Correlation measurements of Atmospheric Pressure
variations and Seismicity during Hurricane Dennis

Randall D. Peters
Physics Department
Mercer University
Macon, Georgia

July 2005

Abstract

During the passage of hurricane Dennis, two functionally different instruments made continuous recordings from their location in Macon, Georgia. These were (i) a non-conventional vertical seismometer, and (ii) a low-level differential pressure sensor. Data were collected for 72 hours, beginning when the eye of the storm was located in the vicinity of Key West, Florida. Over the ensuing three-day period, fluctuations in the outputs from the two instruments were found to be highly correlated, with the exception of one eight hour interval.

1  Background

In a previous study it was shown that hurricane Charley not only generated microseisms as many would expect, but it also at times excited oscillations of some of the free-modes of our planet [1]. It was hypothesized that passage of the eye of a hurricane across a region of the earth where there is a sharp change in acoustic impedance, should result in a driving force for eigenmodes. The forcing function is for this case the reduced pressure in the eye of the storm.

If the above hypothesis is true, then one expects the excitation of localized earth crustal motions to also generate pressure disturbances in the atmosphere. Resulting waves should travel large distances from their source and, at a given observation point, cause pressure fluctuations of infrasonic type.

The present study offers support for this conclusion by demonstrating a strong correlation between the outputs from the two instruments that were monitored: (i) a modified Sprengnether vertical seismometer, and (ii) a highly sensitive differential pressure detector invented by the author.

2  Instruments

2.1  Seismometer

The seismometer is described in reference [1], except that for the present study the (unconventional `weak') force-feedback described there was not utilized. In other words, the instrument was operated open-loop-a mode that is thought by professionals of geoscience to be completely unacceptable! The reason is that conventional professional seismometers use capacitive sensors that are severely restricted in mechanical dynamic range. Thus the standard modus operandus of these instruments is one involving force-balance. A disturbance is monitored by means of the error signal required to keep the mass of the instrument virtually stationary.

As noted in ref. [1] and various other of the author's publications concerned with internal friction [2], strong force-feedback of this type, when coupled with the PID (proptional integral, differential) network that is employed-severely restricts the low frequency performance of the instrument.

The area-varying (as opposed to gap-varying) architecture of the author's patented fully differential capacitive sensor [3] allows a much greater mechanical dynamic range. In turn, this permits the seismometer to operate open loop (without destruction of sensitivity) and allow the non-ideal spring of the instrument to `find its own best' equilibrium position, as it is being continuously influenced by anelasticity responsible for creep.

In previous experiments the open-loop mode was not feasible because the ADC employed was limited to only 16-bits (Dataq DI-700). For adequate low-level sensitivity, the rail voltage was set at +/- 0.1 V. For large earthquakes this value was too low to prevent saturation of peak signals. The present study used a Symmetric Research single-channel ( $100) converter having 24-bits, so that the rails could be increased to +/- 10 V. As seen in later graphs, this permits open-loop diurnal voltage swings as large as 1 V to be accommodated while signals at the 1 mV level (such as by distant earthquakes) can still be resolved. Most large earthquakes should also be observable without waveform clipping.

Seismologists are accustomed to viewing `velocity' output as opposed to the `displacement' output of the present instrument. If one insists on working with the former, it is a simple means to take the numerical derivative of the filtered records. To collect the raw data as velocity rather than displacement causes the signal at low frequencies to be attenuated 20 dB per decade. Though commonly practiced, this severely restricts an instrument's ability to study the most interesting eigenmodes of the earth.

2.2  Pressure Sensor

The pressure sensor operates as a gap-varying fully differential capacitive detector that uses a diaphragm. The principle of its operation is described in the patent literature of [3]. The diaphragm is fabricated from thin aluminized mylar held in tension. The static plates on either side of the diaphragm were fabricated from printed circuit board material. As manufactured and sold by Tel-Atomic Inc. (no longer available), the sensor was operated with their SDC electronics box. For the present work this box was replaced with an autozeroeing electronics package designed by the author for use in a planned, inexpensive earthquake detector [4]. The `return to zero' time constant is about 20 s. This limits the low frequency response of the instrument; in a Bode plot, the falloff occurs at a value close to the lower corner frequency of early-generation seismometers referred to as `long-period' type.

The sensitivity of this differential pressure instrument was estimated 100 mV/ Pa. For the noise level of the electronics this yields a resolution significantly less than one part per million of atmospheric pressure. This is much smaller (about two orders of magnitude) than the resolution of a typical barometer. Barometers are absolute pressure instruments, and their resolution is limited by friction effects, whether internal to their more massive diaphragm, or Coulomb friction (older mechanical instruments) in the mechanism used to communicate diaphragm strain to a recording indicator.

