Novel EarthWave Instruments

Dr. Peters has outfitted two earth monitoring instruments with his patented symmetric differential capacitive (SDC) sensors. In each case, the SDC sensor is in the form of an array. For the WWSN (Sprengnether) vertical seismometer instrument, the array is a linear one. For the tiltmeter, it is an angle array. The seismometer also has a standard output; i.e., the magnet/coil sensor drives a drum recorder of conventional type. This constitutes a velocity detector and thus is sensitive to high frequency earth motions. The instrument is an excellent recorder of traffic that passes by on a nearby road. The response in this case is a vibratory rather than usual mode of the spring in the instrument.

The SDC sensor on the seismometer permits very low frequency variations to be seen. At present, the instruments have not been carefully temperature stabilized, so there are diurnal variations in mean position due to temperature change.

The tiltmeter sees free-earth vibrations on a regular basis, as has been true from the first occasion of their accidental discovery with an instrument of related type (for surface physics studies) about a decade ago.

NOTE: For the present setup, the tiltmeter is situated with its torsion wire lying almost in a direction east-west. Ideally, there should be another instrument oriented orthogonally to this one.

The following figures are results of measurements made with the pair of instruments. The raw data for the ones labeled with *-217 were recorded on day 217 of the present year 2000.
The last datum of those records correspond to 22:26 GMT. They are interesting by virtue of the Russian earthquake that occurred on that day. The last datum for the 221 records corresponds to 10:09 GMT. The records of day 221 are interesting because a 15 minute periodic (free-earth) mode (probably ₀T₆) is evident within the autocorrelation of the tiltmeter (see the very last figure of the list that follows).

The seismometer, though much more sensitive to acceleration, was not able to sense this variation. Thus .../tc-221.gif illustrates the most important feature of the tiltmeter developed by Dr. Peters--it is an instrument which is sensitive to the shape of the earth.

[It should be noted that such free modes are normally to be seen in the autocorrelation only after removing the secular term in the time record. This has been done for all those graphs presently presented.]

Each of the following gifs is of the order of 35K:

Russian Earthquake of August 4, 2000 (day 217)
Seismometer Time Record: s-217.gif	Tiltmeter Time Record: t-217.gif
Seismometer Power Spectrum: sp-217.gif	Tiltmeter Power Spectrum: tp-217.gif

First observed Free Earth mode (period 15 min.), August 8, 2000 (day 221)
Seismometer Time Record: s-221.gif	Tiltmeter Time Record: t-221.gif
Seismometer Power Spectrum: sp-221.gif	Tiltmeter Power Spectrum: tp-221.gif
Seismometer Autocorrelation: sc-221.gif	Tiltmeter Autocorrelation: tc-221.gif

The periods in free decay of the seismometer and tiltmeter (neither critically damped) are respectively 15 s and 10 s, approximately. In the day 217 records above, the natural period of each instrument is obvious in its power spectrum (the sharpest line within the broadened low region of the graph). The sensitivities of the instruments are approximately 2000 V/m and 10,000 V/rad respectively. (The last number applied to the graphs showing free modes indicates that their peak to peak amplitudes are of the order of 50-200 nrad. ) Because the lifetime of each is short, about 120 min., the uncertainty in frequency is large (the Heisenberg uncertainty principle). In this respect, they are much different than free modes seen after large earthquakes--which are highly monochromatic.

The instruments described above do not function like standard seismological ones. To better understand some of the physics involved in their design, refer to the following paper. Especially important to the vertical seismometer's operation is the spring whose clever design was first realized by a physics student named LaCoste at the University of Texas at Austin.

After improving the shielding of the electronics, a ₀T₄ Free Earth mode (period 23 min.) was observed on day 224 of 2000 (click on the last graph of the following six). In each of the graphs that follow, the last datum of each of the 4 x 1800 sec records occurs at 0512 GMT. Though obscured by noise, the free mode is evident within the time record of the tiltmeter; however, it is not to be found, even by autocorrelation, in the seismometer response.

Approaching toward the full moon, the free earth activity is seen to increase (the latest set of measurements which follow) just as has been noted many times before with the tiltmeter. The following tiltmeter results show the very strong presence of a 15 min. periodic oscillation (probably the ₀T₆ mode). The last datum is at 16:25 GMT, day 226 of the year 2000.

Note that the power spectrum has been graphed this time in the more conventional form (log-log). The low frequency features are seen to be essentially 1/f (from very low to about one-half the natural frequency of the instrument), whereas the higher frequency character (electronics) is more nearly white noise. The Nyquist frequency (upper cutoff) in this case is 0.189 Hz. To obtain the Nyquist frequency for a given record, note the length in hours (T) as noted in the time trace. The rightmost frequency point in the power spectrum is then given by (0.2844/T) Hz.

