23.1.8 FOCMEC AUTO

FOCMEC auto FOCMEC has an option to automatically determine the fault plane solution. This is option fa or faa in EEV and it is automatically used in AUTO. For the difference between the two solutions, see below. The automatic solution works as follows: First test for polarities. Start with 0 polarity error and if no solutions, add one to the number of accepted polarity errors. Continue to do so until solutions are found. Once a solution with polarities is found, and there are amplitude ratios available and it has been selected to use them (set in FOCMEC.DEF), start with 0 amplitude ratios and add one until solutions are found. The default ratio error is set to 0.2 initially. If the number of ratio errors is less than 20If the number of ratio errors is more than 50Relative polarity weight is now optionally used (defined in FOCMEC.DEF or the user is asked) if number of polarity errors is larger than 0. The steps used in the search is 10If more than the maximum allowed solutions are found (defined in FOCMEC.DEF), FOCMEC stops searching for solutions and only part of the total grid has been searched so the average solutions will not represent all the possible solutions. The grid for searching is therefore increased in steps of one degree from the default 2 degrees until the number of solutions is below or equal to the maximum allowed solutions. The average of all the solutions is now calculated by averaging the normal vectors of the corresponding fault planes (using a routine from HASH). The two options fa and faa Fa: semiautomatic: there is some user interaction since the user will be asked if amplitudes shall be used and if relative weight shall be used. The type of amplitudes is defined in FOCMEC.DEF. The user, is after solutions are found, returned to the normal menu with the option of showing the obtained solutions and selecting a solution to be saved. The selected solution can be any shown or the average solution (indicated with a thick red marking, selected by pressing a). It is thus possible to evaluate if the average is a good representation of the solutions found. Faa: fully automatic, no questions asked. The average solution will be written to the S-file. The options used for relative weight and amplitudes are set in FOCMEC.DEF. In both cases, the event is relocated but there is no question about accepting the solution as in the manual case.

Output FOCMEC has no error estimates. If an average solution is used, the RMS angular difference between the average normal vectors and the individual normal vectors are calculated for each plane. These values give some idea of the spread of the solutions used for the average, an example F-line is given below:

227.9 56.5 145.7 32. 31. 3 0 BER FOCMEC aF

Example with only polarities In this example only polarities are used and the user has selected relative weight. For each test, a line is printed with the result of the test: number of polarities errors accepted, number of ratio errors accepted, the error limit used for ratios. If solutions are found (sol >0), the average solutions is given together with the rms deviation. Finally at the end of the line, the grid size is shown.

# 3 09 May 2019 02:51 52 LQ 59.397 5.447 31.0 .50 1.5LBER 34 ? fa **** now locating with hyp as a preparation *** 09-0251-24L.S201905 # 0 2019 5 9 0251 51.3 LQ 59.416 5.456 36.9 BER 34 0.4 1.5LBER Number of polarities: 15 Amplitude types: Manual: 0 Automatic: 33 Spectral: 33 Automatic amplitude selected Use amplitudes, (y/n=enter) Total number of polarities and amplitude ratios = 15 gap in az = 111.0 gap in ain = 30.0 0.0 out of 15 pol, 999 out of 0 amp, err=0.2, # sol= 0, rms dev , str dip rak , deg 2 1.0 out of 15 pol, 999 out of 0 amp, err=0.2, # sol= 0, rms dev , str dip rak , deg 2 2.0 out of 15 pol, 999 out of 0 amp, err=0.2, # sol= 172, rms dev 10 21, str dip rak 74 29 110, deg 2 2.0 out of 15 pol, 0 out of 0 amp, err=0.2, # sol= 172, rms dev 10 21, str dip rak 74 29 110, deg 2 Use relative polarity error (y/n=enter) y 0.2 out of 15 pol, 0 out of 0 amp, err=0.2, # sol= 0, rms dev , str dip rak , deg 2 0.4 out of 15 pol, 0 out of 0 amp, err=0.2, # sol= 0, rms dev , str dip rak , deg 2 0.6 out of 15 pol, 0 out of 0 amp, err=0.2, # sol= 391, rms dev 7 7, str dip rak 335 64 -82, deg 2 Stop (Q) Plot saved solution(s) (1) Plot new solutions (2) Plot selected solution (3) Find new solutions (4) -1, -2, -3 also plot station 2

