRD96    2.0  130.   45.   25. 0.860 0.906   4.23   4.23 0.7782
SRFGRD96    3.0  125.   25.   25. 0.896 0.911   4.36   4.36 0.8079
SRFGRD96    4.0  125.   30.   20. 0.897 0.924   4.33   4.33 0.8280
SRFGRD96    5.0  120.   35.   15. 0.898 0.934   4.32   4.32 0.8371
SRFGRD96    6.0  130.   40.   40. 0.904 0.943   4.34   4.33 0.8492
SRFGRD96    7.0   30.   75.   50. 0.896 0.945   4.32   4.32 0.8412
SRFGRD96    8.0  135.   45.   50. 0.904 0.952   4.37   4.37 0.8532
SRFGRD96    9.0  145.   45.   65. 0.911 0.953   4.41   4.41 0.8618
SRFGRD96   10.0  135.   45.   50. 0.915 0.953   4.40   4.40 0.8673
SRFGRD96   11.0  125.   45.   35. 0.908 0.948   4.38   4.38 0.8607
SRFGRD96   12.0   30.   75.   45. 0.891 0.948   4.37   4.36 0.8344
SRFGRD96   13.0  125.   50.   35. 0.884 0.945   4.38   4.38 0.8351
SRFGRD96   14.0   40.   60.   40. 0.878 0.943   4.38   4.38 0.8191
SRFGRD96   15.0   30.   70.   40. 0.871 0.937   4.38   4.38 0.8133
SRFGRD96   16.0   35.   65.   35. 0.858 0.937   4.38   4.38 0.7859
SRFGRD96   17.0   30.   70.   35. 0.846 0.930   4.39   4.38 0.7707
SRFGRD96   18.0   30.   65.   30. 0.829 0.925   4.39   4.38 0.7606
SRFGRD96   19.0   30.   70.   30. 0.820 0.921   4.40   4.39 0.7299
SRFGRD96   20.0   35.   70.   30. 0.805 0.912   4.39   4.40 0.7264
SRFGRD96   21.0   30.   75.   30. 0.791 0.908   4.40   4.40 0.7129
SRFGRD96   22.0   30.   70.   35. 0.778 0.900   4.43   4.43 0.6988
SRFGRD96   23.0   35.   65.   30. 0.761 0.894   4.43   4.43 0.6787
SRFGRD96   24.0   25.   80.   35. 0.737 0.884   4.43   4.43 0.6458
SRFGRD96   25.0   30.   70.   30. 0.737 0.882   4.44   4.44 0.6492

Best mechanism fit as a function of depth. The preferred depth is given above. Lower hemisphere projection

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.


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.

