Predictive Deconvolution Research Articles

Single‐channel digital filter design for seismic applications

A general least‐squares, time‐domain filter design methodology has been developed that is easy to use for a variety of seismic filtering applications. The 1-D finite‐impulse response frequency filter can efficiently provide the noise attenuation and selectivity needed in modern data processing. Flexibility of design allows a choice of all basic types of single‐channel filters commonly used in processing. These include low‐pass, high‐pass, band‐pass, band‐reject, and notch filters. In addition, multiple bands may be passed or rejected using a single operator design without increasing the length of the filter. The ability to reject multiple noise bands with one filter is convenient and also reduces data processing costs. The filter can be viewed as a minimum‐phase Wiener‐Levinson predictive deconvolution filter designed to reject specified frequency bands. The filter is designed from an exact mathematical description of the specified stop bands that provide an explicit expression for the required autocorrelation lags in the normal equations. The filter’s desired frequency response (transition zone width and rejection level) is simply related to two input parameters—operator length and white noise level.

Discrete plane‐wave decomposition by least‐mean‐square‐error method

The recording of a point source wavefield can be decomposed into a set of plane‐wave components, each corresponding to different angles of propagation. Such plane‐wave seismograms have a far simpler structure than the spherical waves of the point source records, which makes them desirable in many steps of seismic data processing such as predictive deconvolution, migration, inversion, etc. The implementation of the plane‐wave decomposition requires the computation of the Radon transform in the discrete data domain. A straightforward application of the integral solutions to geophysical problems fails to compensate for the sampled and limited aperture nature of the actual data. In this paper, we give a new method in which the x-t domain is shown to relate to the p-τ domain by a linear system of equations in the time‐space domain. An iterative least‐mean‐square‐error method is introduced to solve the set of equations. This method is combined with a unique method of alias suppression which uses the reasonable range of dips possible at a given (x, t) location and acts as interpolation of the x-t data. This combination improves the initial estimates and speeds up convergence. Our transform is independent of the number of plane‐waves and selected ray parameter range. We present synthetic and real data examples to demonstrate the accuracy and robustness of the method. The examples are compared against results using the generalized Radon transform approach used by Beylkin (1987) and against conventional slant stack.

Identifying Multiples on Seismic Sections

One of the most serious difficulties faced by geophysicists when interpreting seismic sections from areas like the Northwest Shelf of Australia is the problem of distinguishing multiples from primaries. Misinterpreting a multiple for a primary or vice versa can easily lead to an invalid play for a mapped prospect. Current techniques for identifying multiples on migrated sections are based on periodicity or dip and tend to be speculative and ambiguous. Conflicting dips can not always be resolved by associating one event with a multiple from higher in the section. Identifying an event as part of a reverberation is difficult, especially if processes like predictive deconvolution have been applied pre-stack to suppress periodicities. Correlation with synthetics can also be used when well data are available, but even then the interpreter is rarely able to identify multiple events with certainty. The root of the problem is that current seismic processing techniques for multiple suppression are not fully effective. To demonstrate this, percentage differences in wavelet amplitudes between stack sections produced with and without processes like f-k demultiple are shown. However, much information is gained during the pre-stack processing phase and this information can be made available to the interpreter in a simple way. Multiples and primaries can often be separated with less ambiguity on CMP gathers (during velocity analysis) than they can be after stack. A colour overlay technique is proposed which labels events (both primaries and multiples) on the section by velocity. This labelling is derived during velocity analysis from the deviation of semblance peaks from those corresponding to the primary velocity function. These event labels depend on the choice of primary velocity function and the pre-processing leading up to velocity analysis. The parameters are investigated for key processes used for velocity analysis, such as f-k demultiple, and it is shown how parameter selection in velocity pre-processing affects the interpreter's final decision as to what is a primary and what is a multiple event. The application of these techniques to data from the Timor Sea is presented as a case study. A seismic section with a colour-coded overlay is used to demonstrate how an interpreter may incorporate this extra information to decide on two opposing geologic models for a line.