Example with amplitudes and polarities

# 3 09 May 2019 02:51 52 LQ 59.397 5.447 31.0 .50 1.5LBER 34 ? fa **** now locating with hyp as a preparation *** 09-0251-24L.S201905 # 0 2019 5 9 0251 51.3 LQ 59.416 5.456 36.9 BER 34 0.4 1.5LBER Number of polarities: 15 Amplitude types: Manual: 0 Automatic: 33 Spectral: 33 Automatic amplitude selected Use amplitudes, (y/n=enter) y Q: Local: Qp= 470.0**0.70 Qs= 470.0** 0.7 Global: t*(P)=1.10 t*(S)=4.20 STAT C PH AMP PER TRTIME QCOR ANGINC ANGEMG Fcor AZ DIST KMY Z PG 19 0.30 7.0 1.1 143 32 1.6 208 25 KMY T SG 231 0.28 12.1 1.1 143 32 2.0 208 25 STAV Z PG 12 0.24 10.4 1.1 120 50 1.2 165 55 STAV T SG 342 0.32 17.9 1.2 120 50 2.0 165 55 BLS5 Z PG 21 0.30 10.6 1.1 119 51 1.2 89 56 BLS5 T SG 547 0.32 18.3 1.2 119 51 2.0 89 56 BAS21 Z PG 87 0.28 11.1 1.1 117 52 1.2 33 60 BAS21 T SG 197 0.32 19.0 1.2 117 52 2.0 33 60 BAS22 Z PG 101 0.32 11.3 1.1 116 53 1.2 43 62 BAS22 T SG 254 0.28 19.5 1.2 116 53 2.0 43 62 BAS20 Z PG 71 0.30 11.8 1.1 115 54 1.1 22 66 BAS20 T SG 521 0.32 20.3 1.2 115 54 2.0 22 66 BAS19 Z PG 14 0.34 11.9 1.1 114 54 1.1 16 66 BAS19 T SG 221 0.28 20.5 1.2 114 54 2.0 16 66 BAS23 Z PG 40 0.30 12.6 1.1 113 55 1.1 36 71 BAS23 T SG 204 0.26 21.7 1.2 113 55 2.0 36 71 BAS18 Z PG 12 0.30 12.8 1.1 112 55 1.1 6 73 BAS18 T SG 218 0.30 22.0 1.2 112 55 2.0 6 73 BAS17 Z PG 8 0.26 14.5 1.2 108 57 1.0 357 85 BAS17 T SG 436 0.30 25.0 1.3 108 57 2.0 357 85 ODD1 Z PG 11 0.34 14.6 1.1 108 58 1.0 50 86 ODD1 T SG 108 0.30 25.1 1.3 108 58 2.0 50 86 BAS14 Z PG 2222 0.34 15.1 1.1 107 58 1.0 58 89 BAS14 T SG 158000 0.32 26.0 1.3 107 58 2.0 58 89 BAS11 Z PG 24 0.24 15.2 1.2 107 58 1.0 39 90 BAS11 T SG 658 0.28 26.1 1.3 107 58 2.0 39 90 BAS10 Z PG 9 0.26 15.4 1.2 107 58 1.0 28 92 BAS10 T SG 117 0.30 26.5 1.3 107 58 2.0 28 92 BAS16 Z PG 9 0.28 15.4 1.2 107 58 1.0 350 92 BAS16 T SG 66 0.32 26.6 1.3 107 58 2.0 350 92 BAS09 Z PG 13 0.28 15.8 1.2 106 59 1.0 18 94 BAS09 T SG 228 0.32 27.1 1.3 106 59 2.0 18 94 BAS12 Z PG 13 0.24 15.8 1.2 106 59 1.0 49 94 