Relative precision of vertical and horizontal gravity gradients measured by gravimeter

Abstract

Several recent publications advocate the use of the vertical gradient of gravity from gravimeter measurements at two elevations in a portable tower (ThyssenBornemisza, 1976;Fajklewicz, 1976;Mortimer, 1977). Contrary opinions have also been expressed (Hammer and Anzoleaga, 197.5;Stanley and Green, 1976; Thysen-Bornemisza, 1977;Arzi, 1977). The disagreement revolves around the question of practically attainable precision of the vertical gradient tower method.Although it is possible to calculate both horizontal and vertical gradients from conventional gravity survey data by use of the Hilbert transform (Stanley and Green, 1976), it should be noted that highly precise gravity data are required. Also the need for connected elevation and location surveys, the major cost in gravity surveying, is not avoided. This is a significant advantage of the gradient methods. The purpose here is to present a brief consideration of the relative precision of the horizontal and vertical gradients, as measured in the field by special gravimeter observations. THE VERTICAL GRADIENTThe most comprehensive paper on the subject to date reports extensive vertical gradient studies have been made in Poland over a period of years (Fajklewicz, 1976). That paper reports definitive data on the precision of the observations. Fajklewicz' s Table 1 tabulates the numerical results of 29 vertical gradient determinations (5 gravimeter readings each) at a base station during a period of one month. These 14.5 instrument readings (87 at the base and 58 at the top of the tower) yield a reported average vertical gradient of 3 109.3 * 3.3 E". It is stated that conditions during observations were not favorable.Also stated is that extensive routine ticld work yielded data with an accuracy in the range i-I to 2 10 E". We note the officially allowed reading time per station was seven minutes.If we assume that, on the average, field conditions and instrument performance were comparable, we can calculate the number of readings to achieve the claimed overall survey accuracy. Taking the middle value ?5 E", as representative accuracy, we find that each field station would require a total of (3.3 / 5)* X 29 = 13 setups with up to 65 readings. It certainly is unbelievable that this calculation impresents routine field operations. However, to deny this calculation is to state that reading conditions at the base station were much less favorable than the overall conditions over a period of years in the field. A more rcasonable conclusion would seem to be that the accuracy of the survey data has been overstated.Another consideration is that the data in Table 1 are irregular in two significant respects. (I) The "least count" (final digit) of all values differ by 3 E". This suggests that the reported value for a single determination exceeds the reading accuracy by nearly one decimal. (2) As may be seen on the plotted histogram of all readings (Figure I), the data in Table I fall into two distinct groups whose averages differ by more than 40 E". Comparison of the variances of t...

Interval gravity‐gradient determination concepts

“…Considerable attention has been directed recently to applications of gravity gradients, e.g., Hammer and Anzoleaga (1975) Stanley and Green (1976), Fajklewicz (1976) Butler (1979) Hammer (1979), Ager and Liard (1982), and Butler et al (1982). Gravity-gradient interpretive procedures are developed from properties of true or differential gradients, while gradients are determined in an interval or finite-difference sense from field gravity data.…”

Terrain Corrections are Critical for Airborne Gravity Gradiometer Data

“…Following that, the gravity tower vertical gradient (Fajklewicz, 1976) was applied to the solution of a number of important geologic mining and engineering problems, particularly to the search for and investigation of geological structure and the detection of caves and old mine workings. The accuracy of the survey data reported, however, was considered to be overestimated (Hammer, 1979). It was assumed that the precision of routine field observations of the tower vertical gradient (with five tower readings) can hardly be expected to be better than ± 20 E to ± 30 E. (One Eötvös, E, represents a gravity change of 1 u.ms 2 /km or 10V 2 ).…”