Computers & Geosciences Vol. 22, No. 5, pp. 535-546, 1996 Copyright 0 1996 Elsevier Science Ltd Pergamon oo!B-3004(%)00125-5 Printedin Great Britain. All rights reserved 0098-3004/96 $15.00 + 0.00 zyxwvu AN INTERACTIVE 2D AND 3D GRAVITY MODELING PROGRAM FOR IBM-COMPATIBLE PERSONAL COMPUTERS V. PINTO and A. CASAS Departamento Geoquimica, Petrologia i Prospeccio Geofisica, Facultat de Geologia. Universitat de Barcelona, 08071-Barcelona, Spain (Received 4 January 1995; accepted 16 October 1995) Abstract-An Interactive Graphic System for three-dimensional (3D) gravity modeling is presented. The system uses a highly flexible algorithm for the calculation of theoretical anomalies, which permits accurate 3D simulation of most types of geological bodies, and the simultaneous introduction of several bodies. This ability to combine several objects, together with features such as topographic relief, faults, and erosional process, adds a higher degree of realism to the model. Copyright 0 1996 Elsevier Science Ltd Key Won&: Gravity, 3D gravity modeling, Interactive graphic system. INTRODUCTION Previous work In the early years, 3D gravity modeling was restricted to simulations in terms of gravity anomalies of simple geometrical bodies such as spheres, vertical and horizontal cylinders, and thin sheets. The calcu- lation of anomalies was achieved by either applying mathematical expressions directly or using master charts. The shape of the model was obtained from single bodies or a combination of them. With advances in computer power, complex 3D models became possible, leading to the development of algorithms that allowed for more flexible theoretical shapes. Talwani and Ewing (1960) integrated the volume of the body by dividing it into horizontal, polygonal-shaped slices of uniform thickness. The anomaly at any given point results from the sum of the contributions of each slice. This system, although easily programmable, involved a large number of calculations and complicated spatial handling of the vertices of the polygons. Plouff (1976) and Van Baak (1989) made this method more efficient by drastically reducing the calculation time. Other authors opted to develop algorithms for more complex bodies. Paul (1974) calculated the gravity effect of a homogeneous polyhedron defined by a series of triangular faces. With the coordinates of its vertices defined, a test is carried out to determine the contribution of each face. This technique is valid only for observation points external to the polyhedron. In order to obviate the test, Bamet (1976) developed an alternative method of calculation, involving a complicated coordinate transformation. Okabe (1979) solved the first and second derivatives of the gravity potential with the polyhedron composed of polygonal faces. This method, although allowing interior anomalies to be calculated, is restricted in practice as the coordi- nates of the faces must be defined clockwise. Owing to the complicated 3D geometrical parameters, some authors divide a body into vertical two-dimensional sections: Giitze and Lahmeyer (1988) use the gener- ation of polyhedra; and Ramarao and Murthy (1989) apply a technique similar to that of Talwani and Ewing (1960), but with vertical polygonal-shaped slices whose density changes with depth. This method of defining the shape of the model facilitates its definition and its spatial handling. 30 gravity modeling Methods of 3D gravity modeling are based on simulating, through simple geometrical bodies, the geometrical parameters of geological structures responsible for anomalies. This simplification allows for both quantitative interpretation of the anomalies and, by varying the theoretical parameters, esti- mation of effective parameters of the real geological body. The central process in a 3D gravity modeling system is the resolution of the forward problem, that is, the calculation of the gravity anomaly caused by a specified geometry. The first stage in the modeling process is the construction of a theoretical geometrical model based on geological assumptions. This process usually involves a certain morphological pattern of the struc- tures being modeled. 2D models are constructed using (X,Z) profiles perpendicular to the structure, composed of a series of polygons whose apices define the model geometrically. These polygons may be extended along the Y axis either infinitely, or restricted to a certain value (2.5D). The limitations of this approach are evident, given that geological 535