BAS12 T SG 130 0.32 27.2 1.3 106 59 2.0 49 94 STAT Ratio type T Amp 1 Amp 2 Fcor LogRat KMY SH(T)/P(Z) H 231 19 0.8 1.01 STAV SH(T)/P(Z) H 342 12 0.6 1.24 BLS5 SH(T)/P(Z) H 547 21 0.6 1.21 BAS21 SH(T)/P(Z) H 197 87 0.6 0.15 BAS22 SH(T)/P(Z) H 254 101 0.6 0.20 BAS20 SH(T)/P(Z) H 521 71 0.6 0.65 BAS19 SH(T)/P(Z) H 221 14 0.6 0.98 BAS23 SH(T)/P(Z) H 204 40 0.6 0.49 BAS18 SH(T)/P(Z) H 218 12 0.5 1.04 BAS17 SH(T)/P(Z) H 436 8 0.5 1.47 ODD1 SH(T)/P(Z) H 108 11 0.5 0.72 BAS14 SH(T)/P(Z) H 158000 2222 0.5 1.61 BAS11 SH(T)/P(Z) H 658 24 0.5 1.17 BAS10 SH(T)/P(Z) H 117 9 0.5 0.83 BAS16 SH(T)/P(Z) H 66 9 0.5 0.59 BAS09 SH(T)/P(Z) H 228 13 0.5 0.98 BAS12 SH(T)/P(Z) H 130 13 0.5 0.75 Total number of polarities and amplitude ratios = 32 gap in az = 111.0 gap in ain = 30.0 0.0 out of 15 pol, 999 out of 17 amp, err=0.2, # sol= 0, rms dev , str dip rak , deg 2 1.0 out of 15 pol, 999 out of 17 amp, err=0.2, # sol= 0, rms dev , str dip rak , deg 2 2.0 out of 15 pol, 999 out of 17 amp, err=0.2, # sol= 132, rms dev 10 23, str dip rak 72 30 108, deg 2 2.0 out of 15 pol, 0 out of 17 amp, err=0.2, # sol= 0, rms dev , str dip rak , deg 2 2.0 out of 15 pol, 1 out of 17 amp, err=0.2, # sol= 0, rms dev , str dip rak , deg 2 2.0 out of 15 pol, 2 out of 17 amp, err=0.2, # sol= 0, rms dev , str dip rak , deg 2 2.0 out of 15 pol, 3 out of 17 amp, err=0.2, # sol= 0, rms dev , str dip rak , deg 2 2.0 out of 15 pol, 4 out of 17 amp, err=0.2, # sol= 0, rms dev , str dip rak , deg 2 2.0 out of 15 pol, 5 out of 17 amp, err=0.2, # sol= 0, rms dev , str dip rak , deg 2 2.0 out of 15 pol, 6 out of 17 amp, err=0.2, # sol= 0, rms dev , str dip rak , deg 2 2.0 out of 15 pol, 7 out of 17 amp, err=0.2, # sol= 0, rms dev , str dip rak , deg 2 2.0 out of 15 pol, 8 out of 17 amp, err=0.2, # sol= 9, rms dev 8 26, str dip rak 76 29 120, deg 2 Use relative polarity error (y/n=enter) Stop (Q) Plot saved solution(s) (1) Plot new solutions (2) Plot selected solution (3) Find new solutions (4) -1, -2, -3 also plot station

