John P. Castagna

Spectral decomposition of seismic data with continuous-wavelet transform

This paper presents a new methodology for computing a time-frequency map for nonstationary signals using the continuous-wavelet transform (CWT). The conventional method of producing a time-frequency map using the short time Fourier transform (STFT) limits time-frequency resolution by a predefined window length. In contrast, the CWT method does not require preselecting a window length and does not have a fixed time-frequency resolution over the timefrequency space. CWT uses dilation and translation of a wavelet to produce a time-scale map. A single scale encompasses a frequency band and is inversely proportional to the time support of the dilated wavelet. Previous workers have converted a time-scale map into a time-frequency map by taking the center frequencies of each scale. We transform the time-scale map by taking the Fourier transform of the inverse CWT to produce a time-frequency map. Thus, a time-scale map is converted into a time-frequency map in which the amplitudes of individual frequencies rather than frequency bands are represented. We refer to such a map as the time-frequency CWT (TFCWT). We validate our approach with a nonstationary synthetic example and compare the results with the STFT and a typical CWT spectrum. Two field examples illustrate that the TFCWT potentially can be used to detect frequency shadows caused by hydrocarbons and to identify subtle stratigraphic features for reservoir characterization.

Framework for AVO gradient and intercept interpretation

Amplitude variation with offset (AVO) interpretation may be facilitated by crossplotting the AVO intercept (A) and gradient (B). Under a variety of reasonable petrophysical assumptions, brine‐saturated sandstones and shales follow a well‐defined “background” trend in the A-B plane. Generally, A and B are negatively correlated for “background” rocks, but they may be positively correlated at very high VP/VS ratios, such as may occur in very soft shallow sediments. Thus, even fully brine‐saturated shallow events with large reflection coefficients may exhibit large increases in AVO. Deviations from the background trend may be indicative of hydrocarbons or lithologies with anomalous elastic properties. However, in contrast to the common assumptions that gas‐sand amplitude increases with offset, or that the reflection coefficient becomes more negative with increasing offset, gas sands may exhibit a variety of AVO behaviors. A classification of gas sands based on location in the A-B plane, rather than on normal‐...

Principles of AVO crossplotting

Hydrocarbon related “AVO anomalies” may show increasing or decreasing amplitude variation with offset. Conversely, brine‐saturated “background” rocks may show increasing or decreasing AVO.

Layer-thickness determination and stratigraphic interpretation using spectral inversion: Theory and application

Spectralinversionisaseismicmethodthatusesaprioriinformation and spectral decomposition to improve images of thinlayerswhosethicknessesarebelowthetuningthickness. We formulate a method to invert frequency spectra for layer thickness and apply it to synthetic and real data using complexspectralanalysis.Absolutelayerthicknessessignificantly 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 GulfofMexicoresultsinreliablewelltiestoseismicdata,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, suchasfalsestratigraphictruncationsthatarerelatedtolateralchangesinrockproperties,andmaskinggeologicinformation,suchasupdiplimitsofthinlayers.Weconcludethatdata that are inverted spectrally on a trace-by-trace basis show greater bedding continuity than do the original seismic data, suggestingthatwaveletside-lobeinterferenceproducesfalse beddingdiscontinuities.

Sensitivity of Near-Surface Shear-Wave Velocity Determination From Rayleigh And Love Waves

Rayleigh and Love waves recorded on seismic-shot gathers can be used to determine the thickness and shear-wave velocity of shallow subsurface layers. After the data are transformed into the k-f domain, the dispersion curve for each of the phases can be picked from maxima on the contour plot. This dispersion curve is then inverted for the velocities and depths. Different frequencies in the dispersion curve yield information about different depths. The fundamental mode has proven to be of greater use than higher modes. Both Rayleigh and Love waves are easily inverted. However, the Love waves seem to yield information in a lower portion of the spectrum than the Rayleigh modes. Three examples are given from field experiments conducted near Canton, Texas.

Fluids and frequency dependent seismic velocity of rocks

Summary Compressional and shear velocities of rocks are dependent on frequency and this dispersion may be significant even within the seismic band. The amount and position of dispersion will be largely a function of fluid properties, distribution, and motion in the pores. Velocities are thus directly coupled to rock permeability and pore compliance. Propagation often will be in the high frequency regime, even at a few tens of Hertz. Static, or low frequency models such as Gasmann will fail under such conditions. In addition, Biot theory will not correctly model wave propagation in many cases.

Petrophysical imaging using AVO

Seismic lithology is the process by which rock properties—such as lithology, porosity, and pore fluid content—are determined by analysis of seismic and other data. I emphasize other data because the seismic method is limited in what can be achieved in a vacuum, but can be remarkably robust when combined with other information and constrained by geologically reasonable assumptions. I define “petrophysical imaging” as a seismic lithology method which does not attempt to recover absolute rock properties but rather involves the construction of an image of subsurface rock property variation. For example, for direct hydrocarbon indication, absolute rock properties need not be determined, only the deviation from background nonpay behavior is required.

Inverse Spectral Decomposition

This paper introduces a method which spectrally decomposes a seismic trace by solving an inverse problem. In our technique, the reverse wavelet transform with a library of complex wavelets serves as a forward operator. The inversion reconstructs the wavelet coefficients that represent the seismic trace and satisfy an additional constraint. The constraint is needed as the inverse problem is non-unique. We show synthetic and real examples with three different types of constraints: 1) minimum L2 norm, 2) minimum L1 norm, and 3) sparse spike, or minimum support constraint. The sparse-spike constraint has the best temporal and frequency resolution. While the inverse approach to spectral decomposition is slow compared to other techniques, it produces solutions with better time and frequency resolution than popular existing methods.

Application of spectral decomposition to gas basins in Mexico

Recent reservoir studies involving spectral decomposition on various data sets from the Burgos and Macuspana basins of Mexico document the usefulness of this method as another way to uncover the effects of hydrocarbon accumulations on seismic data. Three such effects are illustrated in this article; attenuation of seismic waves passing through the reservoir, preferential reservoir illumination, and differential reservoir reflectivity.

The petrophysical basis for shallow-water flow prediction using multicomponent seismic data

Physical properties of shallow-water flow (SWF) sands differ from most reservoir and seal rocks studied for petroleum purposes. These materials exist near the transition zone between rocks and sediments. Our investigations, the subject of this article, suggest that physical properties of SWF sands are amenable to a prediction methodology that uses high-resolution multicomponent seismic data. SWF sands are a primary hazard to deepwater drilling operations in the Gulf of Mexico. They have the potential to result in well failures and significant discharges of subsurface fluids into the ocean. However, at present, most operators make only a modest attempt to identify SWF before drilling. They drill through these hazards and mitigate any resulting damage at significant expense if one is encountered. This is not rare. According to a report from Fugro Geoservices, approximately 70% of all deepwater wells have experienced SWF. A method for predrill delineation of sands that are close to failure, and thus likely to exhibit SWF, would be advantageous in selecting optimal drilling locations and in developing cost-effective well plans. The current method of identifying SWF involves predrill hazard studies utilizing conventional and high-resolution seismic data to identify zones that might produce SWF. However, the high incidence of SWF mitigation events in deepwater wells shows that existing techniques do not provide adequate resolution or accuracy. At present, no robust seismic method exists for accurately identifying and characterizing SWF. Operators do not have the option to avoid the hazard instead of mitigating the problem after it has started. A new method is required that will permit operators to identify the hazard before the well is drilled. Using seismic data for accurate understanding of the physical properties and deformational behavior of SWF sands is essential to characterization, prediction, and interpretation of these stratigraphic units. To date, very few core and …