Ray Abma

3D interpolation of irregular data with a POCS algorithm

Seismic surveys generally have irregular areas where data cannot be acquired. These data should often be interpolated. A projection onto convex sets (POCS) algorithm using Fourier transforms allows interpolation of irregularly populated grids of seismic data with a simple iterative method that produces high-quality results. The original 2D image restoration method, the Gerchberg-Saxton algorithm, is extended easily to higher dimensions, and the 3D version of the process used here produces much better interpolations than typical 2D methods. The only parameter that makes a substantial difference in the results is the number of iterations used, and this number can be overestimated without degrading the quality of the results. This simplicity is a significant advantage because it relieves the user of extensive parameter testing. Although the cost of the algorithm is several times the cost of typical 2D methods, the method is easily parallelized and still completely practical.

Lateral prediction for noise attenuation by t-x and f-x techniques

Attenuating random noise with a prediction filter in the time-space domain generally produces results similar to those of predictions done in the frequency-space domain. However, in the presence of moderate- to high-amplitude noise, time-space or t-x prediction passes less random noise than does frequency-space, or f-x prediction. The f-x prediction may also produce false events in the presence of parallel events where t-x prediction does not. These advantages of t-x prediction are the result of its ability to control the length of the prediction filter in time. An f-x prediction produces an effective t-x domain filter that is as long in time as the input data. Gulunays f-x domain prediction tends to bias the predictions toward the traces nearest the output trace, allowing somewhat more noise to be passed, but this bias may be overcome by modifying the system of equations used to calculate the filter. The 3-D extension to the 2-D t-x and f-x prediction techniques allows improved noise attenuation because more samples are used in the predictions, and the requirement that events be strictly linear is relaxed.

Comparisons of interpolation methods

The purpose of this article is to illustrate the characteristics of various interpolation methods. Seismic data need to be interpolated when the spatial sampling of acquired data is coarser than the spatial sampling required for a multichannel process. This multichannel process can be as simple as stacking traces to reduce coherent noise or as complex as prestack depth migration. Interpolation requires some assumptions about the character of the seismic data. One assumption in the methods considered for this article is that seismic events are linear. In practice, the data are not perfectly linear, and we will show later the results of violating the assumption of linearity.

Comparisons of adaptive subtraction methods for multiple attenuation

Coherent noise may be removed from seismic data by first making an approximate model of the noise, then producing an even better estimation of the noise by adaptively matching the modeled noise to the data. This modified model of the noise may then be subtracted from the data, eliminating most coherent noise. The success of this approach depends both on how well the initial model matches the true noise and the success of the adaptive matching in modifying the initial noise prediction to match the true noise. The adaptive matching step is complicated by the presence of the signal and other noise in the data. In this article, the noise of interest is surface-related multiples, although other types of coherent noise may be removed with this approach.

An Analysis On the Simultaneous Imaging of Simultaneous Source Data

Simultaneous source acquisition is gaining more and more interest in the seismic industry due to the possibility of increasing acquisition efficiency and reducing cost. The simultaneous source data could be simultaneously imaged without going through the pre-separation step. One challenge for this simultaneous imaging approach is the undesired crosstalk artifacts. Understanding the origin and nature of this type of noise is important for practical reasons. We start from the modeling and migration equations for conventionally acquired data, and by introducing the concept of “effective” source we extend these equations naturally to simultaneous source data. The crosstalk term presented in the migration equation is analyzed. Assuming the source time delay is a uniform random variable within a certain range, we show that the product of the angular frequency and the range of source time delay plays an important role in “modulating” the crosstalk noise. This might help us to gain some insights on the simultaneousimaging related methods. As a numerical experiment we applied the simultaneous imaging approach to a 2D synthetic simultaneous source dataset. The migration image is close to the conventional migration image.

Independent Simultaneous Sweeping In Libya -full Scale Implementation And New Developments

Recent developments in recording systems allow for a recording spread to be continually active, which we refer to as continuous recording, although it may be more accurately described as recording of a set of contiguous records. This removes the necessity for real time synchronization of sources and recording systems. As long as the continuously recorded data and the source initiation can both be linked to the same time standard, (e.g. GPS time) the traditional shot records can be combed from the continuous dataset at any later stage. We have used the benefit of continuous recording to operate a large number of sources simultaneously on a large recording spread thereby greatly improving the productivity of land acquisition.

Issues in multi-dimensional interpolation

Interpolation of seismic data with multi-dimensional algorithms can produce high quality results. The improvements noted in moving from 2-D to 3-D interpolation suggest that moving from 3-D to 4-D and 5-D interpolation may increase the quality of POCS (Projection Onto Convex Sets) interpolation even more. While this increased capability may help reduce acquisition costs and improve the seismic images created, 5-D interpolation does not always improve the interpolation.

Comparisons of interpolation methods in the presence of aliased events

The need for a process that interpolates beyond aliasing is illustrated by comparing the input in Figure 1 and the simple zero-padded FK interpolation in Figure 2. While the unaliased horizontal event is handled well, the badly aliased dipping event is interpolated poorly. Much of our recorded data contains aliased energy, and simple adjustments, such as NMO, do not always unalias data with overlapping signals such as primaries and multiples, which are often aliased with respect to each other. The methods considered here assume linear events; we will not attempt to consider interpolations that involve parabolic or hyperbolic paths.

Enhancements to prestack frequency‐wavenumber (f-k) migration

Prestack frequency‐wavenumber (f-k) migration is a particularly efficient method of doing both full prestack time migration and migration velocity analysis. Conventional implementations of the method, however, can encounter several drawbacks: (1) poor resolution and spatial aliasing noise caused by insufficient sampling in the offset dimension, (2) poor definition of steep events caused by insufficient sampling in the velocity dimension, and (3) inadequate handling of ray bending for steep events. All three of these problems can be mitigated with modifications to the prestack f-k algorithm. The application of linear moveout (LMO) in the offset dimension prior to migration reduces event moveout and hence increases the bandwidth of non‐spatially aliased signals. To reduce problems of interpolation for steep events, the number of constant‐velocity migrations can be economically increased by performing residual poststack migrations. Finally, migration with a dip‐dependent imaging velocity addresses the issue ...

Fundamentals of 3-D migration, Part 1

This is a tutorial on 3-D migration of seismic data. Subsurface geological features of interest in hydrocarbon exploration are three dimensional in nature. Examples are salt diapirs, overthrust and folded belts, major unconformities, and deltaic sands. The 2-D seismic section is a cross‐section of the 3-D seismic wave field. It contains signals from all directions, including out‐of‐plane of the profile (sideswipe energy). This sideswipe energy can only be handled by 3-D migration of 3-D seismic data.