Bouguer anomaly still confuse many of us despite detailed discussions by such gravity practitioners as LaFehr (1991, 1998), Chapin (1996), and Talwani (1998). In his 1991 article, LaFehr pointed out that incomplete treatment of the subject by major exploration geophysics textbooks is a main reason for the misunderstanding of gravity datareductions. While the mathematical expression for absolute Bouguer anomaly is explicit and available in correct form in some textbooks, that is not true in the case of the relative Bouguer anomaly. The formula for relative Bouguer anomaly seems in conflict with the definition of gravity anomaly. Thus, I present here a mathematical expression for relative Bouguer anomaly that is consistent with thedefinition of gravity anomaly.
Definition of gravity anomaly. The gravity anomaly, Δg, represents variation of the earth’s gravity value due only to lateral density change. It is defined at a point on the physical surface of the Earth as the deviation of the Earth’s normal or theoretical gravity value, gφ, at the point of latitude φ from the observed gravity value, gobs , at the same point: Thetheoretical gravity value can be calculated from any International Gravity Formula (IGF) developed after 1967. The IGF formula of 1987 is:
The symbol g represents the absolute gravity value. The theoretical gravity formula is derived by taking into consideration the ellipsoidal shape, rotation around the geographical axis, and the massive equatorial bulge of the Earth. The angle φ is the latitudein degrees of a point on the reference ellipsoid that best describes the shape of the Earth.
Elevation of a point on the physical surface of the Earth is measured with respect to the geoid, the surface of which is approximately the mean sea level. The surface of the geoid may not coincide with that of the reference ellipsoid. Absolute gravity anomaly. The absolute gravity anomaly is:
in whichFAC is the free-air correction, BC is the Bouguer correction, and TC is the terrain correction. The correct way of writing the formula for absolute Bouguer anomaly is (Parasnis, 1997):
The symbol Δg denotes anomalous gravity value. This is the “correct” way to write the formula because most exploration geophysics texts include equation 5 in the form
Mathematically, equations 5 and 6 areexactly the same and this similarity is the source of misunderstanding about the meaning of Bouguer anomaly. Equation 6 has misled many to believe that the gravity corrections are applied to the observed gravity data. This in turn has created the misconception that observed gravity values are “reduced to the
Relative Bouguer anomaly. The formula for relative Bouguer
anomaly is usuallywritten:
where lc, fac, bc, and tc are latitude, free air, Bouguer, and terrain corrections relative to the arbitrary datum. In this article, capital letters in equations denote gravity corrections relative to sea level and small letters denote gravity corrections relative to the arbitrary datum level.
The symbols δgobs and δgB denote gravimeter readings in mgals at the gravity station and basestation respectively. In a small-scale survey we neither need to measure the absolute gravity value nor use the theoretical gravity formula. According to equation 7, corrections are first applied to the observed gravity readings and then the same base station reading is subtracted from it at each gravity station. This equation creates confusion in two places. First, the definition of gravityanomaly mentioned earlier seems lost; second, it creates the same misconception resulting from equation 6—that gravity values are reduced to the datum level. This second misconception is not serious in this case. Because of the nature of the survey, the relative Bouguer anomaly may be approximated to be reduced to datum level, which is not sea level in this case. To maintain consistency in the...