David J. Monk

Prediction Filtering For 3-D Poststack Data

In designing operators for random noise suppression the following factors are important: uniqueness of operators, insensitivity of the operators to the size of the gate used in their derivation, shortness of operators in all directions, abrupt event termination handling and amplitude variations handling. one less term than the previous lag, small data gates, say 10 traces, give unacceptable prediction error filters with this technique. That is, this approach can’ t even predict one event exactly if the data gate is short( Harris and White, 1991). Gulunay (1986a) similarly used windowed auto-correlations but a different approach to the solution (complex Wiener filter design). He observed that the shortness of the desired output by one sample caused significant prediction errors for small space gates and suggested a hybrid method named “fxdecon” (now used as a generic name) which keeps an extra trace to use in forming the cross-correlation on the right-hand side of the normal equations. The resultant filters are not necessarily minimum-phase. This approach reduces the gate effect to zero for the special case of one event. b)One dimensional noncausal prediction filters for 2D stack data In the frequency domain spatial prediction filtering, operators are generally designed as forward prediction filters through the use of Yule-Walker equations. They are then halved, conjugate flipped and placed in front of the forward filter with one zero in between. The resulting operator is zero phase. We will call such operators “pseudo-forward-backward operators”. As demonstrated in this work, true forward-backward prediction filters (designed using noncausal normal equations) seem to satisfy all of the above criteria much more than their pseudo forwardbackward counterparts. INTRODUCTION Prediction filtering in two dimensions has recently been used for post stack 3-D data (Chase, 1992). Filters of this method are different but similar to pseudo forward backward filters. We use a true forward-backward (ie. noncausal) design technique which has some interesting properties. Before introducing our method we review the previous work on one dimensional forward prediction filters used in the industry. We then introduce one dimensional forward-backward filters. a)One dimensional forward prediction filters for 2-D post stack data One dimensional post stack random noise elimination filters were first introduced by Canales (1984). This approach follows Claerbout (1976), and uses auto-correlation lags . . ) for the prediction error filter (1 , . . ). Resulting prediction error operators are minimum phase in the space direction (forward). The normal equations resulting from this approach are also known as (preand post-) windowed Yule-Walker equations ( Kay and Marple, 1981) and can only predict “impulsive” (minimum phase) inputs or impulsive components of the input (impulsive series are also known as autoregressive or AR processes). The normal equations for the prediction error filter involve auto-correlation lags ( . on the left-hand side of the normal equations and a spike at zero lag on the right-hand side. (The corresponding normal equations for the prediction filter involve auto-correlation lags ( . on the left-hand side and lags , l . . on the right-hand side of the normal equations.) Since each auto-correlation lag involves Because dips are handled properly during filter design, there is no danger of moving events laterally with forward prediction filters. However, residues from unpredictable components, such as sudden truncations in data, move energy forward with the application of forward filters. Therefore it is important to do the processing either both in forward and reverse directions (Gulunay, 1986b) or with zero phase filters in the space direction. This requirement is known to be equivalent to conjugate symmetry in the filter: = for k = 1 In going from one-sided (causal) prediction filters

Random And Systematic Navigation Errors: How Do They Affect Seismic Data Quality?

A quantitative analysis has been performed to assess the effect of navigation errors on marine Seismic data. Two different types of errors were considered The first is a systematic error, that of a rotation of the streamer coordinates which could be caused for example by incorrect magnetic declination The second type models the random errors in the receiver positions due to the limited accuracy of the navigation network. The analysis is performed as a function of streamer feather angle, structural dip, and acquisition parameters. The effects on the seismic data are reported in terms of stack degradation and difference in the apparent NMO velocity. To assess the effect of a rotational error on the final image, we process a synthetic seismogram consisting of a dipping event and a diffractor through DMO and migration. Significant stack degradation as a consequence of a systematic rotational error is found only for lines shot in alternating directions in the presence of notable crossline dip. In all other cases the error is either absorbed by the NMO velocity or inconsequential because of small crossline dip. Stack degradation caused by random position errors are weakly dependent on the crossline dip and can be minimized by collecting the lines with the boat driving in the down dip direction. The changes in the resolution and position of the final image depend on the velocity which is used. For an inline of a survey shot along strike the use of true material velocity minimizes the impact of the rotational error while use of the apparent NMO velocity leads to a significant stack degradation. The misposition is about half a trace laterally and 5 and 10 ms in time for the true velocity and NMO velocity case, respectively. Other cases will be discussed. INTRODUCTION While the effects of streamer feather on binning and stacking of seismic data have been studied in the past (eg. Levin 1983, 1984), a quantitative analysis of the effects of an error in the measurement of the cable feather has not been made. Such a systematic error could be caused, for example, by incorrect magnetic declination and would result in a apparent rotation of the cable. More widespread are random errors in the receiver positions caused by the limited accuracy of the navigation measurements. Houston (1991) estimated the maximum uncertainty in cable receiver positions for a state of the art navigation system to be about 6 m. The high cost and reliability problems introduced by redundant navigat ion networks cal l for an investigation of the tradeoffs between operational cost and quality of the final seismic section. Cost pressures have led to a heightened interest to establish a link between the efforts to reduce the uncertainty in the receiver positions and increased image quality. Ursin-Helm et. al. (1992) studied the effect of infill on the quality of the final image and concluded that in their particular case an infill of 30 % Causes only minor improvements of the section quality. They also studied the effects of less accurate navigation by visual inspection of the final seismic data. In this paper we offer a quantitative analysis of how seismic data is affected by statistical or systematic rotational errors in the position of a marine seismic streamer. PROCEDURE Ray tracing is used to assess the effects of random errors and a particular systematic error, that of an apparent rotation of the cable. Synthetic CMP gathers are collected over a model consisting of one dipping event for different structural dips, bin sizes, and feather angles of a straight single cable. The least squares NMO velocity and the stack response are calculated for data collected with a particular rotation error and compared to the error free case. Two different shooting patterns are investigated. In the first case, all lines are shot in the same direction, while the second case consists of l ines shot in alternating directions. If the stack trace results from the summation of traces which were collected from different boat passes (with feather), then energy from an event in the subsurface will deviate from a perfect hyperbola (Levin 1984). The need for correction to an hyperbola has been examined in relation to velocity modelling and DMO by Meinardus and McMahon (1981). In this paper since we assume that the navigation errors are not known (and therefore not corrected) we do not apply the location correction required to correct for this effect, but rather analyze the results in terms of change to the velocity that is determined. A rotational error of up to +/2 deg is considered. Random errors in the receiver positions are implemented as normal distributions around the true positions which are assumed to fall on a straight line. The standard deviations increase linearly with the offset up to 25 m for the far offset (3000 m). A second set of experiments is used to assess the impact of a rotational navigation error on the resolution and position accuracy of the final migrated image. The synthetic constant velocity 3D model consists of a dipping reflector and a diffractor suspended 200 m above the plane. lnlines and crosslines are processed through 2D DMO and 2D migration, Final sections of error free data and data with rotation error are compared.

Approach to optimum slant stack and its application as a seismic noise attenuator

A new method of transforming seismic data to a zero offset time and dip (7-p) domain is shown, which is based on an approach to optimally stacking seismic traces. Using this technique, a discrete 7-p representation of the data can be determined which minimizes the representation of random noise, and compresses the r-p response of linear events so that aliasing effects are much reduced. The new transformation can be implemented as a poststack noise attenuator if small local slant stacks are used, and as such it has significant benefits compared to conventional approaches to noise attenuation. Examples of both real and synthetic data are shown that demonstrate the method as a noise attenuation technique. The method is also shown to have potential in other seismic processing applications.