Digital Reprocessing of Shallow Seismic Data from the Great Barrier Reef

The feasibility of transferring conventional reflection processing techniques to analog, shallow-marine seismic surveying has been assessed. The test data are of high-resolution boomer profiles recorded on the Great Barrier Reef. The analog data were digitised using an off-the-shelf, PC-based converter, provided appropriate precautions are observed with respect to timing accuracy, sampling, and dynamic range. The raw digitised data exhibited trace-to-trace timing shifts which could be attributed to changes in the relative vertical positions of boomer and hydrophone streamer. Such static errors were significantly reduced using a conventional pilot-trace residual statics' algorithm. An alternative algorithm which does not use a pilot trace, and whose model is more specifically tailored to the single-fold problem at hand, provided subtle, though significant, enhancement when compared to the pilot-trace technique. Predictive deconvolution was not appropriate owing to failure of required assumptions. On the other hand, deterministic signature deconvolution was successfully applied.Dominant-horizon extractions on the water bottom, and on the prominent Pleistocene reflector, indicate that the intrinsic signature is consistent laterally and temporally. An optimum Wiener spiking filter, designed on the extracted signature, significantly simplified the reflection structure on the test section.

Characteristics and processing of seismic data collected on thick, floating ice: Results from the Ross Ice Shelf, Antarctica

Coincident reflection and refraction data, collected in the austral summer of 1988/89 by Stanford University and the Geophysical Division of the Department of Scientific and Industrial Research, New Zealand, imaged the crust beneath the Ross Ice Shelf, Antarctica. The Ross Ice Shelf is a unique acquisition environment for seismic reflection profiling because of its thick, floating ice cover. The ice shelf velocity structure is multilayered with a high velocity‐gradient firn layer constituting the upper 50 to 100 m. This near surface firn layer influences the data character by amplifying and frequency modulating the incoming wavefield. In addition, the ice‐water column introduces pervasive, high energy seafloor, intra‐ice, and intra‐water multiples that have moveout velocities similar to the expected subseafloor primary velocities. Successful removal of these high energy multiples relies on predictive deconvolution, inverse velocity stack filtering, and frequency filtering. Removal of the multiples reveals a faulted, sedimentary wedge which is truncated at or near the seafloor. Beneath this wedge the reflection character is diffractive to a two‐way traveltime of ∼7.2 s. At this time, a prominent reflection is evident on the southeast end of the reflection profile. This reflection is interpreted as Moho indicating that the crust is ∼21-km thick beneath the profile. These results provide seismic evidence that the extensional features observed in the Ross Sea region of the Ross Embayment extend beneath the Ross Ice Shelf.

Multiple Suppression By a Wave-equation Extrapolation Method

The wave-equation-based multiple suppression method, unlike predictive deconvolution and stacking, makes no assumptions on periodicity or moveout patterns of multiples, and can cope with complex sea-bottom and sea-surface variations. It entails multiple prediction by wave equation extrapolation of the seismic data and then multiple subtraction from the recorded seismograms. In general, the multiple subtraction method requires the calculation of a subtraction scalar (a reflection coefficient function), which is a function of the ratio of the original data to the extrapolated multiple model traces. The success of the method depends on establishing the correct scalar. However, it is difficult to get a good subtraction scalar when the wavelet of the original data is different from that of the multiple model traces. This occurs for the long offset traces because of geophone ghosting, and changes of amplitude and phase in the reflection waveform beyond the critical angle. In this paper, we develop a superior alternative scheme, based on a simple 2-D Butterworth-type gain function, calculated from the original data and the (extrapolated) multiple model data. This gain function will attenuate the multiples and preserve the primaries. A simple synthetic example is used to demonstrate the efficacy of the method in multiple suppression.

