Local seismic attributes

Introduction

Seismic attribute is defined by Sheriff (1991) as a ``measurement derived from seismic data''. Such a broad definition allows for many uses and abuses of the term. Countless attributes have been introduced in the practice of seismic exploration, (Chen and Sidney, 1997; Brown, 1996), which led Eastwood (2002) to talk about ``attribute explosion''. Many of these attributes play an exceptionally important role in interpreting and analyzing seismic data (Chopra and Marfurt, 2005).

In this paper, I consider two particular attribute applications:

1. Measuring local frequency content in a seismic image is important both for studying the phenomenon of seismic wave attenuation and for processing of attenuated signals.
2. Measuring local similarity between two seismic images is useful for seismic monitoring, registration of multicomponent data, and analysis of velocities and amplitudes.

Some of the best known seismic attributes are instantaneous attributes such as instantaneous phase or instantaneous dip (Taner et al., 1979; Barnes, 1993,1992). Such attributes measure seismic frequency characteristics as being attached instantaneously to each signal point. This measure is notoriously noisy and may lead to unphysical values such as negative frequencies (White, 1991).

In this paper, I introduce a concept of local attributes. Local attributes measure signal characteristics not instantaneously at each data point but in a local neighborhood around the point. According to the Fourier uncertainty principle, frequency is essentially an uncertain characteristic when applied to a local region in the time domain. Therefore, local frequency is more physically meaningful than instantaneous frequency. The idea of locality extends from local frequency to other attributes, such as the correlation coefficient between two different datasets, that are conventionally evaluated in sliding windows.

The paper starts with reviewing the definition of instantaneous frequency. I modify this definition to that of local frequency by recognizing it as a form of regularized inversion and by changing regularization to constrain the continuity and smoothness of the output. The same idea is extended next to define local correlation . I illustrate a practical application of local attributes using an example from multicomponent seismic image registration in a nine-component land survey.

Local seismic attributes