The last datum in the above records was at 13:55 GMT on day 227. The periodicity shown in the autocorrelation (also visible in the time record and the power spectrum) evidently corresponds to a ₀T₅mode.

{Note: To the un-initiated, the autocorrelation may appear mysterious. It is obtained by taking the inverse of the product of the Fast Fourier Transform with its conjugate (using the Wiener Kintchin theorem). Before FFT processing, it was not computationally feasible to employ this incredibly useful technique for seeing low frequency periodic signals in noise. To show that it actually works, black marks have been provided in the tiltmeter time trace of day 227 above--showing clearly the presence of the 18 min. variation.)

It is straightforward to simulate the linear system response to Brownian noise. Since it is common for personnel in the geoscience industry to assume this for purpose of estimating sensitivity, let's see how the results compare with the present pair of instruments.

A damping coefficient for the simulated system was chosen to yield a free decay spectral width comparable to that of the instruments. The result is as follows: (i) (a) simulation time trace, and (b) assoc. power spectrum. Notice that the natural frequency of the instrument (though broadened) is quite obvious in the spectrum. It is also quite evident (though far from monochromatic) in the time trace. Neither the seismometer nor the tiltmeter produce records like this unless arbitrary mechanical noise is introduced. Compare (i) (a) and (b) above with the following for the tiltmeter (ii) and for the seismometer (iii):

It is obvious that, unlike the simulation results, the characteristic frequency of the instrument in both cases has been suppressed. At these low levels, mesoanelastic complexities cause the system to be "latched" in a metastable state. By walking around on the ground in the vicinity of the package, dithering of the instruments is accomplished; i.e., the effects of latching are largely removed as follows:

Notice, however, that the seismometer is not as effectively freed from latching as the result of this dithering.

It should be noted that latching, as the word is used here, does not mean the instrument has "seized-up" and has no low level response at any frequency. Rather, it means that the system refuses to oscillate at its natural frequency, f, and evidently at other frequencies in an unknown region below f (and perhaps also above). Clearly, the system still responds to ultra-low frequencies, as evidenced by the seismometer's apparent response to tidal forcing with a 12-hr period.

A final example of nonlinearity is provided--one showing a nearly discontinuous jump in the position of the tiltmeter on one occasion. Such jumps were first seen in the strain of alloys back in the 1920's by Frenchmen Portevin and LeChatelier. Their results were published in Comptes Rendu, but even the physics community hardly knows about them.

NOTE: It is not possible to prove that this jump occurred in the instrument, as opposed to somewhere in the earth (most likely local, c.f. anecdote). A clear distinction between earth and wire is not necessary, however, because both systems are capable of demonstrating this phenomenon.

These results provide additional evidence that assumed linearity is not valid in all ranges for seismic instruments. One might try to argue that force balance eliminates the problems. In fact, force balance should be even more conducive to latching. The latching is a natural consequence of friction in the instruments. As noted elsewhere, this is internal friction--the most important kind of friction, and one which no one seems to know about.

Substantial change in the character of the output from the instruments was seen in one week's time, as the moon went from approximately 1/4 phase to 2/4 (full). On day 221 (near 1/4), variations in both were small as the moon and sun were near quadrature, corresponding to minimum tidal force. On day 228 (near 2/4), both instruments showed larger variations, the seismometer especially so. Also, by day 228 the free earth modes seen are very short period, around 3 to 4.5 minutes. The results are as follows:

(Note: the cause for the sharp downward going spikes in the seismometer day 221 record is unknown.)

(Note: all records are day 228--representing 3 consecutive files, last datum of 3rd file at 15:46 GMT)

The periods of the three preceding files are approximately 3, 4.3 and 4.5 minutes respectively.

Later, on day 228, there was a 1-hr record which contains a mixture of 15-min and 4-min free earth oscillations, which showed up only in the tiltmeter data. To demonstrate that these are not the possible result of temperature variation, which might be affecting the tiltmeter but not the seismometer; nine records are provided. They correspond to time, power spectrum, and autocorrelation--for each of (i) the tiltmeter, (ii) the seismometer, and (iii) the temperature sensor, which is a solid state device whose constant is 10 mV/C. It is seen that the temperature is stable to within 0.1 C during the time of the records. Shown on the tiltmeter power spectrum are three (black) lines. From lowest to highest frequency on the graph (for which the Nyquist freq., highest = 0.284 Hz) these correspond to, respectively, the 15 min. oscillation, the 4 min oscillation, and the 10 s period of the instrument. Whereas the tiltmeter's characteristic frequency is slightly present as indicated by its line in the spectrum, the seismometer's characteristic is missing from its power spectrum (Evidence once again for "latching" due to anelasticity). (Note: Because of variations that have been driving the seismometer SDC sensor from "rail to rail", the electronics gain on the unit was reduced by a factor of 4 as compared to previous cases.)

