Multi-disciplinary inversion of Earth models

Abstract

Now that Earth-modelling packages are used routinely by most petroleum companies, efforts are under way to adapt multi-disciplinary data inversion techniques to better constrain these models by geological, geophysical and dynamic data. There is a convergence between techniques developed in various fields of application, such as Bayesian or geostatistical inversion, regularisationbased optimisation or data assimilation. Geostatistical conditional simulations are usually built using sequential gaussian simulation or by generating non-conditional simulations and conditioning them with a kriged correction. These approaches allow conditioning simulations by any kind of data, as long as these data can be approximated by a linear combination of the inverted Earth model parameters. Kriging, the average of all realisations, gives the best estimate in a least-squares sense. This is illustrated by examples where we invert multioffset seismic data into higher-resolution realisations of the logarithm of P- and S-impedances. Sensitivities to the various input parameters, such as the variogram, are discussed in detail. In this linear context, a regularized inversion of borehole and seismic data should lead to similar results to those obtained by kriging. In the same way, both geostatistical stochastic inversion and Kalman Filtering should produce similar a posteriori probability density functions of model parameters. Unfortunately, the forward model cannot always be approximated by a linear operator. This happens when production data must constrain a 3-D dynamic reservoir model. In these situations, algorithms such as Markov Chain Monte Carlo (MCMC) are required. Ensemble Kalman Filtering (EnKF) appears to be less time-consuming than many other MCMC methods, albeit it is not quite as rigorous. An example is given of a recent application of EnKF to an inversion problem on a UK field.