Use of multiattribute transforms to predict log properties from seismic data

Abstract
We describe a new method for predicting well-log properties from seismic data. The analysis data consist of a series of target logs from wells which tie a 3-D seismic volume. The target logs theoretically may be of any type; however, the greatest success to date has been in predicting porosity logs. From the 3-D seismic volume a series of sample-based attributes is calculated. The objective is to derive a multiattribute transform, which is a linear or nonlinear transform between a subset of the attributes and the target log values. The selected subset is determined by a process of forward stepwise regression, which derives increasingly larger subsets of attributes. An extension of conventional crossplotting involves the use of a convolutional operator to resolve frequency differences between the target logs and the seismic data.
In the linear mode, the transform consists of a series of weights derived by least-squares minimization. In the nonlinear mode, a neural network is trained, using the selected attributes as inputs. Two types of neural networks have been evaluated: the multilayer feedforward network (MLFN) and the probabilistic neural network (PNN). Because of its mathematical simplicity, the PNN appears to be the network of choice.
To estimate the reliability of the derived multiattribute transform, crossvalidation is used. In this process, each well is systematically removed from the training set, and the transform is rederived from the remaining wells. The prediction error for the hidden well is then calculated. The validation error, which is the average error for all hidden wells, is used as a measure of the likely prediction error when the transform is applied to the seismic volume.
The method is applied to two real data sets. In each case, we see a continuous improvement in predictive power as we progress from single-attribute regression to linear multiattribute prediction to neural network prediction. This improvement is evident not only on the training data but, more importantly, on the validation data. In addition, the neural network shows a significant improvement in resolution over that from linear regression.