# Phase Decomposition and Its Applications

Phase decomposition is a novel technique that decomposes a composite seismic signal into different phase components, which can improve reservoir characterization. The technique is particularly useful in those areas where thin-bed interference causes the phase of the input seismic response to differ from the phase of the embedded wavelet in the data.

For a zero-phase wavelet in the data and thin low-impedance layers below tuning thickness, the waveform phase response generated after carrying out phase decomposition is found to be minus 90 degrees, which stands out as an anomaly. On the contrary, a corresponding high-impedance thin layer exhibits a similar (plus) 90-degree phase waveform response. By generating a synthetic response with use of well data and a zero-phase wavelet, such observations for thin reservoir layers can be understood with confidence and correlated with real seismic data. Phase decomposition can help immensely in direct interpretation of seismic data in terms of reservoir and non-reservoir zones, among other applications.

Another important aspect is that the seismic waveform is amplitude, phase and frequency dependent. Consequently, for thin layers below tuning, the frequency content of the associated seismic response must be monitored for targets with variable thicknesses. Phase decomposition does not use well data for the generation of phase components, but the synthetic traces generated from well data can be used to establish the relationships between amplitude/phase/frequency that may be desirable for a given problem. In this context, application of spectral decomposition to a synthetic trace could produce a frequency gather and provide the required frequency-dependent behavior. Likewise, the application of phase decomposition to the generated synthetic gather will provide a set of phase component gathers. Thus, between the spectral and phase decomposition applications, the desired amplitude/phase/frequency information can be sought.

We begin this article with a brief description of some of the spectral decomposition techniques available in different commercial software packages, and then showcase their application to a seismic dataset under study. We take the discussion forward from there to the description of phase decomposition and its applications. Finally, we draw some convincing conclusions.

## Spectral Decomposition

Spectral decomposition is an effective way of analyzing the seismic response of stratigraphic geologic features. It is carried out by transforming the seismic data from the time domain into the frequency domain. This can be done simply by using the short time window discrete Fourier transform (STFT), but there are other methods that can be used for the purpose, namely the continuous wavelet transform (CWT), S-transform, matching pursuit, constrained least-squares spectral analysis (CLSSA), particle swarm spectral decomposition (PSSD), and the optimal Gaussian spectral analysis (OGSA).

Some of these methods and their applications have been described in previous Geophysical Corner articles (December 2013, March 2014 and March 2015) and will not be repeated here.

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