The output of predictive deconvolution

The method of predictive deconvolution, with prediction distance greater than unity, is widely used in the oil industry to eliminate multiple reflections from seismic reflection data. When the prediction distance is unity the method corresponds to autoregressive modeling. In this case the output of the deconvolution becomes the reflectivity series of the subsurface for a minimum‐phase wavelet. For prediction distances greater than unity, prediction filters are related recursively (Ulrych et al., 1973). We show that another interesting relationship exists between the autoregressive prediction error operator and the prediction error operator with arbitrary prediction distance. This relationship can be used to investigate the output of predictive deconvolution applied to nonminimum‐phase wavelets. As a consequence, we can show that predictive deconvolution and the phase correction method for Vibroseis data (Ristow and Jurczyk, 1975) are nearly identical.

Migration of wide‐angle seismic reflection data from the Grenville Front in Lake Huron

Under the auspices of the Great Lakes International Multidisciplinary Program on Crustal Evolution (GLIMPCE), coincident steep‐ and wide‐angle seismic reflection data sets were acquired in Lake Huron. The wide‐angle data were recorded at stationary onshore receivers during the shooting and recording of the conventional marine steep‐angle survey. To extract information from the wide‐angle data, a variety of processing techniques including automatic trace editing, amplitude balancing, F‐K filtering, static corrections, and predictive deconvolution were applied to the wide‐aperture common‐receiver gather before migration. The application of a slowness‐weighted depth migration algorithm, which was first tested on synthetic data and which included a slowness filter, resulted in an image of the Grenville Front tectonic zone (GFTZ) remarkably similar to that observed in the multichannel steep‐angle section. The migrated wide‐angle data suggest that prominent bands of east dipping seismic reflections observed across the GFTZ extend unattenuated to depths of at least 45 km.

Gaussian scaling noise model of seismic reflection sequences: Evidence from well logs

A simple model for reflection series is desirable for two reasons: first, to have a means of generating model reflection sequences on which to test geophysical data processing techniques, specifically methods of predictive deconvolution, and second, to suggest a way of parameterizing real reflection sequences for classification and further geologic study. In this note we wish to discuss a model suggested by Hosken (1980); our discussion is founded upon the powerful ideas of self‐similarity and scaling developed by Mandelbrot (1983) and on the paucity of typical lengths in geology. Typical lengths are common in physics problems; for example, the length of an organ pipe governs the wavelengths of the notes played. When taking photographs, geologists include some manmade object to give scale to the photo. Otherwise it is very hard to tell if, say, folds are of centimeter size or form whole mountains.

EFFECTIVENESS OF WIDE MARINE SEISMIC SOURCE ARRAYS1

AbstractIn recent years, the use of wide source arrays in marine seismic surveys has been a topic of interest in the seismic industry. Although one motivation for wide arrays is to get more guns in a source array without increasing the in‐line array dimension, wide arrays can also provide the benefit of suppressing side‐scattered energy. Comparisons of common midpoint (CMP) stacks of data acquired offshore Washington and Alaska with wide and conventional‐width source arrays, however, show only small and sometimes inconsistent differences. These data were acquired in areas where side‐scattered energy is a problem. Comparisons of pre‐stack data, however, show substantial differences between the wide and conventional source array data.The disparity between the stacked and prestack data is explained by analysing the effective suppression of back‐scattered energy by CMP stacking. Energy reflected from scatterer positions broadside to a given CMP location has a lower stacking velocity than that of the primary reflection events. Thus, CMP stacking attenuates the side‐scattered energy. In both survey areas the action of CMP stacking was so powerful in suppressing the broadside energy that the additional action of the wide array was inconsequential in the final stacked sections. In other areas, where the scattering velocity is comparable to the primary stacking velocity, wide arrays could provide considerable advantage.Even though CMP stacked data from wide and conventional‐width arrays may appear similar, the reduced amount of side‐scattered energy in wide‐array prestack data may provide a benefit for data dependent processes such as predictive deconvolution and velocity analysis. However, wide arrays cannot be used indiscriminately because they can degrade cross‐dipping primary events. They should be considered primarily as a special tool for attacking severe source‐generated noise from back‐scattered waves in areas where the action of CMP stacking is insufficient.

