Exploration Geophysics - Volume 26, Issue 2-3, 1995

Conventional imaging of seismic data includes an approximate NMO and DMO prior to velocity analysis. The NMO and DMO imaging steps are approximate only in the sense that an approximate (simple) velocity field is used; the algorithms themselves are accurate. After velocity analysis, NMO is reapplied with the more detailed velocity field derived from the analyses. In the constant velocity case, DMO is almost independent of velocity and the iterative procedure described above plus post-stack migration yields an accurate image. The derived velocities may also be used for multiple suppression. Also, DMO itself may change the stacking velocities of dipping noise in such a way as to suppress the noise.

An improved approach to velocity estimation and imaging is to apply the conventional approximate NMO and DMO and then also to apply an approximate zero-offset time migration to each common offset dataset prior to velocity analysis (3D MOVES). After velocity analysis, the NMO is re-applied and the data stacked. Post stack, either a residual migration or full diffraction plus full time or depth migration is applied. The pre-stack migration is either a constant velocity or single function v(z) algorithm. This is consistent with the NMO, DMO approach of accurate algorithms in an approximate velocity field. The algorithms are fast and can be inverted post stack to allow depth migration.

The technique has been extensively used in 2D and 3D for imaging primaries and yielding accurate velocities. However, as with DMO, the derived velocity field may also be used for multiple suppression and the migration process may itself attenuate noise and multiples. For example, multiple diffractions may be focused and then attenuated in the stack process or with standard de-multiple methods. Alternatively, dipping noise and multiples may be migrated up dip and be located above the NMO mute pattern at middle and far offsets; the subsequent NMO, mute and stack remove the multiples from the data. In these applications, the migration process should be viewed as a transformation rather than an imaging tool, and the velocity used for migration need not be geologically correct, i.e. the velocity is a transformation parameter which is tuned to obtain the optimum noise suppression. Optimal imaging is obtained with residual, post-stack migration.

3D marine acquisition techniques which use multi-source, multi-cable methods have well known sampling and data processing problems. Low-fold acquisition and aliasing can be caused by the undersampling in shot, i.e. too large a shot interval. The use of multi-cable recording can result in irregular offset and azimuth distributions. In this paper we describe possible methods for handling some of these problems by use of pre-stack interpolation techniques.

Traditional seismic processing methods such as CMP stacking and predictive deconvolution often fail in the attenuation of long period multiples. Stacking often fails due to the lack of velocity differentiation between the multiple and surrounding events and because of the amplitude of the multiple reflections. Predictive deconvolution and Event Prediction (DePledge and Uren, 1992) fail because of the non-periodic nature of the multiples and to a lesser extent because of the variation of the wavelet with angle of incidence.

A four step procedure to precondition and attenuate surface related long period multiples has been devised. The first two steps of this procedure solve both the periodicity problem and the variation of wavelet with angle of incidence. The third step, therefore, is the attenuation of the surface related multiples using the standard techniques mentioned above. The remaining step is to reverse the transforms applied in the first two steps.

An example is given to demonstrate the performance of this method on field data. The procedure is simple, fast to apply and gives results superior to other existing techniques.

Lateral velocity variations in the subsurface are a departure from the simple horizontally layered model on which the extraction of NMO velocities and interval velocities are based. Significant differences between stacking velocity and interval velocity may result in complex geological areas when the estimation is based on this horizontally layered media assumption. In this paper methods are presented of velocity estimation that are both quick and accurate in the presence of lateral velocity variations.

The method developed here solves an analytic expression by fitting an unknown smooth velocity function, and also determines the reflector depth using only two simple assumptions: (1) that the ray in the laterally varying medium travels along the same path as in the homogeneous medium; and (2) that the subsurface velocity can be approximated by a smoothly varying lateral velocity function. Assumption (1) is shown to introduce only higher order correction terms to the travel time for a given source-receiver pair. It is demonstrated by assumption (2) how the use of a stable, smooth and continuous velocity function across the section results in a better migration velocity than a velocity analysis performed at an isolated CDP location.

By estimating the degree of lateral velocity variation across the seismic section at an early stage in the processing sequence, a decision on whether to use pre- or post-stack migration can be made with reliable velocity information. This method has the advantage of using an analytic expression for the travel time instead of complicated ray tracing by solving differential equations. This makes it useable in an interactive velocity analysis mode. An example using field data from the North West Shelf of Australia shows how the new travel time equation can improve the velocity analysis over a fault zone.

In marine seismic surveys, reverberations in the water layer known as multiples obscure primary reflections from deeper geological boundaries. This is especially a problem in areas of the North West Shelf of Western Australia, where the geology of the area can produce very strong multiple events, often with similar NMO velocity to primary events. Because of this lack of velocity discrimination, conventional multiple attenuation methods often fail.

An effective method of multiple attenuation using 1D Feedback Autoconvolution in the Radial Domain has been devised. This does not rely on a velocity discrimination between primary and multiple events, and can be applied interactively via a Motif X11 Graphical User Interface, and with minimal user input.

A radial transform has been written that converts either CMP or shot record data, to make both simple water bottom and pegleg multiples from a horizontal sea floor, periodic on each trace, and is suitable for the application of autoconvolution.

The extension of the radial transform to a dipping sea floor has been modelled using the mathematical modelling package MAPLE, and an approximate solution has been devised.

