Measurement of differential earth tides

Abstract

Recently several communications [ 1 ]and [2] have discus& the possibility of using a laser beam to measure earth tides. These suggested experiments would measure the distance between two points on the earth's surface by an interference experiment. Because of atmospheric effects the two points must be fairly close together. Thus, although the interference experiment promises very high precision, its range of usefulness overlaps that of other strain measuring devices.We would like to suggest an alternative method. This method sacrifices the extreme precision of an interference experiment but permits measurement over a much greater distance. This longer baseline will permit measurement of the influence of geological structure on tidal displacement. I t is proposed to measure the relative velocity between two stations by utilizing the Doppler shift of a laser beam. A laser a t station 1 has its beam split by a partially silvered mirror. One beam is sent to station 2 where it is reflected by a mirror back to station 1. The two beams are then compared and the Doppler frequency shift is measured.Present helium-neon lasers have -Av = 10-14. Townes and co-workers [3] hope to push this to e = l O -1 5 before reaching the limit imposed by thermal fluctuations a t room temperature. The above figures refer to stability over the order of 1 second. In the proposed experiment, the requirements are much less stringent since we require stability (against frequency drift) over a time equal to the travel time of the beam of -100 pet.The effect of atmospheric fluctuations can be estimated in the following way. If the total path length is L and the turbulon size is 1, then a simple argument [4] gives the root-mean-square phase deviation as V where x is the wave-length of the radiation and A n is the root-mean-square fluctuation in the atmospheric refractive index. In T seconds the total accumulated phase isCombining equations we find where c=velocity of light. This expression is in agreement with the results of other, more detailed, calculations [ 5 ] . As an example, let us take the distance between stations as 5 miles (L = 10 miles) and a measuring time, T = 5 minutes. A realistic value of 1 seems to be Z=200 feet [SI. Taking A n = 10-7 and substituting we find = lo-".With regard to An, we are primarily con-Manuscript received December 11. 1964.cerned with thermal fluctuations since other forms of turbulence commonly encountered have very little effect on the refractive index. At sea level An= -10-( A T ) . (Here T=OC) [ 6 ] . Our example, then, has assumed A T = & O C over a measuring time of 5 minutes. Becker [ 7 ] has shown that at certain times of day (near sunset and sunrise) the atmosphere achieves remarkable stability. Actual measurements with fast thermocouples [8] have yielded root-meansquare values of the temperature fluctuations of 0.2 O F a t favorable times of day. This value is for a time interval of 11 minutes. We conclude that under quiet conditions atmospheric fluctuations will limit our frequency measurements to...