Chapter 1 Introduction
4.2 Phase Data from Millikan II Experiments
the frequency of excitation, the phase velocity is computed.
End End
As can be seen from Tables 4.19 to 4.36, the phase velocity values obtained are stable for similar experiments for a particular seismometer line. Furthermore, the difference for experiments with large variations in the values comes from competing local minima, similar to the ones shown in Figure 4.6. It should be noted that most of the plots have clear global minima, and that the case shown in Figure 4.6 is a worst-case scenario. Furthermore, for the particular case shown in this figure, the transverse component is located on a node for the EW shake, and the phase data could be unreliable. However, the scatter shown for the transverse component is consistent for similar experiments, and this further demonstrates the repeatability of the collected waveforms, as the data is also repeatable for instruments located on nodal lines. Therefore, it can be assumed that the observed waveforms are not dominated by noise, and that they are reliable (as are the measurements made from them).
The measured relative waveform phases lead to the supposition that there may be superimposed surface wave modes, or that 3-D effects are important for the problem being studied. The presence of multiple modes might also explain the large error between the measured and the best-fitting linear phases, as a constant phase velocity should not be expected to fit the data in this case. Furthermore, this could explain why the calculated phase velocities differ for different seismometer setups, as both the seismometer spacing and the distance between measurements have an influence on the linear fit.
Similarly to the previous section, the waveforms collected for stations at distances less than 150 meters from the building were removed (100 meters for instrument lines containing only 4 instruments), to minimize the near-field effects. The results of these linear fits are provided in Tables 4.28 through 4.36. The phase velocity values
Experiment A Experiment B Experiment C Experiment D
East line 1026 591 533 967
EN E line 824 836 836 832
North line 989 995 952 1069
NE line 691 683 683 683
NNE line 747 724 730 707
NNW line 622 626 630 633
Table 4.19 Phase velocities in meters/second computed for the radial component for an East-West Shake
Experiment A Experiment B Experiment C Experiment D
East line 1211 581 1704 1123
EN E line 725 723 731 731
North line 545 546 547 544
NE line 530 529 531 832
NN E line 548 547 553 555
NNW line 501 501 500 498
Table 4.20 Phase velocities in meters/second computed for the transverse component for an East-West Shake
Experiment A Experiment B Experiment C Experiment D
East line 1708 767 688 1549
EN E line 1128 1143 1171 1170
North line 1102 1114 1057 1240
NE line 1029 1039 1067 1069
NN E line 1186 1232 1312 1485
NNW line 910 940 967 1034
Table 4.21 Phase velocities in meters/second computed for the vertical component for an East-West Shake
Experiment A Experiment B Experiment C Experiment D
East line 567 513 560 493
EN E line 570 567 564 567
North line 565 566 565 565
NE line 794 309 308 310
NN E line 605 604 608 611
NNW line 477 476 480 482
Table 4.22 Phase velocities in meters/second computed for the radial component for a North-South Shake
Experiment A Experiment B Experiment C Experiment D
East line 510 474 505 448
EN E line 537 534 534 536
North line 512 512 512 511
NE line 578 269 271 270
NN E line 478 481 482 483
NNW line 492 497 492 493
Table 4.23 Phase velocities in meters/second computed for the transverse component for a North-South Shake
Experiment A Experiment B Experiment C Experiment D
East line 544 509 539 474
EN E line 719 716 716 718
North line 642 638 638 638
NE line 314 315 315 316
NN E line 648 647 648 651
NNW line 520 519 523 524
Table 4.24 Phase velocities in meters/second computed for the vertical component for a North-South Shake
Experiment A Experiment B Experiment C Experiment D
East line 540 458 535 572
EN E line 571 572 572 571
North line 490 516 482 517
NE line 286 290 250 289
NNE line 318 935 919 949
NNW line 566 575 573 572
Table 4.25 Phase velocities in meters/second computed for the radial component for a Torsional Shake
Experiment A Experiment B Experiment C Experiment D
East line 540 587 535 569
EN E line 527 526 528 527
North line 456 456 457 457
NE line 460 461 464 463
NN E line 460 466 466 465
NNW line 449 457 455 456
Table 4.26 Phase velocities in meters/second computed for the transverse component for a Torsional Shake
Experiment A Experiment B Experiment C Experiment D
East line 528 451 528 565
EN E line 755 765 767 779
North line 602 603 601 609
NE line 578 584 582 587
NN E line 596 605 606 611
NNW line 546 561 557 562
Table 4.27 Phase velocities in meters/second computed for the vertical component for a Torsional Shake
Experiment A Experiment B Experiment C Experiment D
East line 1567 523 466 1257
EN E line 809 817 809 806
North line 1066 1069 985 1103
NE line 694 681 678 684
NN E line 848 795 789 740
NNW line 661 660 665 671
Table 4.28 Phase velocities in meters/second computed for the radial component for an East-West Shake with the data close to the building removed.