Note that the secular terms have been removed from both earth instruments, but not the thermometer. It just so happened, for the seismometer during this time, that there was insignificant curvature in the graph (inflection point of the response to tidal forcing). The following graph is the time trace of the seismometer with the secular term retained, showing that the instrument was not against a mechanical stop.

It will be interesting to see if the free-earth modes change character according to the phase of the moon (a Texas Tech University colleague hinted this would likely be true, suggesting that Peters' work was that of a 'lunatic'.) All kidding aside, change of some sort is expected, if the Peters hypothesis concerning the origin of short lived free-earth eigenmodes is correct--that they result from rapid internal relaxation of the earth under the influence of 12-hour period tidal strain. Such a relaxation must result in oscillation, as even most students of physics quickly realize.

On days 229 and 230 (16 and 17 August 2000), eigenmodes of respective period 6.7 min and 15 min were noted as follows:

This figure shows five of the tiltmeter time traces in which autocorrelation indicated free-earth oscillations. The top two records are each 1.5 hrs in length, and the bottom three are each 1.0 hr. The records are from days 226, 227, 228, 229, and 230 --corresponding to free-earth periods (respectively) of 15, 18, 4&15 mix, 6.7, and 15 minutes.

A review of the autocorrelations given above shows that not a single free-earth oscillation could be sensed with the seismometer. Analogously, it seems reasonable to assume that such modes would not be visible when using a gravimeter. This is consistent with the paucity of such data as obtained with instruments in use by the geoscience community.

Contrariwise, it is seen from the day 217 earthquake data that the tiltmeter does not respond very well to earthquakes. These observations support the claim made elsewhere concerning the tiltmeter--that it is relatively immune to localized linear accelerations, but is sensitive to changes in the shape of the earth. It also obviously responds to tilt.

Occasionally, there are disturbances that show up in both instruments with similar magnitude, as shown in the following two traces, obtained on day 231.

The tiltmeter shows much the same response as the seismometer to two events (indicated by the black lines), but it also shows a piecewise linear sequence of changes unseen by the seismometer. Such abrupt changes in slope, with associated ringing in some cases, have not been previously observed with the instrument. They appear to be from the earth and not from the instrument itself as the result of structural rearrangement.

Later, partial insight into the piecewise linear response may have been realized. Heavy equipment working to remove broken sidewalk in the neighborhood was shown to cause a tilt dislocation. Because the soil in the area (and along the 'fall-line' of Macon) is fairly unstable, it is believed that the tiltmeter is responding to soil settling. This would be consistent with damage to buildings in the area which have for decades experienced problems with broken mortar joints.

After a few days absence of obvious periodic variations in the tiltmeter records, free-earth eigenmodes are once again seen on day 234. The following tiltmeter records show an 18 min. mode (₀T₅), that is immediately followed by a 30 min mode (₀T₃):

Mixture of modes again: On day 236 (23 Aug), a mixture of 30 min and 7.5 min oscillations was seen:

Not only have both periods of the mixture doubled as compared to day 228, a comparison of time traces shows that the rss variation in the records is at a lower level (about one-half). This appears to be consistent with expectations based on the difference in lunar phase for the two dates.

Moreover, it appears that the tiltmeter traces, in an rss sense, are similar for lunar phases near 1/4 and 3/4-having gone through a maximum around 2/4 (full moon). These observations are consistent with previous (published) claims that the tiltmeter is driven at higher levels near new and full moon--and that the short lived free earth oscillations seen with the instrument (usually low level, using autocorrelation) derive from tidal forcing of the anelastic earth.

Just when it appeared that the tiltmeter traces might retain their low rss levels (until several days closer to new-moon), two events were noted--both of which involve large deviations about the zeroed mean and slope (removal of secular variation). The first event shows presence of the longest possible period for a free earth mode (S₂ mode of 54 min), and the 2nd event is an example of bistability. Then following the bistability, an S₃ mode appears.

Bistability: The 3.5 h record comprises 7 concatenated files, each of which (like all other data presented) is 30 min in duration (2048 samples). The jumping between two states first occurs in the second record of the set, the last datum of which corresponds to 03:41 GMT on day 238 (25 Aug 2000).

