A New Approach to Seismic Data Integration During Reservoir Characterization Using Optimal non-Parametric Transformations
Authors: Xue Guoping , Datta-Gupta Akhil 
Published: December 2007

Abstract
We propose a two-stage approach to integrating seismic data into reservoir characterization. First, we use a non-parametric approach to calibrate the seismic and well data through an optimal transformation to obtain the maximal correlation between two data sets. These optimal transformations are totally data-driven and do not assume any a priori functional relationship. Next, cokriging or stochastic cosimulation is carried out in the transformed space to generate conditional realizations of reservoir properties. The proposed approach allows for non-linearity between reservoir properties and seismic attributes and exploits the secondary data to its fullest potential. Furthermore, cokriging or cosimulation is considerably simplified when carried in conjunction with the optimal transformations because of a significant reduction in the variance function calculations particularly when multiple seismic attributes are involved.
The proposed approach has been applied to synthetic as well as field examples. The synthetic examples involve reproducing a pre-generated primary data set using sparse primary and multiple dense secondary data sets. A comparison with traditional kriging and cokriging is also presented to illustrate the superiority of our proposed approach. The field example uses 3-D seismic and well log data from a 2 mi2 area of the Stratton gas field in South Texas — a fluvial reservoir system. Using multiple seismic attributes in conjunction with well data, we estimate pore-footage distribution for a selected zone in the middle Frio formation.

Introduction
It is well-recognized that integration of seismic data into reservoir characterization can play a significant role in reducing uncertainties in interwell reservoir properties. However, use of seismic data in reservoir characterization still remains rather limited primarily due to the inexact nature of the relationship between seismic and reservoir properties. Many seismic characteristics exhibit complicated effects of reservoir parameters such as lithology, petrophysics and fluid content. Hence, the link between seismic and reservoir properties is often non-unique, multivariate, and non-linear.
Currently, there are two common approaches for integrating seismic data during reservoir characterization. The first approach involves inversion of seismic data to obtain seismic velocity distribution and then generating reservoir properties either using empirical models or through data calibration with existing wells. This approach is rather straight-forward and easy to implement. However, when applied to reservoirs complicated by large variations in lithology, fluid saturation, and other petrological factors, the inverted seismic velocity alone may not be sufficient to characterize reservoir properties with confidence. The second approach is more statistical in nature. It involves extraction of various seismic attributes from the formation under consideration and then estimating reservoir properties using multivariate statistical correlation or pattern, recognition algorithms. This approach, although not as direct as the first approach, can incorporate as many seismic attributes as might be available and thus is able to deal with more complicated reservoirs. However, traditional stochastic cosimulation techniques are not suitable for cases where multiple seismic attributes are involved.
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