A type of iterative deconvolution that extracts the source waveform and reflectivity from a seismogram through the use of zero memory, non-linear estimators of reflection coefficient amplitnde is developed. Here, we present a theory for iterative deconvolution that is based upon the specification of a stochastic model describing reflectivity. The resulting parametric algorithm deconvolves the seismogram by forcing a filtered version of the seismogram to resemble an estimated reflection coefficient sequence. This latter time series is itself obtained from the filtered seismogram, and so a degree of iteration is required. Algorithms utilizing zero memory non-linearities (ZNLs) converge to a family of processes, which we call Bussgang, of which any colored Gaussian process and any independent process are members. The direction of convergence is controlled by the choice of ZNL used in the algorithm. Synthetic and real data show that, generally, five to ten iterations are required for acceptable deconvolutions. I N T R O D U C T I O NThe problem of removing the source waveform from a seismogram has traditionally been attempted using predictive deconvolution. The phase of the waveform, however, is indeterminable with this technique, and to assure a unique solution, minimum phase is usually assumed. But the concept that the earth's reflection coefficients are non-Gaussianly distributed allows both the color and phase of the waveform to be determined. Some recent non-Gaussian models have had significant success. Wiggins (1977) developed a deconvolution technique that minimized, heuristically, the entropy in a deconvolution. Since Gaussian models maximize the entropy, his use of a non-Gaussian model is evident. Gray (1979), following Wiggin's lead, proposed using a variable measure of entropy and developed algorithms to optimize these measures. Another approach, pioneered by Claerbout and Muir (1973) and subsequently refined by Taylor, Banks and McCoy (1979), uses the L1 versus L2 norm to minimize deconvolution residuals. In both papers the robustness property of the L1 *

In recent years dip moveout (DMO) has come into routine use in the seismic processing industry. The main benefits of including DMO in the processing sequence are that (1) stacking velocities after DMO are dip‐independent, and (2) “reflection point smear” associated with dipping events is eliminated by laterally shifting the reflection points to their zero‐offset position. These effects of DMO are also beneficial for estimation of stacking velocities by simplifying the interpretation of velocity analysis. Dip moveout also has an inherent dip filtering effect (Bolondi et al., 1984) by lowering the frequency content on the stacked section of steeply dipping aliased events, which leads to reduced migration noise.

Acoustic impedance is modeled as a special type of Markov chain. one which is constrained to have a purely exponential correlation function. The stochastic model is parsimoniously described by M parameters. where M is the number of states or rocks composing an impedance well log. The probability mass function of the states provides M-l parameters. and the "blockiness" of the log determines the remaining degree of freedom. Synthetic impedance and reflectivity logs constructed using the Markov model mimic the blockiness of the original logs. Both synthetic impedance and reflectivity are shown to be Bussgang, i.e.. if the sequenceis input into an instantaneous nonlinear device. then the correlation of input and output is proportional to the autocorrelation of the input. The final part of the paper uses the stochastic model in formulating an algorithm that transforms a deconvolved seismogram into acoustic impedance. The resulting function is blocky and free of random walks or sags. Low-frequency information. as provided by moveout velocities. can be easily incorporated into the algorithm

No abstract

This paper presents the results from a research project focusing on permanent cross‐well geophysical methods for reservoir monitoring during steam‐assisted gravity drainage. A feasibility study indicated detectable differences in seismic and electrical reservoir properties based on expected changes in temperature and fluid saturation during the production of extra heavy oil. As a result of this, a permanent cross‐well system was installed at the Leismer Demonstration Area, located in the Athabasca Oil Sands region in Alberta, Canada. Baseline data sets, including cross‐well seismic, three‐dimensional vertical seismic profiling and cross‐well electrical resistivity tomography, have been acquired. Comparisons between conventional surface seismic and downhole seismic data show an increase in resolution and frequency content as expected. Steam‐assisted gravity drainage‐induced time‐lapse effects are clearly visible in the 3D vertical seismic profiling and electrical resistivity tomography data sets, even after a few months of oil production. In general, the 3D vertical seismic profiling images show a higher resolution than the surface seismic data, in particular when dealing with vertical positioning of the time‐lapse events. The electrical resistivity tomography baseline shows clear separation between zones of high and low electrical resistivity, and during 23 months of electrical resistivity tomography measurements the maximum reduction of resistivity is 85%. Time‐lapse observations from acoustic and electrical borehole data correspond well, and are also supported by temperature measurements in the two observation wells. Emerging technologies, updated models, improved flexibility, and reduced costs will allow future reservoir monitoring with surface and borehole data in combination, or even with borehole data exclusively.