Spectral Decomposition and Attributes for Evaluating Seismically Thin Layers



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The reflectivity series and resulting waveform for a generalized-simple layer (arbitrary reflection coefficients on top and base) can be separated into unique even and odd components, each having a different tuning curve. Amplitudes at peak frequency of pure-impulse pairs are independent of thickness, for either the original reflectivity, its odd, or even component. For seismic data with a non-flat spectrum, dividing the data spectrum over some useable band by the wavelet spectrum results in amplitudes at peak frequency that are independent of thickness. Comparing peak-frequency amplitudes for even and odd components to that of the total waveform, provides clues as to the nature of the layering. Correlations between spectral-isofrequency-amplitude traces (time-varying-spectral amplitude at individual frequencies) provide a means of finding frequency notches induced by layer reflectivity. Isofrequency-amplitude traces tend to be strongly correlated amongst frequencies at spectral nulls; and amongst those that are not at those frequency notches. Spectral-principal-component-amplitude attributes take advantage of this property, and are indicative of layer thickness. With proper trace scaling and spectral balancing, spectral-PC amplitudes are independent of layer’s reflection coefficients. Layers with only odd and even pair reflection coefficients have distinctive-spectral-principal component to thickness relationships in synthetic-wedge models. Three spectral-PC attributes individually delineate amplitudes from: 1) an isolated reflection not affected by tuning; 2) tuning of an even reflection pair; and 3) tuning of an odd reflection pair in a 3-D-synthetic-channel model. As with the synthetic model, a good attribute versus true-reservoir-thickness relationship is seen in real seismic and well data from the Hoover field in the Gulf of Mexico.



Spectral decomposition, Generalized simple layer, Seismic thickness delineation


Portions of this document appear in: Zhou*, Jian, Arnold Oyem, and John P. Castagna. "An algorithm for frequency-dependent principal component spectral analysis." In SEG Technical Program Expanded Abstracts 2014, pp. 2636-2640. Society of Exploration Geophysicists, 2014.