Gravity modeling of 21/2-D sedimentary basins — a case of variable density contrast☆
Introduction
Calculation of basement depths where the density contrast varies significantly is an important geological study of the gravity method in hydrocarbon exploration. Negative gravity anomalies are generally observed over sedimentary basins having a large thickness of low-density sedimentary rocks. The interpretation of gravity anomalies due to such sedimentary basins mimics the mathematical process of trying to fit a suitable geometry to the low-density sedimentary load over the basement and tries to identify the parameters of the model in such a manner that the theoretical gravity anomalies fit the observed ones.
Many methods to interpret gravity anomalies due to sedimentary basins are available in the literature (Won and Bevis, 1987, Murthy and Rao, 1989). The above strategies assume that the sedimentary basins are 2-D in nature and the density of sedimentary rocks is constant throughout the cross-section. However, it is well known that the density of sedimentary rocks is seldom uniform (Cordell, 1973; Garcia-Abdeslem, 1992; Ferguson et al., 1988; Abdoh et al., 1990; Hinze, 2003). Garcia-Abdeslem (1992) has elucidated that the exponential density function could provide geologically meaningful results if simple differential compaction is assumed to be the most important diagenetic process in the evolution of sedimentary basins. Chai and Hinze (1988) also used the concept of exponential density function in their interpretation of gravity anomalies within the frequency domain. However, it is not possible to derive a closed form analytical gravity expression even for a simple mathematical model using an exponential density–depth function in space domain. On the other hand, Rao (1990) used a quadratic density function to interpret the gravity anomalies due to sedimentary basins. However, Chakravarthi and Rao (1993) shown that the quadratic density function would pose problems in modeling and inversion of gravity anomalies due to sedimentary basins having large thickness as this density function differ from true values not only in sign but also in magnitude. Chakravarthi and Rao (1993) suggested a parabolic density function and used it to develop an interpretation strategy to model sedimentary basins to overcome the enlisted drawbacks. Further, Chakravarthi et al. (2001) developed an inversion scheme to interpret gravity anomalies of 2-D density interfaces using the concept of parabolic density function.
Many sedimentary basins on continental platforms have limited strike lengths. Therefore, it is essential to approximate such sedimentary basins by geometries having finite strike lengths. Mickus and Peeples (1992) proposed a method to invert gravity and magnetic anomalies of 21/2-D sedimentary basins assuming a constant density for sedimentary rocks.
A few methods are in vogue to interpret gravity anomalies due to 21/2-D sedimentary basins using variable density–depth profiles, although many geological situations mimic the density–depth variation. In this paper, we develop an interpretation technique and the corresponding code, GRA2P5MOD, to determine the depths of a density interface above which the density contrast varies parabolically (PDP) with depth forms a simple extension of Bott's (1960) method.
Section snippets
Gravity anomaly of a 21/2-D prism with PDP
The geometry of a 21/2-D vertical prism is shown in Fig. 1A. Let the z-axis be perpendicular to the plane of the paper and positive inward with and as depths to top and bottom of the prism, respectively. Let the -axis be transverse to the strike of the prism. Further, let and be the strike length and width of the prism, respectively. Placing the origin, , vertically above the centre of the prism, the analytical expression of gravity anomaly at any point, , on the
Modeling of sedimentary basins
The modeling of a sedimentary basin mimics a mathematical process of trying to fit theoretical gravity anomalies with observed ones by adjusting the thickness of the basin within the appropriate permissible limits. A sedimentary basin is approximated by an ensemble of 21/2-D vertical juxtaposed prisms with top of each prism coinciding with the plane of observation (Fig. 2A). Furthermore, profile DD′ is assumed to be extending far from the boundary of the basin to stations resting on basement
Computer code
A Fortran 77 code, GRA2P5MOD, on MS-DOS/Window based environment is developed to interpret the gravity anomalies due to an outcropping sedimentary basin in which the density contrast varies parabolically with depth (FTP server). Input to this code consists of (number of observations on the profile), SD (observed density contrast at the surface between the basin and surrounding rocks expressed in gm/cm3), ALPHA (constant of the parabolic density function expressed in gm/cm3/km), DDX (station
Applications
Reliability of the method and efficiency of the corresponding code are demonstrated by interpreting two gravity profiles, one over a synthetic model and the other over the Godavari sub-basin of India.
Conclusions
A parabolic density function, which ascribes the density contrast–depth data of sedimentary rocks, is used to derive an analytical gravity expression of a 21/2-D vertical prism in the space domain. Interpretations based on both the parabolic and constant density depth profiles over a synthetic and a field profile reveal that the structural solution obtained with parabolic density profile is more consistent with geological information than the corresponding one obtained with a constant density
Acknowledgements
The authors record their sincere and profound thanks to Dr. Neil Anderson and another anonymous reviewer for their constructive review and useful suggestions to improve the text as presented here. Dr. V.P. Dimri, Director, National Geophysical Research Institute is sincerely thanked for his constant encouragement and permission to publish this work. The first author (VC) extends his sincere thanks to Council of Scientific and Industrial Research (CSIR), Government of India, for financial
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