The technique of successive autoconvolution on each seismic trace in a feedback loop, predicts surface related multiple events, at the correct time, reverse polarity, and theoretically correct amplitudes. In practice a scaling algorithm has been incorporated to match the predicted multiples to the original data.

A program module to apply 1D Feedback autoconvolution on radial transformed data for both horizontal layer and dipping water bottom models has been developed, and applied successfully to both simple water bottom multiples and water bottom peg-legs.

Dip moveout (DMO) processing is frequently used to enhance stacked seismic sections. All DMO methods strictly require that the input data have been normal-moveout (NMO) corrected using the true medium velocity rather than the stacking (or RMS) velocity function. Unfortunately this is rarely the case in that most data which are input to DMO have been NMO-corrected according to the stacking velocity, in order to maximise semblance on a CMP gather. Such data are incompatible with the basic DMO assumption. Under such circumstances only a partial DMO process, which produces a parabolic impulse response, should be used rather than a full DMO algorithm, such as that of Hale, which entails an elliptical impulse response. The partial DMO operator accounts for the inaccuracy of the velocity information used in the NMO correction, and leads to superior results.

A fundamental assumption in seismic reflection processing is that the spikes comprising the earth’s reflectivity series are randomly distributed in time, and hence exhibit a white (flat) power spectrum. The validity of this assumption is examined via spectral analysis of log data from the Amadeus, Surat and Bowen Basins, Australia. Reflectivity spectra generated over entire wells from each of these basins are distinctly non-white, supporting observations from previous overseas studies. Typically such whole-well spectral slopes range from 0.5 in the Bowen Basin, up to 1.5 in the Surat Basin, a somewhat broader range than observed in previous investigations.

A more detailed analysis of spectra within individual geological formations has also been undertaken. It has previously been suggested that non-repetitive, randomly-bedded sedimentary rocks might be expected to possess whiter reflectivity spectra than more cyclic sedimentary deposits. In the Amadeus and Surat Basins, spectral slopes are typically moderate to high in sandstone formations, while smaller slopes are found in formations comprising finer-grained materials. In the Bowen Basin, formation spectra exhibit a greater range of slopes as a consequence of coal seams occurring in a variety of stratigraphic relationships with other lithologies. For example, thick composite seams comprising interbedded coals and shales can generate very steep spectra. Conversely, thin isolated coal seams have a strong whitening influence on spectra. Whilst such coal-seam related influences may be obvious in log data, not all controls on formation spectra are evident in the time domain. For example, relatively low amplitude reflectivities can also generate strongly non-white spectra. This is because it is the distribution of spikes in time which influences the degree of non-randomness.

Fine-tuning of deconvolution to account for non-random behaviour may be feasible in regions where spectral character is constant over significant depth ranges. However, stratigraphic controls on spectral character are quite subtle, and true formation-based deconvolution will be non-trivial.

In recent years, generalised linear inversion or GLI, has been used to process seismic refraction data in order to determine the long wavelength statics correction not adequately addressed by residual statics routines. With GLI, a model of the subsurface is refined after comparing the traveltimes of the model with the field data. This approach of constructing a model which agrees with the data is known as Backus-Gilbert construction. Unfortunately, it does not produce a unique solution. Furthermore, the forward modelling aspect using ray tracing is of questionable efficacy because of incomplete knowledge of the surface layer velocities as a function of depth and direction, the widespread occurrence of diffractions with irregular refractors, and inadequate spatial sampling. Furthermore, the accuracy of the inversion can be poor with complex weathering problems.

An alternative approach is the formation of linear combinations of the data to generate unique averages of the model. This is known as Backus-Gilbert appraisal, and includes the GRM. However, the spatial sampling employed with most CMP acquisition programs precludes the use of any detailed refraction method, such as a fully optimised GRM approach. Instead a migration distance of a single station separation is used to compensate for the effect of the extended receiver array, to produce an effective CRM model.

The CRM linear averages, also known as time-depths, are converted to a weathering replacement correction, using a ratio which is a function of the ratio of the weathering and sub-weathering seismic velocities. These CRM corrections are within a few milliseconds of the values computed with a fully optimised GRM approach.

Crosswell and VSP seismic survey data are frequently contaminated by coherent noise trains in the form of direct tube waves and tube-wave-to-body-wave conversions. The problem was especially acute in a recent high resolution underground seismic experiment that was conducted in a hard rock environment. Conventional processing, such as f-k filtering, was ineffective in suppressing such noise events.

A procedure, based on singular value decomposition (SVD) of a seismic section, was employed for cancelling coherent tube-wave related noise. An eigen-analysis splits the section into linearly independent eigenimages. Each eigenimage is a characteristic content of the seismic record. Its energy contribution to the total energy of the seismic section is represented by the magnitude of its corresponding eigenvalue. The leading eigenimages, obtained after windowing and flattening, represent high amplitude and correctable energies such as tube wave noise. The trailing eigenimages represent low amplitude and least correctable energy such as random background noise. Useful records can be extracted by subtracting those eigenimages dominated by the noise from the total seismic gather.

The optimal removal of the tube waves requires the amplitude balancing of traces and the precise alignment of the tube wave event across the traces before eigen-analysis. The procedure is illustrated through application to reversed VSP data acquired in a metalliferous mine. Superior results are obtained in comparison to that of a conventional f-k filter.