Shortly following the bistability is an S₃ mode whose period is about 37 min. (last datum at 09:43 GMT, day 238):

Bistability was seen with the tiltmeter on two additional occasions, following the first observation (noted above) by about 20 h and 37 h respectively. case 2, case 3

Interestingly, the magnitude of the transitions (largest possible) is roughly the same in all three cases. The seismometer did not exhibit similar behavior during the time of these instabilities, although it was prone to much larger 'meanderings' than expected.

First Macon observation: 12 h before the Indonesian earthquake of 28 Aug 2000 (15:38 GMT), an S₂ (54 min) mode was observed with the tiltmeter.

Several years ago Dr. Peters also saw (while at West Point) an S₂ mode which preceded by 12 h the occurrence of a large earthquake in Mexico. Much more data will be needed before a case for earthquake prediction might be made on this basis; however, the12 h interval of these cases is considered important, because of the period of tidal forcing, and the physics that is hypothesized.

Just before the Indonesian earthquake, a strong T₃ (30 min) mode was observed with the instrument.

Seismometer time trace during the Indonesian earthquake, and its power spectrum. The hump near the Nyquist frequency is the free period of the instrument, about 15 s.

Interestingly, the low frequency components of the tiltmeter response suddenly almost disappear as the quake response is registered on the seismometer.

Tiltmeter time trace & power spectrum , & autocorrelation during the quake. An inspection of the power spectrum suggests that the high frequencies are two orders of magnitude more intense than most of the other cases that have been previously presented; however, there was apparently a grounding problem in the electronics responsible for this noise rather than earth noise. The free period of the instrument is not visible in the spectrum of this 3.5 h record; however it does show up (8.5 s per.) in a calculation of the power spectrum using only the first 0.5 h record.

Second Macon observation: The start of the following 3.5 h record precedes by 12 h the Indonesian earthquake of 7 Sep 2000, 13:44:27 GMT. The surprising thing about this record is the diversity of modes in addition to the S2 component that is here emphasized. Elsewhere (plethora ....) it is shown that a 6 min mode is present in the 2nd half hour interval of the record, and then 5 h later in a 2 h span there is first a two component mixture of (i) T6 mode (15 min per.) and (ii) a superposed mode with a period of 90 s, followed by a mode whose period is 210 s.

On days 243 and 244 (30 and 31 Aug) the S2 mode (54 min) was observed once and a T4 mode (22 min) once, and an S3 mode (37 min) once as follows, using the tiltmeter:

Five years ago at West Point, some shorter period coherent modes were noted with the tiltmeter. The most unusual of these (30 Jul 95) was one in which a 50 s oscillation was seen to persist for the entire 50 min. record. The power spectrum shows the presence of 2nd, 3rd, 4th, and 5th harmonics (the prominent, broadened instrument free period feature in the graph corresponds to 0.25 Hz; i.e., period 4 s--less than half the present approx. 10 s period of the tiltmeter.):

Some 5 min, rather than the usual 30 min records, were collected on 2 Sep 2000. Two of them, separated in time by 10 min, contained coherent oscillations with periods of 30 s and 50 s respectively:

Also, 10 min after the record with the 50 s variation, the tiltmeter appears to be driven at 10 s--the free period of the instrument being much more monochromatic than usual: pwr. spectr., assoc. autocorr.

Especially interesting is the 75 s oscillation that shows up first on the seismometer, and then on the tiltmeter but delayed by 5 min. :

From 11 August to 7 September 2000, 19 short-lived free earth eigenmodes were observed with the tiltmeter. They are as follows:

Note that coherent oscillations that were seen, but having period less than 15 minutes, have not been included in this list.

Most of the free earth modes that have been seen prior to this were ones which existed for only about half a dozen cycles. Early on day 253 (9 Sep 2000), an S4 mode (26 min) was observed to last for over 6 h, about 15 cycles. Whether this is related to the earthquake in the Philippines (22:41:24, 9/8/00) is not known. The quake preceded the first part of the record by about 4 h.

Earlier tiltmeter data exhibited features of bistability; i.e., the instrument shows discontinuous jumps back and forth between two (or more) states. Or there was piecewise linear variation (see just above anecdote). Once the source of the instability (presumably local) had died away, the instrument seems to have experienced no significant net displacement.

Unlike the bistabilities, a new feature was observed on day 252 (8 Sep 2000). A significant Portevin LeChatelier type jump was observed by the tiltmeter--first in the morning at 05:07 GMT and then 12.6 h later in the afternoon at 16:29 GMT. Because these are quite large (5 to 10 micro-rad), they are being called dislocations. Curiously, the latter dislocation occurred 36.4 h before the Taiwan earthquake of 08:54:42 GMT on 10 September.

