Comput Geosci (2011) 15:421–429 DOI 10.1007/s10596-010-9212-4 ORIGINAL PAPER Application of EM algorithms for seismic facices classification Mei Han · Yong Zhao · Gaoming Li · Albert C. Reynolds Received: 25 August 2009 / Accepted: 4 October 2010 / Published online: 23 October 2010 © Springer Science+Business Media B.V. 2010 Abstract Identification of the geological facies and their distribution from seismic and other available ge- ological information is important during the early stage of reservoir development (e.g. decision on initial well locations). Traditionally, this is done by manually in- specting the signatures of the seismic attribute maps, which is very time-consuming. This paper proposes an application of the Expectation-Maximization (EM) algorithm to automatically identify geological facies from seismic data. While the properties within a certain geological facies are relatively homogeneous, the prop- erties between geological facies can be rather different. Assuming that noisy seismic data of a geological facies, which reflect rock properties, can be approximated with a Gaussian distribution, the seismic data of a reser- voir composed of several geological facies are samples from a Gaussian mixture model. The mean of each Gaussian model represents the average value of the seismic data within each facies while the variance gives the variation of the seismic data within a facies. The proportions in the Gaussian mixture model represent the relative volumes of different facies in the reservoir. In this setting, the facies classification problem becomes a problem of estimating the parameters defining the Gaussian mixture model. The EM algorithm has long been used to estimate Gaussian mixture model para- M. Han · G. Li (B ) · A. C. Reynolds University of Tulsa, 800 S. Tucker Dr., Tulsa, OK 74104 USA e-mail: gaoming-li@utulsa.edu Y. Zhao 600 North Dairy Ashford (77079-1175) P.O. Box 2197, Houston, TX 77252 USA meters. As the standard EM algorithm does not con- sider spatial relationship among data, it can generate spatially scattered seismic facies which is physically unrealistic. We improve the standard EM algorithm by adding a spatial constraint to enhance spatial continuity of the estimated geological facies. By applying the EM algorithms to acoustic impedance and Poisson’s ratio data for two synthetic examples, we are able to identify the facies distribution. Keywords EM · Facies · Poison’s ratio · Acoustic impedance 1 Introduction Traditionally, stratigraphic reservoir characterization is conducted within the framework of depositional envi- ronment and facies models. In order to obtain a reason- able reservoir description, it is desirable to integrate all available data to identify and map rock facies. Usually, facies identification is done by manually analyzing core, well log and seismic data, which requires time and ex- perience and does not necessarily guarantee consistent results from different sources of data. Liu and Oliver [15] and Zhao et al. [24] applied the ensemble Kalman filter method to assimilate the production and seis- mic data for mapping the rock facies. However, these methods require core, logging and production data and they can only be applied after the wells are drilled and the reservoir is put on production in the development phase. As drilling wildcat wells is risky and expensive, it is important to identify the distribution of rock facies based on seismic data obtained during exploration, which is the focus of this paper.