APPLIED GEGPHWSICS Journal of Applied Geophysics 34 ( 1995) 69-74 Modelling; of density interface with binomial density variation V. Chakravarthi Ground W ater Department, Chittoor 517 001, India Received 6 January 1994; accepted 23 April I994 Abstract The concept of variable density plays an important role in interpreting the gravity anomalies of sedimentary basins and in obtaining the real basement depth values. A second-order binomial density function has been introduced to model the rapid density variation of sedimentary rocks with depth. A recursive analytical expression for the gravity anomaly of an out-cropping two-dimensional vertica.1 prism is then derived. Based on the expression, a computer-based algorithm is developed to solve the structure of the sedimenlary basin from its gravity anomalies. The sedimentary strata above the density interface are approximated by a series of juxtapose’d prisms and their thicknesses are adjusted accordingly until the theoretical anomalies fit the observed anomalies. The first term of the binomial density function is used in the Bouguer slab formula to obtain the initial depth estimates of the basin. The gravity anomaly profile of the Godavari basin, India, where the density of sedimentary rocks is found to vary with depth, is interpreted. 1. Introduction Negative gravity anomalies are usually observed over sedimentary basins. While utilising these gravity anomalies to model the sedimentary basins, most of the interpretational techniques have assumed that the sed- imentary rocks filling the basin are homogeneous; thus a uniform density contrast is generally used in model- ling and inversion sch,emes (Bott, 1960; Qureshi et al., 1968; Bhaskara Rao et al., 1970; Mishra et al., 1987; Ramakrishna and Chayanulu, 1988; Chakravarthi, 1991) . However, seismic and well log studies proved that the density of sedimentary rocks varies with depth in a complicated manner which was confirmed by sev- eral authors (see e.g. PJhy, 1930; Nettleton, 1934; Hed- berg, 1936; Crowe and Redmond, 1962; Howell et al., 1966). Code11 (1973) and Chai and Hinze (1988) have equated this variation of density with depth to an exponential function, IRadhakrishna Murthy and Bhas- kara Rao ( 1979) assumed a linear density variation for the bodies at large depths, Litinsky (1989) has pro- posed a hyperbolic density variation, and Visweswara Rao et al. ( 1993, , 1994) have introduced the parabolic density variation. The concept of variable density was also proposed by Bhattacharya and Chan ( 1977) and Gendzwill ( 1970). However, in some sedimentary basins (see Fig. 1) , the density of sedimentary rocks is found to vary rapidly with depth, mainly because of differential compaction. Such type of density variation is rarely explained by the existing density functions. In the present paper, a binomial density function is intro- duced in order to explain such type of density variation as described above. The binomial density function is defined as: P(z)=A+&“,forvaluesofz< I( -AIB)““l (1) In my laboratory experiments, several density func- tions have been fitted to the density-depth data of the Godavari basin (Fig. I), and it was found that the 0926-9851/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSD10926-985 1(94) 00048-4