A new spectral decomposition method utilizing wavelet transforms reveals seismic direct hydrocarbon indicators that are not obvious on conventional stacked seismic data. The method can be applied to existing seismic datasets as a low-cost post-processing step.

Two years ago the Gas Technology Institute awarded a research contract to Fusion Geophysical to investigate the use of wavelet transform-based seismic attributes for gas detection. The proposed idea was that wavelet transforms could be used to obtain frequency spectra with high temporal resolution and without the windowing problems associated with traditional Fourier analysis, a process used to transform data from the time to the frequency domain. The question was: Can such improved spectral analysis of seismic data reveal hydrocarbon indications that are not apparent on conventional seismic data or that are not resolved using Fourier-based spectral decomposition methods? Our investigations indicate that the answer to this question is a resounding "yes!" By performing a number of case studies, we have identified three distinct spectral hydrocarbon indicators that are best revealed by proper spectral decomposition. These are:
• abnormal seismic attenuation;
• low frequency shadows associated with hydrocarbon related bright spots; and
• differences in "tuning" frequency between gas and brine sands.
The purpose of this article is to briefly describe the spectral decomposition method that we use, to provide illustrative examples of spectral hydrocarbon indicators and to discuss how these can be used in a practical manner for exploration applications.
Wavelet transform-based spectral decomposition
Once one accepts the notion that a seismogram can be represented as a superposition of wavelets, it follows immediately that the frequency spectrum of that seismogram must be a superposition of the frequency spectra of the wavelets. Thus, once a seismogram has been decomposed into constituent wavelets, a time-versus-frequency analysis (spectral decomposition) can readily be constructed by weighted superposition of wavelet spectra as a function of record time. Notably, such an approach to time-frequency analysis requires no windowing and no use of the Fourier transform if an appropriate wavelet dictionary (set of wavelets) is utilized. Consequently, the method has excellent time resolution and eliminates "Gibbs phenomena" and other undesirable effects of windowing such as spectral notches caused by multiple seismic reflection events occurring within the analysis window. We refer to our wavelet transform-based spectral decomposition technique as Enhanced Spectral Processing (ESP) in order to call attention to the fact that processing applications of the method go well beyond hydrocarbon indication.
Figure 1 compares ESP and the Short-Time Window Fourier Transform (STFT) for a synthetic waveform. ESP better defines the frequency content for each discrete event, especially for the composite signals. Note that multiple arrivals occurring in close proximity cause "ribs" and other pronounced spectral notches in the STFT. Note also that for ESP, the spectral energy for any particular arrival is spread out in time only for the duration of the arrival. For the STFT, the spectral energy is spread out over the length of the analysis window, irrespective of the actual time duration of the event. The ESP spectrum clearly resolves arrivals closely spaced in time, whereas the STFT cannot temporally resolve any features shorter than the window length.
Seismic attenuation
It is well established that gas-filled reservoirs exhibit higher frequency-dependent seismic attenuation than similar rock fully saturated with brine. What is not well established is how to validly measure this attenuation using surface seismic reflection measurements. A naïve approach is to presume that the slope of the ratio of frequency spectra for two time windows is directly related to the attenuation coefficient. This is what most commercial "energy absorption" procedures try to do. The fundamental problem with this approach is that spectral notches caused by local reflectivity dramatically bias the spectral ratio, thereby inhibiting valid attenuation measurement. As is evident in Figure 1, however, it is clear that the ESP method, by better separating events in time, is also freer of spectral distortions caused by the occurrence of multiple reflecting interfaces occurring in close temporal proximity.