3  Method of differential-pressure measurement

One side of the diaphragm is open to the atmosphere. The other side communicates through a tube to a bottle. The bottle is housed in a thermally insulated container, so that temperature fluctuations are minimized. With ideal electronics, the lower corner frequency is determined by the leak rate of the bottle. This rate determines the properties of this mechanical high-pass filter. Even if the electronics of the instrument was not low frequency limited as mentioned earlier, this method of measurement would still place a limit on the maximum period of pressure variation that could be detected.

4  Results

4.1  Pressure data

The two instruments were not co-located, but rather separated in distance by two miles. The pressure sensor was located in the Willett Science center of Mercer University and the seismometer was located in the quieter location of the author's home basement.

Shown in fig. 1, for the pressure sensor, are two days worth of temporal data from the three-day recording session. Indicated with the red arrows are various places where coherent oscillations were found by using Dataq's frequency-domain software [5]. When present, these oscillations in the range from 5 to 13 mHz must be large, since electronics attenuation has reduced them by a factor of about 25 dB (rough estimate). An example oscillation is provided in fig. 2. The decibel scale for this graph differs (subscript `D' for Dataq) from the other cases of this paper. It is referenced to the full scale (10 V) gain setting of the 16-bit ADC (DI-700). To convert a dBD value to the conventional scale, one simply uses (for this gain setting) dB  =  dBD - 70.31.

The convenience of the Dataq software makes easy the task of finding oscillations in the pressure data, by locating spectral lines after FFT calculation with a Hanning window. Different regimes of frequency require different `compression', which Dataq refers to as `input averaging'. Exploration is straightforward by means of rapid `mouse click' transformations between the time and frequency domains. Once a line is identified, the raw data can be manipulated by a variety of filter possibilities, such as the bandpass capability employed for fig. 2. Uncorrected for electronics attenuation, the 5.3 mHz oscillation level, at 47.5 mV; corresponds to a pressure amplitude of approximately 0.5 Pa. In units common to meteorology this is 5 mbar, 5 parts per million of atmospheric pressure. For comparison, the pressure in the eye of Dennis at this time was estimated from NOAA advisories to be about 960 mbar; i.e., a deficit relative to std pressure of 53 mbar.

Just as oscillations were easily discovered in the pressure data, so oscillations could also be easily found in the data of hurricane Charley [1]; since a Dataq ADC was also used with the seismometer for that study. Unfortunately, such ease is not yet available for the present seismic data, which was collected with the ADC sold by Symmetric Research; the output of which was analyzed using QuickBasic generated code written by the author. Because of the user `unfriendliness' of this software (severe as compared to the Dataq algorithms) no serious effort was mounted to try and find similar oscillations in the records generated by the seismometer. If such oscillations could be located and shown to correlate in both frequency and time with the pressure data, such a discovery would lend even greater support to the present hypotheses.

In addition to the oscillations noted in fig. 1, a number of prominent features are evident within the time-varying level of the signal. The discussion of these is postponed until later graphs, where the same features manifest themselves in data from the seismometer.

4.2  Seismic data

Instead of plotting seismic temporal data in the manner of the pressure results of fig. 1, the seismic results are given in terms of frequency plots as a function of time. These display spectral evolution as hurricane Dennis interacted with various land masses. For example, a noteworthy graph is that of fig. 3, labeled in time as 9.1 h. From the Advisory Archive data provided by NOAA's National Hurricane Center, it was determined that the eye of the storm was at this time located near the edge of the continental shelf west of Naples, Florida. As with hurricane Charley, Dennis grazed a continental shelf. With Charley the grazing produced a pronounced disturbance in both the seismic time and frequency plots. In the present case with Dennis, only the spectrum appears to change significantly during this shelf interaction. The transient appearance at this time, of a lower frequency `hump' in the spectrum, is thought to be consistent with the short-lived 12.9 mHz oscillation that occurred in the pressure data at this time (refer to fig. 1).

In the majority of the graphs of figures 3 through 5 there is an unmistakeable presence of microseisms-the sawtooth structure with a peak typically near 0.2 Hz. This structure is very nearly the same as was observed with Charley when the eye of the storm was located in the Gulf as opposed to the Atlantic. As noted in [1], the difference in character is attributed to ocean depth differences.

5  Earthquakes

Three earthquakes were large enough to be obviously registered by the seismometer during the three days of data collection. In each case they show a spectral feature with frequencies lower than that of the microseisms, as seen in figures 3 through 5. In figure 3, time-case 13.6 h, the structure labeled with the question mark may or may not be associated with quakes in Japan and Indonesia. Records from USGS do not show a sizeable earthquake that could have been responsible for the hump that is attributed to interaction of hurricane Dennis with the continental shelf.