Processing and attenuation of noise in deep seismic-reflection data from the Gulf of Maine

The U.S. Geological Survey deep crustal studies reflection profile across the Gulf of Maine off southeastern New England was affected by three sources of noise: side-scattered noise, multiples, and 20-Hz whale sounds. The special processing most effective in minimizing this noise consisted of a combination of frequency-wavenumber (F-K) filtering, predictive deconvolution, and spectral whitening, each applied in the shot domain (prestack). Application of the F-K filter to remove side-scatter noise in the poststack domain resulted in a much poorer quality profile. The prestack noise suppression processing techniques resulted in a reflection profile with good signal-to-noise ratios and reliable strong reflections, especially at depths equivalent to the lower crust (24–34 km). Certain geologic features, such as a buried rift basin and a crustal fault are resolved much better within the upper crust after this processing. Finite difference migration of these data using realistic velocities produced excellent results. Migration was essential to distinguish between abundant dipping and subhorizontal reflections in the lower crust as well as to show an essentially transparent upper mantle.

Multiple attenuation: some current techniques

Multiple attenuation techniques have to be based on some difference between the multiples and the primary reflections. The two major differences that are exploited are firstly velocity, and secondly the fact that multiples are periodic sequences of events, and hence are predictable, while the primaries are non-periodic. The widely used frequency-wavenumber (F-K) domain techniques rely on velocity difference only, but a recent variation of this method also makes use of any difference in dip between primaries and multiples to give significantly greater multiple attenuation. For short period multiples, velocity differences may be insufficient for much attenuation, and the process has to be based on the multiple's periodicity, using some type of long predictive deconvolution operator. One problem with this approach is that the multiple period varies with time, particularly at long offsets. Transforming the record to the tau-p domain removes this variation however, allowing more effective deconvolution of the multiples. Another recent approach is to model a multiples-only record by wave equation methods, and subtract it from the recorded data. At present however, this is limited to well defined multiple generators, such as the water layer. With the variety of multiple attenuation processes available today, the geophysicist needs to understand the types of multiple problem to which each is most suited, in order to select the technique most applicable to his data.

Source directivity and its effects on resolution and signature deconvolution

When a source pattern is directional, particularly in the 'in-line' direction, serious losses of high-frequency data can occur in the recorded signal at large offsets. Furthermore, since source directivity increases with frequency, signature deconvolution becomes less and less effective as one moves up the frequency band. In this artiele a controlled marine field experiment is described where the same line was shot with two source arrays, the only variable being the in-line dimension of the source pattern. Though the source was waterguns, the author believes that either sleeve airguns or marine vibrators would also have the required bandwidth to demonstrate the effect illustrated. Raw field records from the two source arrays, which have overall lengths of 30 and 10 m, are compared after filtering with a narrow bandpass filter. Thereafter constant offset sections with signature deconvolution and predictive deconvolution applied are compared for the same offsets.

Modeling and processing of scattered waves in seismic reflection surveys

Various wave‐scattering mechanisms are known to degrade reflection signals by producing noise in seismic reflection data. Synthetic 2-D acoustic‐wave finite‐ difference data sets illustrate the effects of two such mechanisms. Twenty‐five shot gathers were generated for each of two models and the data were processed as standard CMP surveys. In one model, an irregular low‐ velocity surface layer produced multiply scattered surface waves that appear as linear noise trains in common‐shot gathers and stacked sections. The scattering of upcoming reflections at the lower interface of the layer also produced a significant amount of noise. When predictive deconvolution was applied before stack to reduce reverberations, the spectral character of the scattered surface waves seriously inhibited the action of that process. In the second model, a zone of smooth, random velocity variation was imposed between two reflectors deeper in the model. The heterogeneous zone (±5 percent rms velocity variation) substantially degraded the signal reflected from below it; events produced by body‐wave scattering are characterized by higher phase velocities than those seen in the first model. Conventional CMP stacking produced discontinuous subhorizontal events from the disturbed zone. The limited bandwidth of the propagating signal and spatial filtering attributable to CMP stacking cause these events to bear no simple relation to the velocity anomalies of the model, even after migration.

