Spectral inversion is a seismic method that uses a priori information and spectral decomposition to improve images of thin layers whose thicknesses are below the tuning thickness. We formulate a method to invert frequency spectra for layer thickness and apply it to synthetic and real data using complex spectral analysis. Absolute layer thicknesses significantly below the seismic tuning thickness can be determined robustly in this manner without amplitude calibration. We extend our method to encompass a generalized reflectivity series represented by a summation of impulse pairs. Application of our spectral inversion to seismic data sets from the Gulf of Mexico results in reliable well ties to seismic data, accurate prediction of layer thickness to less than half the tuning thickness, and improved imaging of subtle stratigraphic features. Comparisons between well ties for spectrally inverted data and ties for conventional seismic data illustrate the superior resolution of the former. Several stratigraphic examples illustrate the various destructive effects of the wavelet, including creating illusory geologic information, such as false stratigraphic truncations that are related to lateral changes in rock properties, and masking geologic information, such as updip limits of thin layers. We conclude that data that are inverted spectrally on a trace-by-trace basis show greater bedding continuity than do the original seismic data, suggesting that wavelet side-lobe interference produces false bedding discontinuities.

An inversion-based algorithm for computing the time-frequency analysis of reflection seismograms using constrained least-squares spectral analysis is formulated and applied to modeled seismic waveforms and real seismic data. The Fourier series coefficients are computed as a function of time directly by inverting a basis of truncated sinusoidal kernels for a moving time window. The method resulted in spectra that have reduced window smearing for a given window length relative to the discrete Fourier transform irrespective of window shape, and a time-frequency analysis with a combination of time and frequency resolution that is superior to the short time Fourier transform and the continuous wavelet transform. The reduction in spectral smoothing enables better determination of the spectral characteristics of interfering reflections within a short window. The degree of resolution improvement relative to the short time Fourier transform increases as window length decreases. As compared with the continuous wavelet transform, the method has greatly improved temporal resolution, particularly at low frequencies.

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L Lo oc ca al l f fr re eq qu ue en nc cy y a as s a a d di ir re ec ct t h hy yd dr ro oc ca ar rb bo on n i in nd di ic ca at to or r L Lo oc ca al l f fr re eq qu ue en nc cy y a as s a a d di ir re ec ct t h hy yd dr ro oc ca ar rb bo on n i in nd di ic ca at to or r S Sh he en ng gh ho on ng g T Ta ai i, , C Ch ha ar rl le es s P Pu ur ry ye ea ar r, , J Jo oh hn n P P. . C Ca as st ta ag gn na a, , U Un ni iv ve er rs si it ty y o of f H Ho ou us st to on n. . SummaryAs a seismic wave propagates, it loses energy due to spherical divergence, scattering, intrinsic absorption and reflection at interfaces where rock properties change. The amplitude and frequency responses of the reflected seismic wave are influenced by a variety of factors including: geologic structure, layer thickness, lithology, and pore fluid properties. When the seismic wave travels back to the surface, it also bring back the information related to stratigraphic features, rock property changes and hydrocarbon accumulations. Each reservoir has its own characteristic seismic frequency response because of its unique rock and fluid properties discriminating it from the surrounding environment. We utilize a spectral decomposition method to extract the characteristic frequency components from seismic data and identify low frequency anomalies. To understand the underlying physical factors of the low frequency anomaly, we build a set of wave-equation based synthetic forward modeling. The result of our analysis shows that seismic waves travel more slowly through gas zone than the background material is a main reason for seismic time series delay and low frequency anomaly in the thin layer reservoir. Our explanation has been applied in the analysis of frequency anomalies corresponding to gas-bearing sands in the Gulf of Mexico fields.

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