Spectral Decomposition and Attributes for Evaluating Seismically Thin Layers

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.