CORRECTING FOR COLOURED PRIMARY REFLECTIVITY IN DECONVOLUTION1

ABSTRACTStatistical deconvolution, as it is usually applied on a routine basis, designs an operator from the trace autocorrelation to compress the wavelet which is convolved with the reflectivity sequence. Under the assumption of a white reflectivity sequence (and a minimum‐delay wavelet) this simple approach is valid. However, if the reflectivity is distinctly non‐white, then the deconvolution will confuse the contributions to the trace spectral shape of the wavelet and reflectivity.Given logs from a nearby well, a simple two‐parameter model may be used to describe the power spectral shape of the reflection coefficients derived from the broadband synthetic. This modelling is attractive in that structure in the smoothed spectrum which is consistent with random effects is not built into the model. The two parameters are used to compute simple inverse‐ and forward‐correcting filters, which can be applied before and after the design and implementation of the standard predictive deconvolution operators. For whitening deconvolution, application of the inverse filter prior to deconvolution is unnecessary, provided the minimum‐delay version of the forward filter is used.Application of the technique to seismic data shows the correction procedure to be fast and cheap and case histories display subtle, but important, differences between the conventionally deconvolved sections and those produced by incorporating the correction procedure into the processing sequence. It is concluded that, even with a moderate amount of non‐whiteness, the corrected section can show appreciably better resolution than the conventionally processed section.

Deconvolution filter in seismic data processing.

Information of importance in reflection seismic method resides in the reflectivity series. In order to extract this information from obtained data, a deconvolution filter is the core of seismic data processing. Since whitening deconvolution was first introduced by Robinson1), it has been used in the oil industry on a routine basis. Whitening deconvolution is based on following assumptions: (1) A reflectivity series is an uncorrelated random series. (2) A seismic wavelet is minimum phase. Deconvolution outputs, however, ofter show that the minimum phase assumption on seismic wavelet is incorrect. In this paper we deeply investigate in depth this assumption and consider several types of deconvolution methods. Predictive deconvolution can be applied to both minimum and non-minimum phase wavelets and it is equivalent to phase correction method2), 3) for Vibroseis data, in a mathematical sense. In the case of whitening deconvolution, to obviate the minimum phase assumption, a statistical wavelet estimation approach, 4) using property of reflectivity series, is explained.

The critical reflection theorem

In predictive deconvolution of seismic data, it is assumed that the response of the earth is white. Any nonwhite components are presumed to be caused by the source wavelet or by unwanted multiples. We show that this whiteness assumption is invalid at precritical incidence. We consider plane waves incident on a layered acoustic half‐space. At exactly critical incidence at any interface in the half‐space, the lower layer acts similar to a rigid plate. The response of the half‐space is then all‐pass, or white. This result we call the critical reflection theorem. The response is also white if the waves are postcritically incident on the lower half‐space. In normal data processing these postcritical components are removed by muting. Thus the whiteness assumption is normally applied to exactly that part of the data where it is invalid. The demarcation between precritical and postcritical incidence can be exploited for the purposes of deconvolution, provided the data can be decomposed into plane waves. To develop this application, we consider the response of a point source in the uppermost layer of the layered half‐space, with a free surface above. The response is simply a superposition of the plane‐wave responses already studied, with complications introduced by the source and receiver ghosts and by multiples in the upper layer. At postcritical incidence the earth response is white for all plane‐wave components; the source spectrum may be estimated from the postcritical plane‐wave components after removing the effects of ghosts and multiples in the upper layer. If the source signature is already known, the demarcation criterion can be used to separate intrinsic absorption effects from attenuation effects caused by scattering.