Experiment A Experiment B Experiment C Experiment D
East line 1503 512 432 1725
EN E line 695 687 699 700
North line 434 434 434 423
NE line 507 508 508 511
NN E line 515 517 524 521
NNW line 502 494 490 484
Table 4.29 Phase velocities in meters/second computed for the transverse component for an East-West Shake with the data close to the building removed.
Experiment A Experiment B Experiment C Experiment D
East line 1708 633 560 1725
EN E line 1414 1426 1480 1474
North line 1664 1664 1667 1658
NE line 1057 1069 1054 1058
NN E line 1437 1617 1670 1663
NNW line 1102 1142 1197 1313
Table 4.30 Phase velocities in meters/second computed for the vertical component for an East-West Shake with the data close to the building removed.
Experiment A Experiment B Experiment C Experiment D
East line 552 478 542 444
EN E line 580 567 551 551
North line 601 490 494 491
NE line 794 258 257 257
NNE line 587 588 598 600
NNW line 503 504 508 510
Table 4.31 Phase velocities in meters/second computed for the radial component for a North-South Shake with the data close to the building removed.
Experiment A Experiment B Experiment C Experiment D
East line 534 471 524 427
EN E line 545 534 544 546
North line 527 523 524 523
NE line 578 238 238 239
NN E line 503 502 513 515
NNW line 528 525 546 549
Table 4.32 Phase velocities in meters/second computed for the transverse component for a North-South Shake with the data close to the building removed.
Experiment A Experiment B Experiment C Experiment D
East line 699 601 681 521
EN E line 787 716 771 770
North line 689 676 669 669
NE line 314 271 272 272
NN E line 699 700 710 710
NNW line 549 548 554 557
Table 4.33 Phase velocities in meters/second computed for the vertical component for a North-South Shake with the data close to the building removed.
Experiment A Experiment B Experiment C Experiment D
East line 540 413 526 588
EN E line 558 559 561 560
North line 243 399 240 397
NE line∗ 267 271 264 273
NN E line 361 714 710 741
NNW line 543 550 552 555
Table 4.34 Phase velocities in meters/second computed for the radial component for a Torsional Shake with the data close to the building removed.
Experiment A Experiment B Experiment C Experiment D
East line 556 599 544 606
EN E line 527 528 528 530
North line 428 426 427 423
NE line 295 294 297 298
NN E line 481 489 490 488
NNW line 483 487 487 491
Table 4.35 Phase velocities in meters/second computed for the transverse component for a Torsional Shake with the data close to the building removed.
Experiment A Experiment B Experiment C Experiment D
East line 558 425 542 613
EN E line 839 858 855 865
North line 529 532 521 524
NE line 335 579 579 580
NN E line 580 585 585 583
NNW line 529 536 536 539
Table 4.36 Phase velocities in meters/second computed for the vertical component for a Torsional Shake with the data close to the building removed.
0 200 400 600 -4
-3 -2 -1 0 1
Distance (m)
0 200 400 600
-1 0 1
Distance (m)
0 500 1000 1500
0 0.2 0.4 0.6 0.8 1
Wavelength (m) Wavelength: 1064 m Velocity: 1211 m/s
0 200 400 600
-4 -3 -2 -1 0 1
Phase (rad)
Distance (m)
0 200 400 600
-2 -1 0 1 2
Distance (m)
Residual Error (rad)
0 500 1000 1500
0 0.2 0.4 0.6 0.8 1
Wavelength (m)
Avg. RMS Error (rad) Wavelength: 901 m
Velocity: 1026 m/s
0 200 400 600
-3 -2 -1 0
Distance (m)
0 200 400 600
-2 -1 0 1 2
Distance (m)
0 500 1000 1500
0 0.2 0.4 0.6 0.8 1
Wavelength (m) Wavelength: 1500 m Velocity: 1708 m/s
A) Radial component B) Transverse component C) Vertical component
Figure 4.6 Phase velocity minimization curves for an East-West shake recorded along the east line. The phase data shown are for the first shake (A). Shown are the radial, transverse, and vertical components. Sub-figures A and C show worst case scenarios for the linear fits, as there are outliers in the data.
calculated from the data of all of the seismometers and those obtained after removing the data for the closest instruments are very similar, which is incompatible with the observed displacements being due to the interference of multiple surface wave modes.
The good agreement between these results also supports that there is no interaction between near and far-field waves, as otherwise the measured phase velocities would be different for the two cases.