Summary

Spikes in complex trace attributes are caused by reflection interference, discontinuities, and noise. They complicate quantitative interpretation, but they may have qualitative value as stratigraphic and structural markers. Destructive reflection interference is the chief cause of spikes. Spikes caused by interference are a function of the reflection spacing and frequency spectrum of the seismic wavelet. They occur at envelope minima and are associated with reflection tails or weak reflectivity. Spikes do not indicate thin beds or stratigraphic terminations, but they can identify faults. Attributes computed horizontally, such as instantaneous wavenumber magnitude, serve as crude discontinuity measures.

Introduction

Spikes are ubiquitous in complex trace attributes. Attribute spikes are large, transient values, positive or negative, caused by reflection interference, discontinuities, and noise. Spikes confound quantitative interpretation, but their locations mark stratigraphic and structural boundaries.

The initial response to spikes was to remove them. Observing that spikes in instantaneous frequency coincide with minima in the trace envelope, or reflection strength, Taner et al. (1979) suppressed them through envelopeweighted averaging. Bodine (1984) removed spikes through the nonlinear .response frequency. method. Both approaches produce attributes with intuitive meaning as time-variant spectral averages. In this way the problem of spikes in quantitative analysis has long been solved.

The second response to spikes was to treat them as markers. Hardage (1987, p. 217) observed that spikes in instantaneous frequency form stratigraphic markers between reflections, and Hardage et al. (1998) argued that they also identify stratigraphic terminations and lateral discontinuities. In related studies, Oliveros and Radovich (1997) implicitly used spikes in the second derivative of the envelope as the basis for a discontinuity attribute, and Taner (2001) suggested that frequency spikes indicate thin beds. Nonetheless, the value of spikes in qualitative analysis remains uncertain.

I investigate the nature of spikes in complex seismic trace attributes. I show that spikes caused by reflection interference depend on the seismic wavelet and the reflection spacing, and argue that they do not reveal thin beds or stratigraphic terminations. Finally, I look at how spikes in instantaneous wavenumber and amplitude change highlight faults and other discontinuities.

Theory

All complex trace attributes that involve differentiation are prone to spikes. This includes instantaneous frequency, instantaneous wavenumber, and relative amplitude changes (Figure 1). Instantaneous frequency is the scaled time rate of change of the instantaneous phase (Taner et al., 1979). Instantaneous wavenumber is defined similarly as the scaled rate of change of the phase in the x or y direction (Scheuer and Oldenburg, 1988). Horizontal wavenumber magnitude is the square root of the sum of the squares of the instantaneous wavenumbers in the x and y directions (Oliveros and Radovich, 1997). Relative amplitude changes are derivatives of the trace envelope normalized by the envelope (Oliveros and Radovich, 1997; Barnes, 2008), and are similar to the coherent amplitude gradients introduced by Marfurt and Kirlin (2000).

Destructive reflection interference is the major cause of spikes in complex trace attributes. Such spikes occur between reflections at minima in the trace envelope and are a sensitive function of the reflection spacing and the frequency content of the seismic wavelet.

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