Imaging deep reflectors in the presence of signal-generated noise

Summary. In contrast to the continuous character of reflectors seen in seismic data from the sedimentary column, a pervasive feature of deep crustal reflections is their laterally discontinuous nature. Deep reflections often appear on the seismic section as groups of flat-lying or dipping segments. The length of the individual segments may vary by an order of magnitude. Moreover, the segments are often shorter than the Fresnel zone for a specular reflection. The apppearance of deep flat-lying reflectors of this type has motivated geologic hypotheses of a layered and heterogeneous lower crust. Dipping bands of discontinuous reflectors are interpreted variously as decollement surfaces, sutures, or faults penetrating to midcrustal or deeper levels. A significant geophysical concern is whether truly discontinuous reflectors in the deep crust can be distinguished from an inaccurate or incoherent image. Incoherence can result from the presence of signal-generated noise created at the earth's surface or along the transmission path. Given the types of signal-generated noise likely to be present in deep crustal data, we wish to know how well we can resolve both laterally continuous and discontinuous reflectors using standard reflection data acquisition and processing. To test the effects of such noise on the CMP stack we have conducted finite-difference synthetic seismogram experiments for two similar layered models each having two specular reflectors. One model contained an irregular surface layer, the other contained a zone of random velocity fluctuations between the two reflectors. We processed the data normally, from shot gather to CMP stack and migrated section. The two numerical experiments produced CMP sections with substantially different character. Processing the surface model data produced a clear image of the two deep reflectors as the CMP stack suppressed noise generated in the irregular surface layer. The surface generated noise limited the vertical resolution as it degraded the action of predictive deconvolution applied before stack. Signal-generated noise in the second model did not affect the deconvolution process because the scatterers were located below the zone of surface layer reverberations. The laterally inhomogeneous zone degraded the image of the deepest reflector. The signal-generated noise in the second model may be viewed as signal reflected from the random zone. The dip-filtering action of the CMP stack resulted in reflection events from the random zone having greater horizontal continuity than is present in the velocity model, causing further smearing by a standard time-migration technique.

To: “The use of the conjugate‐gradient algorithm in the computation of predictive deconvolution operators,” by Fulton Koehler and M. Turhan Taner, which appeared in the December 1985 issue of GEOPHYSICS, p. 2752–2358:

Several errors have been detected in the article To: “The use of the conjugate‐gradient algorithm in the computation of predictive deconvolution operators,” by Fulton Koehler and M. Turhan Taner, which appeared in the December 1985 issue of Geophysics, p. 2752–2358:

The F-X plot: Uses for seismic data analysis and quality control

Examination of the autocorrelation functions of seismic traces is widely used to obtain information to be used in the design of deconvolution operators. The length of gap to be used in predictive deconvolution, for example, may be determined from the time-lags at which zerocrossings occur in the autocorrelation functions (Peacock & Treitel, 1969). In order to determine by how much autocorrelation functions vary between traces, the autocorrelation may be appended to the seismic trace so that the trace and its autocorrelation function may be examined together. With the advent of the Fast Fourier Transform (FFT), frequency domain deconvolution procedures become practicable. In this domain, the log of the amplitude spectrum is used to design the amplitude and phase spectrum of the deconvolution operator. Hence it is useful to be able to examine the log spectra of traces in order to specify the frequency domain deconvolution parameters correctly. The BMR in-house seismic processing system (Brassil et al., 1986) made extensive use of frequency domain processing, and for this reason a facility for appending the log of the amplitude spectrum to seismic traces was developed. An appropriate name for this type of display is an F-X plot, as it shows the frequency content of the traces as a function of position. Such displays were first used in the optical processing of seismic data (Jackson, 1965) and some use was made of the displays for interpretation (Fitton & Dobrin, 1967), but this is believed to be the first application to digital data. During the use of this facility for deconvolution parameter estimation, it became clear that F-X plots had a much wider use for data quality control, and this paper aims to draw attention to some of these applications.