Gravity inversion of 2D basement relief using entropic regularization João B. C. Silva 1 , Alexandre S. Oliveira 1 , and Valéria C. F. Barbosa 2 ABSTRACT We have developed a gravity interpretation method for es- timating the discontinuous basement relief of a sedimentary basin. The density contrast between the basement and the sediments is assumed to be known, and it could be either con- stant or vary monotonically with depth. The interpretation model consists of a set of vertical, juxtaposed prisms, whose thicknesses are the parameters to be estimated. We used the entropic regularization that combines the minimization of the first-order entropy measure with the maximization of the ze- roth-order entropy measure of the solution vector. We vali- dated the method by applying it to synthetic data produced by a simulated basin bordered by high-angle step faults; we ob- tained a good definition of the relief, particularly of the dis- continuities. We also applied the method to a profile across the Büyük Menderes Valley in West Turkey and obtained a solution exhibiting a gravity fault with large slip on the north- ern border of the valley. When applied to the interpretation of a discontinuous basement relief, the method has a better per- formance than the global smoothness method. It is compara- ble to the weighted smoothness method, but it does not re- quire the a priori knowledge about the maximum basin depth. INTRODUCTION The knowledge of the basement relief of a sedimentary basin is important in oil prospecting because it could indicate probable loca- tions of stratigraphic and structural traps. Stratigraphic traps such as pinch-outs might be formed at the flanks of a smooth positive relief feature associated with oscillations of the basement relief, which can be mapped by gravity inversion methods that stabilize the solution by assuming it is smooth Leão et al., 1996; Barbosa et al., 1997; Chakravarthi and Sundararajan, 2007. On the other hand, structural traps might be associated with faults that displaced the sedimentary layers and basement. In this case, the knowledge of the discontinu- ous relief could help to locate oil structural traps, which might be as- sociated with the discontinuity. Applying the above-mentioned methods to map a discontinuous relief has yielded unsatisfactory re- sults. Barbosa et al. 1999 developed a method, named weighted smoothness, which manages to map high-angle faults in the base- ment topography, but it requires the knowledge of the maximum ba- sin depth. We present a gravity inversion method suited to map a discontinu- ous basement relief based on entropic regularization, which consists in minimizing the first-order entropy measure of the vector contain- ing the depth-to-basement estimates at discrete points, inhibiting at the same time any excessive minimization of the zeroth-order entro- py. The latter imposition is necessary to prevent the collapse of the solution into an unrealistic basin estimate consisting of an exces- sively narrow and deep relief. The proposed method has been tested on synthetic data produced by a simulated extensional basin whose density contrast between the sediments and the basement decreases with depth according to a hy- perbolic law. The modeled basin presents an overall smooth relief defined by terraces and local sharp discontinuities separating them. The results demonstrate the good performance of the method in de- lineating the sharp basement discontinuities, and reinforce confi- dence in the interpretation of real data, which consist of two gravity profiles. The first one is a profile across the Poema Bridge at the Fed- eral University of Pará campus. At ebb tide, the river channel is ex- posed, and its bottom topography might therefore be estimated from a gravity profile across it similar to the procedure used to interpret the basement relief of a sedimentary basin with constant density con- trast between the sediments and the basement. The overall features of the channel were detected using the proposed method. The second profile runs across the Büyük Menderes Valley in West Turkey.An interpretation model, assuming a density contrast decreasing with depth, led to a solution exhibiting a gravity fault with large slip on the northern border of the valley, in accordance with the geology of the area. For comparison, we applied the global and weighted smoothness methods to the same sets of synthetic and real data. Manuscript received by the Editor 17 July 2009; revised manuscript received 16 November 2009; published online 13 May 2010. 1 Federal University of Pará, Geophysics Department, Belém, Brazil. E-mail: joaobcsy@yahoo.com.br; alexandrecn8@yahoo.com.br. 2 Observatório Nacional, Geophysics Department, Rio de Janeiro, Brazil. E-mail: valcris@on.br. © 2010 Society of Exploration Geophysicists. All rights reserved. GEOPHYSICS, VOL. 75, NO. 3 MAY-JUNE 2010; P. I29–I35, 6 FIGS. 10.1190/1.3374358 I29 Downloaded 14 May 2010 to 200.218.195.12. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/