Love-wave radiation patterns

Rayleigh-wave radiation patterns

Broadband station distributiuon

Sta Az(deg)    Dist(km)   
E15A	  341	  121
E14A	  318	  155
G13A	  259	  168
F13A	  285	  177
D15A	  351	  186
H13A	  242	  191
E13A	  307	  198
MSO	  315	  205
D14A	  331	  216
RLMT	  101	  223
MOOW	  152	  224
I13A	  224	  228
H12A	  247	  235
LOHW	  151	  243
TPAW	  159	  244
F12A	  280	  247
SNOW	  156	  253
D13A	  317	  261
J13A	  217	  275
HLID	  221	  289
C14A	  335	  292
D12A	  308	  309
H11A	  257	  315
C13A	  324	  316
F11A	  281	  319
G11A	  272	  324
EGMT	   32	  327
K14A	  195	  327
E11A	  290	  334
J12A	  226	  336
K13A	  208	  343
I11A	  243	  345
BW06	  146	  367
J11A	  235	  368
D11A	  301	  373
H10A	  258	  375
B13A	  333	  376
K12A	  217	  379
G10A	  270	  391
L13A	  202	  395
I10A	  250	  398
F10A	  281	  402
E10A	  289	  405
WALA	  341	  416
BMO	  261	  420
HVU	  188	  422
K11A	  228	  427
J10A	  241	  429
L12A	  214	  429
A13A	  337	  430
B12A	  324	  431
M15A	  184	  437
D10A	  297	  438
G09A	  270	  443
H09A	  261	  443
M14A	  193	  443
F09A	  276	  453
L11A	  220	  462
B11A	  318	  467
LAO	   72	  468
I09A	  252	  472
A12A	  327	  476
K10A	  234	  478
M13A	  201	  478
C10A	  306	  479
E09A	  287	  483
NEW	  310	  491
M12A	  208	  496
N15A	  184	  501
J09A	  245	  503
B10A	  312	  505
L10A	  225	  508
A11A	  322	  510
D09A	  294	  511
N14A	  190	  512
F08A	  277	  520
H08A	  262	  525
M11A	  215	  531
N13A	  199	  532
G08A	  271	  535
I08A	  254	  537
K09A	  238	  539
C09A	  302	  541
E08A	  285	  551
J08A	  248	  554
D08A	  292	  555
N12A	  206	  557
M10A	  221	  559
B09A	  308	  569
A10A	  316	  573
L09A	  232	  583
HAWA	  282	  587
N11A	  211	  587
K08A	  242	  589
G07A	  271	  591
C08A	  299	  593
H07A	  264	  593
DUG	  186	  597
I07A	  259	  602
O13A	  195	  604
O12A	  202	  608
E07A	  285	  612
J07A	  251	  614
L08A	  237	  614
MPU	  177	  615
M09A	  226	  616
A09A	  312	  630
N10A	  216	  630
WVOR	  239	  631
D07A	  291	  636
B08A	  304	  640
K07A	  245	  644
H06A	  266	  650
O11A	  208	  652
C07A	  296	  659
I06A	  259	  660
G06A	  272	  667
N09A	  223	  668
M08A	  231	  669
O10A	  214	  670
F06A	  277	  676
P13A	  194	  678
DGMT	   59	  680
J06A	  252	  682
L07A	  240	  691
P12A	  200	  696
B07A	  302	  697
E06A	  284	  697
D06A	  290	  700
N08A	  226	  708
PNT	  309	  708
K06A	  249	  711
O09A	  217	  713
P11A	  206	  714
G05A	  272	  720
H05A	  267	  721
M07A	  234	  723
C06A	  296	  727
F05A	  278	  729
Q13A	  193	  732
P10A	  210	  733
I05A	  262	  736
Q12A	  198	  740
A07A	  306	  745
O08A	  223	  751
N07B	  230	  756
E05A	  283	  757
K05A	  250	  762
J05A	  255	  763
P09A	  214	  768
C05A	  293	  776
Q11A	  203	  783
D05A	  288	  785
B06A	  299	  792
R14A	  186	  792
L05A	  245	  793
H04A	  268	  796
P08A	  220	  799
O07A	  226	  801
F04A	  278	  804
Q10A	  207	  810
G04A	  272	  811
R12A	  196	  811
N06A	  233	  812
A06A	  304	  818
M06C	  238	  821
B05A	  296	  824
ISCO	  138	  827
K04A	  252	  829
E04A	  283	  831
R11A	  201	  833
I04A	  261	  835
Q09A	  212	  840
D04A	  287	  844
S14A	  186	  852
A05A	  302	  853
P07A	  223	  855
M05C	  242	  856
O06A	  230	  856
R10A	  205	  862
L04A	  249	  863
Q08A	  215	  869
C04A	  291	  870
G03A	  273	  873
ELFS	  236	  878
M04C	  246	  880
S13A	  190	  880
H03A	  269	  882
A04A	  298	  884
J03A	  259	  891
R09A	  209	  894
S12A	  196	  894
E03A	  282	  895
I03A	  264	  897
P06A	  228	  899
Q07A	  220	  904
S10A	  206	  909
S11A	  200	  912
HATC	  239	  913
B04A	  293	  917
D03A	  286	  917
LLLB	  311	  923
O04C	  236	  923
R08A	  214	  926
T14A	  185	  929
M03C	  244	  930
NLWA	  287	  930
T15A	  181	  930
T16A	  177	  935
H02A	  269	  938
I02A	  265	  939
J02A	  260	  939
O05C	  233	  939
T11A	  197	  942
T13A	  190	  942
S09A	  208	  951
K02A	  256	  955
P05C	  229	  971
R06C	  221	  974
M02C	  247	  975
T12A	  194	  987
L02A	  253	  990
R05C	  224	  991
R07C	  218	  994
SHB	  301	  996
U14A	  185	 1001
O03C	  237	 1008
U13A	  189	 1009
S08C	  212	 1011
U12A	  192	 1016
TPNV	  202	 1017
LAVA	  227	 1024
K01A	  258	 1028
U11A	  196	 1033
N02C	  245	 1040
M01C	  252	 1044
O02C	  240	 1046
SUTB	  233	 1049
Q04C	  230	 1055
V13A	  189	 1071
R04C	  226	 1077
CMB	  223	 1083
OZB	  295	 1085
V14A	  185	 1087
V11A	  196	 1097
V12A	  193	 1098
Q03C	  231	 1109
CBB	  301	 1114
WUAZ	  177	 1114
O01C	  243	 1119
S05C	  220	 1125
T06C	  217	 1126
HELL	  213	 1127
P01C	  238	 1131
W14A	  184	 1133
W15A	  181	 1134
W12A	  193	 1144
W13A	  188	 1153
S04C	  224	 1164
X13A	  188	 1208
U05C	  216	 1209
X15A	  180	 1211
X14A	  183	 1215
X16A	  177	 1220
EDB	  298	 1226
U04C	  219	 1238
ECSD	   94	 1240
BNLO	  226	 1243
V05C	  214	 1244
CBKS	  122	 1260
AGMN	   70	 1268
Y15A	  181	 1270
Y14A	  184	 1274
HAST	  222	 1275
PHC	  302	 1278
Y16A	  177	 1280
V03C	  220	 1292
Y19A	  168	 1293
Y13A	  187	 1294
Y12C	  190	 1309
V04C	  217	 1311
ULM	   61	 1314
Z14A	  183	 1338
Z16A	  177	 1340
BMBC	  332	 1365
Z18A	  172	 1378
BBB	  308	 1386
115A	  180	 1409
119A	  169	 1423
116A	  178	 1425
117A	  175	 1428
118A	  172	 1428
109C	  199	 1453
KSU1	  114	 1456
AMTX	  140	 1474
216A	  178	 1488
218A	  172	 1501
219A	  170	 1508
318A	  172	 1560
SCIA	   98	 1566
319A	  170	 1576
EYMN	   73	 1588
MNTX	  157	 1641
WMOK	  132	 1644
FNBB	  338	 1659
MOBC	  308	 1666
JFWS	   92	 1761
COWI	   80	 1776
WRAK	  318	 1857
DLBC	  326	 1881
YKW2	  356	 1887
YKW1	  356	 1892
YKW3	  356	 1902
FCC	   33	 1905
HDIL	   99	 1927
SLM	  105	 1953
FVM	  108	 1976
JCT	  143	 1983
MIAR	  122	 1986
UALR	  119	 2052
SIUC	  107	 2082
PVMO	  111	 2126
BLO	  100	 2208
WHY	  326	 2250
KAPO	   68	 2253
OXF	  115	 2276
AAM	   89	 2296
ACSO	   94	 2432
SADO	   80	 2571
TZTN	  103	 2579
ERPA	   87	 2589
BLA	   98	 2782
GOGA	  109	 2782
EGAK	  330	 2783
LONY	   78	 2925
NCB	   80	 2972
NHSC	  106	 3048
LBNH	   78	 3140