Example with polarities only and increasing grid size

# 4 17 May 2019 01:22 59 LQ 59.769 5.380 12.1 N .40 1.6LBER 38 ? fa **** now locating with hyp as a preparation *** 17-0122-11L.S201905 # 0 2019 517 0122 58.6 LQ 59.771 5.404 18.5 BER 38 0.2 1.6LBER Note: The following floating-point exceptions are signalling: IEEE_UNDERFLOW_FLAG IEEE_DENORMAL Number of polarities: 15 No amplitude data available Total number of polarities and amplitude ratios = 15 gap in az = 187.0 gap in ain = 42.0 0.0 out of 15 pol, 999 out of 0 amp, err=0.2, # sol= 500, rms dev 10 12, str dip rak 291 35 -53, deg 2 0.0 out of 15 pol, 0 out of 0 amp, err=0.2, # sol= 500, rms dev 10 12, str dip rak 291 35 -53, deg 2 0.0 out of 15 pol, 0 out of 0 amp, err=0.2, # sol= 500, rms dev 17 23, str dip rak 300 40 -49, deg 3 0.0 out of 15 pol, 0 out of 0 amp, err=0.2, # sol= 500, rms dev 32 35, str dip rak 304 44 -48, deg 4 0.0 out of 15 pol, 0 out of 0 amp, err=0.2, # sol= 500, rms dev 42 38, str dip rak 307 48 -49, deg 5 0.0 out of 15 pol, 0 out of 0 amp, err=0.2, # sol= 500, rms dev 36 33, str dip rak 320 60 -27, deg 6 0.0 out of 15 pol, 0 out of 0 amp, err=0.2, # sol= 388, rms dev 32 29, str dip rak 325 68 -19, deg 7 Stop (Q) Plot saved solution(s) (1) Plot new solutions (2) Plot selected solution (3) Find new solutions (4) -1, -2, -3 also plot station

In this case, 388 solutions are found due to a bad distribution of polarities and grid size has to be increased in order to find less than 500 solutions. The limit of max 500 could have been decreased to get fewer solutions but then grid size would have been increased. The solution found is the most likely. The other fault plane programs in SEISAN also finds the most likely solution with the given data, see Figure xx for the solution given by HASH, PINV and FPFIT.

It is seen that the 4 programs give very similar solutions so despite the many solutions obtained, the average seem the represent the most likely solution. The solutions are also what we would be expected for the area.

Using multiple models with FOCMEC It is well known that the model can be very critical for the fault plane solutions since different models will give different angle of incidence. If a model change will change an arrival from direct to refracted, the azimuth will change 180 degrees so it is particularly the hypocentral depth that is a critical parameter. In order to check the sensitivity to the model, FOCMEC has an option to make automatic solutions for any number of models in order to compare the solutions and possibly select one solution or more likely an average of the different model solutions. The original HASH program has a similar option, but it has not been implemented in SEISAN. The different models are defined in different STATIONx.HYP files where x indicates the different files. In the test example we will use 5 models defined as a,b,c,d,e. The definition line in FOCMEC.DEF is then:

MODELS For multi model, one char abcde

The models are

a b c d e depth 6.65 6.10 6.72 6.40 6.20 0.0 6.75 6.53 6.81 6.50 6.60 12.0 6.88 7.41 6.92 7.11 7.10 23.0 8.39 7.56 8.66 7.32 8.05 31.0 8.49 7.76 9.04 8.54 8.25 50.0

where a-e are the P-velocities (km/s) and depth is depth to interface (km). The multi model can only be used in eev. The command in EEV is FAAA. If multi models are defined in FOCMEC.DEF, the event will be located with each model and the automatic FOCMEC used to get a solution. Each solution is written into the S-file:

338.1 44.9 -14.8 2. 2. 11.0 0H10 BER FOCMECe aF 343.0 35.4 -3.7 1. 1. 11.4 0H10 BER FOCMECd aF 313.7 6.7 -0.0 1. 1. 6.8 0H12 BER FOCMECc aF 287.6 36.0 -91.7 2. 3. 12.1 0H 9 BER FOCMECb aF 279.0 1.2 -32.5 3. 3. 7.9 0H12 BER FOCMECa aF

The free field 63 has an H to indicate that the hypocentral depth is given in field 51-55 which is not used by FOCMEC. The H then indicates a multi model solution. The model indicator is given in column 76. The 5 average solutions can then be plotted by FOCMEC in EEV, command FO:

Although the models are quite different, the solution are not very different so in this case the solution is no very model dependent. Both P-polarities and amplitudes were used.

After quitting FOCMEC, the user will have option to save the average solution, see example below:

319.2 23.6 -21.4 20. 28. BER FOCMEC AF

where the A at end of line indicated that this is an average of the multi model solutions. If any of the individual solutions are wanted, the user must edit the S-file.