Summary
Three-dimensional (3D) earth models are best created with a combination of well logs and seismic data. Seismic data have good lateral resolution but poor vertical resolution compared to wells. The seismic resolution depends on seismic acquisition and reservoir parameters, and is incorporated into the 3D earth model with different techniques depending on this resolution relative to that of the 3D model. Good vertical resolution of the seismic data may warrant integrating it as a continuous vertical variable informing local reservoir properties, whereas poor resolution warrants using only a single map representing vertically averaged reservoir properties. The first case best applies to thick reservoirs and/or high-frequency seismic data in soft rock and is usually handled using a cokriging-type approach. The second case represents the low end of the seismic resolution spectrum, where the seismic map can now be treated by methods such as block kriging, simulated annealing, or Bayesian techniques. We introduce a new multiple map Bayesian technique with variable weights for the important middle ground where a single seismic map cannot effectively represent the entire reservoir.
This new technique extends a previous Bayesian technique by incorporating multiple seismic property maps and also allowing vertically varying weighting functions for each map. This vertical weighting flexibility is physically important because the seismic maps represent reflected wave averages from rock property contrasts such as at the top and base of the reservoir. Depending on the seismic acquisition and reservoir properties, the seismic maps are physically represented by simple but nonconstant weights in the new 3D earth modeling technique.
Two field examples are shown where two seismic maps are incorporated in each 3D earth model. The benefit of using multiple maps is illustrated with the geostatistical concept of probability of exceedance. Finally, a postmortem is presented showing well path trajectories of a successful and unsuccessful horizontal well that are explained by model results based on data existing before the wells were drilled.
Introduction
Three-dimensional (3D) earth models are greatly improved by including seismic data because of the good lateral coverage compared with well data alone. The vertical resolution of seismic data is poor compared with well data, but it may be high or low compared with the reservoir thickness as depicted in Fig. 1. Seismic resolution is typically considered to be one-fourth of a wavelength (?/4) although zones of thinner rock property contrasts can be detected. The seismic resolution relative to the reservoir thickness constrains the applicability of different geostatistical techniques for building the 3D earth model.
Fig. 1 is highly schematic and not meant to portray seismic data as a monochromatic (single-frequency) wave. The reference to wavelength here is based on the dominant frequency in the seismic data. Fig. 1 is meant to illustrate the various regimes of vertical resolution in seismic data relative to the reservoir thickness. While there are all sorts of issues, such as tuning, that must be considered in the left two cases, we need to address these cases because of their importance.
Seismic data having little vertical resolution over the reservoir interval, as in the left case of Fig. 1 can use geostatistical techniques that incorporate one seismic attribute map. The single attribute can be a static combination of multiple attributes in a multivariate sense but the combination cannot vary spatially. These techniques include sequential Gaussian simulation with Block Kriging1 (SGSBK), simulated annealing,2 or sequential Gaussian simulation with Bayesian updating.3,4 Some of these methods are extendable beyond a single seismic map with modification.
Seismic data having good vertical resolution over the reservoir interval, as in the right seismic trace of Fig. 1, can use geostatistical techniques that incorporate 3D volumes of seismic attributes. Techniques include simulated annealing, collocated cokriging simulation,5 a Markov-Bayes approach,6 and spectral separation. The term "3D volume" of seismic, as used here, is distinguished from the term "3D seismic data." (A geophysicist speaks of 3D seismic data when it is acquired over the surface in areal swaths or patches for the purpose of imaging a 3D volume of the earth. Two-dimensional (2D) seismic is acquired along a line on the surface for the purpose of imaging a 2D cross section of the earth.) The 3D volume distinction is made based on the vertical resolution of the seismic relative to the reservoir. To be considered a 3D volume here, we require both lateral and vertical resolution within the reservoir. Seismic data often do not have the vertical resolution within the reservoir zone to warrant using a 3D volume of seismic data.
The low and high limits of vertical resolution leave out the case of intermediate vertical resolution as depicted by the middle curve of Fig. 1. Because typical seismic resolution often ranges from 10 to 40 m and many reservoirs have thicknesses one to two times this range, many reservoirs fall into this middle ground. These reservoirs have higher vertical seismic resolution than a single map captures, but not enough to warrant using a 3D volume of seismic. It is this important middle ground that is addressed by a new technique presented in this paper.
Gas Saturated Sandstone Reservoir Modeling Using Bayesian Stochastic Seismic Inversion