Waveform comparison for this mechanism

Since the analysis of the surface-wave radiation patterns uses only spectral amplitudes and because the surfave-wave radiation patterns have a 180 degree symmetry, each surface-wave solution consists of four possible focal mechanisms corresponding to the interchange of the P- and T-axes and a roation of the mechanism by 180 degrees. To select one mechanism, P-wave first motion can be used. This was not possible in this case because all the P-wave first motions were emergent ( a feature of the P-wave wave takeoff angle, the station location and the mechanism). The other way to select among the mechanisms is to compute forward synthetics and compare the observed and predicted waveforms.

The velocity model used for the waveform fit is a modified Utah model .

The fits to the waveforms with the given mechanism are show below:

This figure shows the fit to the three components of motion (Z - vertical, R-radial and T - transverse). For each station and component, the observed traces is shown in red and the model predicted trace in blue. The traces represent filtered ground velocity in units of meters/sec (the peak value is printed adjacent to each trace; each pair of traces to plotted to the same scale to emphasize the difference in levels). Both synthetic and observed traces have been filtered using the SAC commands:

hp c 0.02 n 3
lp c 0.05 n 3

Discussion

The Future

Should the national backbone of the USGS Advanced National Seismic System (ANSS) be implemented with an interstation separation of 300 km, it is very likely that an earthquake such as this would have been recorded at distances on the order of 100-200 km. This means that the closest station would have information on source depth and mechanism that was lacking here.

Acknowledgements

Dr. Harley Benz, USGS, provided the USGS USNSN digital data. The digital data used in this study were provided by Natural Resources Canada through their AUTODRM site http://www.seismo.nrcan.gc.ca/nwfa/autodrm/autodrm_req_e.php, and IRIS using their BUD interface

Appendix A

The figures below show the observed spectral amplitudes (units of cm-sec) at each station and the theoretical predictions as a function of period for the mechanism given above. The modified Utah model earth model was used to define the Green's functions. For each station, the Love and Rayleigh wave spectrail amplitudes are plotted with the same scaling so that one can get a sense fo the effects of the effects of the focal mechanism and depth on the excitation of each.

Quality Control

Here we tabulate the reasons for not using certain digital data sets

The following stations did not have a valid response files:

Last Changed Fri May 11 09:32:44 CDT 2007