Furthermore, any processing method that relies on regression or other automated procedures to calculate an attribute (such as Q) is subject to breaking down as necessary assumptions (such as the appropriate frequency band over which to measure the attenuation) are not necessarily conducive to characterization by simple predefined rules. It is more robust to directly compute attribute sections that require no assumptions and rely on the interpreter to observe abnormal attenuation. One simple method of doing this is to display the spectral decomposition results as seismic sections representing instantaneous amplitude at specific frequencies. To obverse frequency-dependent attenuation, the interpreter simply looks for amplitudes that are lower on a high-frequency section than on the corresponding low-frequency section. Thus, as displayed in Figure 2, the instantaneous amplitude sections at frequencies of 30 Hz and 60 Hz over a known gas reservoir readily reveal that reflections below the reservoir top are dramatically more attenuated at high frequencies (60 Hz) than at low frequencies (30 Hz). To the contrary, the reservoir top and overlying reflectors do not experience preferential high attenuation at high frequencies as the seismic travel paths, for these reflections do not go through gas-saturated rock.
Experience indicates that such attenuation is usually only readily observable for reservoirs of thicknesses sufficient (1) to accumulate significant attenuation as the seismic energy propagates down and up through reservoir and (2) to avoid complications due to interference of top and base reflections. Sometimes, frequency-dependent attenuation can be observed in a thin reservoir if the reservoir rock frame is extremely unconsolidated.
Low frequency shadows
The use of low frequency shadows as hydrocarbon indicators is nearly as old as bright spot detection. The shadows are usually erroneously presumed to be due to abnormal high-frequency attenuation. Our investigations suggest that these shadows are often in fact related to additional energy occurring at low frequencies rather than preferential attenuation of higher frequencies. One possible explanation is that these are locally converted shear waves that have traveled mostly as P-waves and thus arrive slightly after the true primary event.
On a broad-band stacked seismic section, such shadows are often not apparent to the naked eye, but as illustrated in Figures 3 and 4 for two different Gulf of Mexico reservoirs, shadows are difficult to miss on ESP instantaneous amplitude sections.
Preferential illumination
The frequency content of a broad-band stack of seismic data is essentially an accident of nature resulting from the interplay of acquisition, earth filtering and data processing and is not necessarily optimized to reveal information about a particular target. This leads to the obvious question: Why should the seismic amplitudes and other attributes that we use in seismic interpretation be those derived from this accidental dominant frequency? The prevalent idea of a tuning thickness, the thickness at which a reservoir is preferentially illuminated at a given dominant frequency, is an archaic concept when viewed from the perspective of having an ESP dataset. Since single-frequency seismic volumes can be obtained over any range of frequencies permitted by signal-to-noise ratio, there is no one tuning thickness. Rather, there is a tuning frequency at which the target is preferentially illuminated.
This idea leads to several interpretive insights. First of all, for a layer of constant thickness, the tuning frequency will be different for brine- and gas-saturated rock, and the tuning frequency itself can be mapped as a hydrocarbon indicator. Secondly, by observing how amplitudes change with frequency for thin reservoirs, one can readily see thickness changes that otherwise would not be apparent. For example, in Figure 3, the maximum reservoir amplitude shifts from right to left as the frequency changes from 10 Hz to 30 Hz as a result of the reservoir thinning to the left.
Discussion
ESP time-frequency analysis has much better resolution than conventional spectral decomposition. The ESP spectral attribute potentially can be used to directly detect hydrocarbons for gas reservoirs using high-frequency attenuation anomalies and/or low frequency shadows. The ESP technique can also be used to detect amplitude anomalies at given frequencies for thin reservoirs that are not as apparent on conventional broad-band seismic sections. We believe these potential applications of ESP will help us to improve upstream performance by reducing drilling uncertainties, helping to unravel complex variability in reservoir heterogeneity and thickness, and predicting physical reservoir properties. Although our particular spectral decomposition method is computationally intensive, it can be applied to existing seismic datasets at minimal cost. The major hurdle for routine use of this technology is in training and education of seismic interpreters and in providing appropriate visualization and analysis tools needed to handle the multiple volumes of data that can be produced.

Editor's note: This article first appeared in the Summer 2002 issue of GasTIPS.

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