Summary

Self-organizing maps are a practical way to identify natural clusters in multi-attribute seismic data. Curvature measure identifies neurons that have found natural clusters from those that have not. Harvesting is a methodology for measuring consistency and delivering the most consistent classification. Those portions of the classification with low probability are an indicator of multi-attribute anomalies which warrant further investigation.

Introduction

Over the past several years, the growth in seismic data volumes has multiplied many times. Often a prospect is evaluated with a primary 3D survey along with 5 to 25 attributes which serve both general and unique purposes. These are well laid out by Chopra and Marfurt, 2007. Selforganizing maps (Kohonen, 2001), or SOM for short, are a type of unsupervised neural network which fit themselves to the pattern of information in multi-dimensional data in an orderly fashion.

Multi-attributes and natural clusters

We organize a 3D seismic survey data volume regularly sampled in location X, Y and time T (or depth estimate Z). Each survey sample is represented by a number of attributes, f1, f2, …, fF. An individual sample is represented in bold as a vector with four subscripts. The sample of Figure 1 resides in attribute space as shown in Figure 2. Included in the illustration are other samples with similar properties. These natural clusters are regions of higher density which can constitute various seismic events with varying attribute characteristics. A natural cluster would register as a maximum in a probability distribution function. However, a large number of attributes entails a histogram of impractically high dimensionality.

Self-Organizing Map (SOM)

A SOM neuron lies in attribute space alongside the data samples. Therefore, a neuron is also an F-dimensional vector noted here as

w

in bold. The neuron

w

lies in a topology j called the neuron space. At this point in the discussion, the topology is unspecified so use a single subscript t as a place marker for any number of dimensions.

Curvature measure

To search for natural clusters and to avoid the curse of dimensionality (Bishop, 2007), we allow the SOM to find them for us. However, there is no assurance that at the end of such a SOM analysis the neurons have come to rest at or near the centers of natural clusters. To address this issue, we turn to the simple definition of a maximum. A natural cluster is by definition a denser region of attribute space. It is identified as a maximum in a probability distribution function through analysis of a histogram. In 1D the histogram has a maximum; in 2D the histogram is a maximum in 2 orthogonal directions and so on. In F-dimensional attribute space, a natural cluster is revealed by a peak in the probability distribution function of all F attributes. Recall that at the end of an epoch there is a one-to-one relationship between a data sample and its winning neuron. That implies that to every winning neuron there corresponds a set of one or more data samples.

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