**How to Model the Thermal Evolution of Extensional Sedimentary Basins and Passive Margins**

**Nicky White, Glyn Edwards, and John Haines**

*University of Cambridge, UK*

It is widely agreed that many basins and margins form by stretching of continental lithosphere. Nevertheless, there is considerable disagreement about the way in which stretching is accommodated at depth. Does lithosphere ever stretch uniformly? If depth-dependent stretching does occur, what form does it take? The answers to these general and important questions have profound implications for the structural, thermal and magmatic evolution of margins. Ten years ago, the hydrocarbon industry began to explore deep-water margins in earnest. A quantitative understanding of the way in which these highly stretched margins develop will play a central role in reducing exploration risk (White et al., 2003). Two contrasting strategies have been used to address the problem of depth-dependent stretching. One approach exploits increasingly sophisticated dynamical models, which assume that body forces act upon the rheological framework of the lithosphere to produce deformation. These forward models have two drawbacks. First, the rheological framework is based upon extrapolating the results of laboratory experiments by over ten orders of magnitude and so is poorly understood. For example, it is still unclear whether the strength of the lithosphere is controlled by crust or by lithospheric mantle. Secondly, dynamical algorithms are slow and the more useful inverse problem cannot yet be posed. An alternative approach has concentrated on developing simple kinematic algorithms which are fast enough to be used as the basis of inverse modelling. These inverse algorithms seek patterns of deformation which generate the best possible match between model and observation. We have developed a flexible inverse model which assumes that the lithosphere deforms by spatial and temporal variation of the strain rate tensor. In this kinematic model, strain rate can vary with time, with distance across the margin, and with depth. Crucially, and in contrast to other groups, we make no assumptions about the way in which strain rate varies with depth. Instead, we invert for the existence and form of depth dependency. This strategy is therefore a logical generalization of our previously published work (Bellingham & White, 2000). To ensure computational speed and conservation of mass, we employ a spectral approach. In order to invert, we must assume an initial distribution of strain rate. This starting model is calculated by setting the thermal expansion coefficient of the lithosphere to zero and by assuming that material does not move sideways. The algorithm then seeks the smoothest spatial and temporal distribution of strain rate which yields the smallest misfit between predicted and observed subsidence and crustal thinning profiles. Different search algorithms have been tested and we conclude that the conjugate gradient method is a suitably efficient and stable search engine. This general inverse model has been tested on synthetic datasets which display different patterns of depth dependency. In general, depth dependency is recoverable when its existence is manifested by changes in the pattern of subsidence. We have also modelled datasets from basins (e.g. North Sea, Gulf of Suez) and from margins (e.g. South China Sea, Black Sea). The results from these regions suggest that depth dependency is mild and that lithosphere stretching is largely, but not completely, uniform. Our inverse algorithms are flexible and powerful tools for mitigating exploration risk at deep-water margins where the stratigraphic record is poorly known. These algorithms are also the starting point for calculating thermal histories of margins (Jones et al., 2004). They are of considerable interest to the hydrocarbon industry who is sponsoring further research effort.

*References*

Bellingham, P. and White, N., 2000, A general inverse method for modeling extensional sedimentary basins, Basin Research, 12, 219-226.

White, N., Thompson, M. & Barwise, T., 2003, Understanding the thermal evolution of deep-water continental margins, Nature, 426, 334-343.

Jones, S.M., White, N.J., Faulkner, P., and Bellingham, P., 2004, Animated models of extensional basins and passive margins, Geochemistry, Geophysics, Geosystems, 5, 8, Q08009, doi:10.1029/2003GC000658.

AAPG Search and Discover Article #90066©2007 AAPG Hedberg Conference, The Hague, The Netherlands