To illustrate the significant difference between the present seismometer and conventional instruments, fig. 6 provides the time and spectral signatures of the Easter Island earthquake.

6  Correlation

A strong basis for the claims of this paper (including those of ref. [1]) is found in the results shown in fig. 7. Surprisingly strong correlation between seismometer output and pressure sensor output is seen to occur everywhere except for the short segment that was excised before doing the right-side correlation plot. With a correlation coefficient (R2 from the linear fit) of nearly 80%, there is evidence for significant coupling between ground motion and atmospheric dynamics.

For fig. 7 the seismic data was high-pass filtered. Motions with periods greater than about 200 s were suppressed as follows. After reading each individual record of length 1024 binary-data-words (sample rate 5 per s), both mean value and linear trend were numerically removed using Excel. By concatenating every fifth value of these adjusted records in a composite of length 4096 s , the frequency regime of the seismic data and the pressure data were more closely matched. The effect of this unconventional filtering operation can be appreciated by comparing the earthquake data of fig. 8 (Fiji Island) with that of fig. 6 which used no filtering. In particular, notice the difference in the spectra.

All spectra shown in this paper were calculated using the FFT algorithm of Excel [6]. The artifact shown in the spectrum of fig. 8 is not due to any anomalous behavior of the excel software. Rather it results from the concatenation of segmented records (filtering process mentioned earlier, in which mean and trend were removed from each of the individual segments).

If the low frequency information in the seismic data is not removed, then some of the `event' features are even more pronounced, as seen from fig. 9. Here the double hump associated with grazing of the continental shelf is dramatic. The two other humps are also reasonably explained; i.e., when the eye (i) hit the gulf shore and when it was (ii) closest to the instruments located in Macon, Georgia.

6.1  Anomalous segment

The reason for legitimately excising the segment (left-side) of fig. 7 from the correlation plot can be understood as follows. During this time the storm was responsible for considerable turbulence in the Macon area. For example, a close neighbor's house was the only one severely damaged by a huge sweetgum tree that was broken by strong winds at its half-height point. The influence of such localized turbulence is of much greater influence on a pressure sensor than it is on a seismometer. Its small spatial extent is incapable of greatly disturbing the ground.

7  Arrival time issues

In the correlation analysis the pressure and seismicity data were adjusted timewise to maximize the correlation coefficient. It was observed that peaks of the pressure data preceded those of the seismic data in all cases by a couple of hours. Explanation for this arrival time difference can probably be understood in detail only with additional experiments involving more than one pair of sensors, preferably an array of sensors. It is thought that the pressure variations are the result of buoyancy waves that travel at much lower speed than seismic waves responsible for the seismometer response. Thus the tardiness of the seismic data suggests that the origin of excitation is different for the two. In particular, it is deduced that the pressure data derives mainly from the outer bands of the storm (between eye and sensors), whereas the seismometer data derives from its eye. Because the outer bands encounter a land discontinuity before the eye gets there, the pressure should be first to announce the encounter.

References

[1]
R. Peters, ``Hurricane excitation of earth eigenmodes", online at http://arxiv.org/html/physics/0506162
[2]
see, for example, R. Peters, ``Damping'', chapters 20 and 21, Vibraton and Shock Handbook, CRC Press, 2005,
and also R. Peters, ``Friction at the mesoscale'', Contemporary Physics, Vol. 45, No. 6, 475-490 (2004).
[3]
Symmetric differential capacitive (SDC) sensor, U. S. Pat. No. 5,461,319. Online information is available at http://physics.mercer.edu/petepag/tutorial.html
[4]
``An affordable earthquake detector'', Popular Science, p. 104, April (2005).
[5]
From exploratory analysis of frequency domain features of a record, using the *.wdq files generated by a Dataq ADC.
[6]
Examples of the use of Excel's calculation of FFT's is to be found in the article by R. Peters, ``Spreadsheet filtering by FFT Gaussian-based Convolution'', online at http://physics.mercer.edu/hpage/filter/gauss.html

press-comp.gif

Figure 1: Pressure vs time for two of the three days of recording.

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Figure 2: Oscillation thought to be triggered by passage of the eye onto shore.

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Figure 3: Seismogram spectral characteristics the first day.

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Figure 4: Seismogram spectral characteristics the second day.

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Figure 5: Seismogram spectral characteristics the third day.

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Figure 6: Records from the Easter Island earthquake that occurred at 12:01:35 UTC on 11 July 2005.

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Figure 7: Correlation of fluctuations from the pressure sensor and the seismometer.

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Figure 8: Fiji Islands earthquake; observe that the filtering technique has introduced a numerical artifact (line with frequency of 5.2 mHz).

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Figure 9: Comparison of seismic fluctuation data after filtering (top) and without filtering (bottom).


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On 16 Jul 2005, 12:30.