These dislocations are not believed to be local--mainly because in each case a significant coherent oscillation appears to have been triggered by each; i.e., the first case being a mode of 10 min period and the 2nd case a mode of 15 min. period (T6 or S6).

A delay of 12 h between three observed S2 events and earthquakes has already been noted. Should one postulate a predilection of dislocation events at integer multiples of 12 h before earthquakes? Once again the generic model of earthquakes suggests that the idea may not be farfetched!

It should be noted that a tilt dislocation in the opposite direction from the above two was seen on 11 Sep. It does not have an earthquake associated with it (n times 12 h) later. It may have been local, since there is no coherent mode following the jump.

Before the full moon of 13 Sep 2000, a number of unusal things were seen with the tiltmeter. First there was a strong T3 (29 min mode) on 12 Sep.

The T3 mode was followed by records which show a monotonically increasing root sum square (rss) activity without obvious (sustained) coherent oscillations. In the first time traces provided, the indicated rss = 4.3 mv corresponds to the top 3.5 h. Below it are subsequent 3.5 h traces, in which the rss activity increases first to 5.2 mv and then to 6.3 mv. On the heels of this are additional similar cases, the first of which is rss = 8.5 mv. The first two hours of this record also show a 15 min periodicity (S6 or T6) that is so obvious that autocorrelation is not necessary to see it. Then suddenly, the tiltmeter grows quiet--with rss levels around 3 to 4 mv (the 'quiet before the swarm', pun intended), until 'all hell breaks loose' during the approximately dozen earthquakes that were reported with magnitudes between 3 and 6 during one 24 h period near 13 Sep. Dr. Peters does not have first hand experience with tiltmeter response called 'swarming'--associated with volcanoes. His Earth Science colleague, Dr. Bruce Dod, suggested that this is an appropriate term to describe the indicated response.

The swarming has largely disappeared by 14 Sep, but a final significant earthquake (day later) occurs at about the midpoint of the 2nd 2.5 h trace. Though not especially noticeable by the tiltmeter, the quake is picked up by the seismometer.

The T2 mode, having a period of 44 min was seen for the first time (present studies) on 19 Sep 2000. The last datum of the 2nd of the pair of 2 h records was recorded at 05:48 GMT. The eigenmode is sufficiently strong to be visible without autocorrelation, esp. by means of the six dark vertical lines which were added. Bear in mind that each of the concatenated records has had removed from it the mean and secular terms. Thus the left start of the bottom trace does not line up with the right finish of the upper trace.

Novel EarthWave Instruments , Randall D. Peters	Department of Physics Mercer University Macon, Georgia 31207
(1) Description of the tiltmeter, (2) An Amer. Geophy. Union paper, and (3) Some Related Links:
(i) Physics of a Seismic Instrument, (ii) Physics of the LaCoste Zero-Length Spring (iii) some generic earthquake physics (iv) (a) Free decay of the SDC outfitted Sprengnether vertical seismometer, and (b) its associated power spectrum, (v) (a) Tiltmeter free decay, and (b) its assoc. power spectrum.
"Quiet" time records with associated power spectra: These are compared against simulated Brownian motion of a linear oscillator to demonstrate that "low and slow" mechanical oscillators (seismometers) are influenced by mesoanelastic complexity. Additionally there is an example of a Portevin-LeChatelier jump in a tiltmeter record--one more clue to the fact that mesodynamics is important to these instruments.

Changes in the course of a week (1/4 moon's period)	Mixture of free earth modes (day 228), again on day 236)
Response Differences, Tiltmeter versus Seismometer	First recent observation of the earth's lowest frequency eigenmode
Examples of bistability	Earthquake precursors?
Free mode activity near the new moon	Shorter period coherent oscillations
Plethora of modes near lunar quadrature (unexpected)	one month's free earth oscillation statistics
S4 mode enduring for 15 cycles	Tilt dislocations
Unusual Full Moon Results, 13 Sep 2000 ('swarming')	First observation of the T2 mode

August 11, 2000 (day 224) Free Earth mode (period 23 min.)
Seismometer Time Record: s-224.gif	Tiltmeter Time Record: t-224.gif
Seismometer Power Spectrum: sp-224.gif	Tiltmeter Power Spectrum: tp-224.gif
Seismometer Autocorrelation: sc-224.gif	Tiltmeter Autocorrelation: tc-224.gif