Enhancement of Seismic Stacking Energy with Crossdip Correction for Crooked Survey Lines

Abstract

In seismic reflection data processing, the crossdip correction effectively focuses the stacking energy near the sharp bends of a crooked survey line. Additionally, approximate 3-D information on the reflector (e.g., true crossdip angle and lateral continuity) are locally investigated as a by-product of the crossdip correction procedure. Improvement of the signal-to-noise ratio and estimation of reflector crossdip attitude are tested, in terms of both common midpoint bin direction and processing-line type, using synthetic seismic reflection data. To effectively image the reflection energy near bends in seismic survey lines, straight-line binning is preferred to slalom-line binning.

Introduction

Dipping reflectors introduce difficulties in seismic data processing and subsequent interpretation. Further complications arise when the direction of the survey line changes abruptly; thus, considerable effort is put into survey planning to keep the survey lines straight. However, it is sometimes impossible to conduct a straight-line survey, as logistical access and geological complications may make it unfeasible to place survey lines in desired directions. For crooked-line data, the common midpoints (CMPs) are not folded on the survey line but tend to be more broadly scattered across the line, forming a transverse-offset gather. Therefore, we should consider the effect of cross-line offset (crossdip correction), as well as in-line offset (normal moveout (NMO) corection), in the travel time correction for CMP stacking. Here, “crossdip” is defined as the component of dip perpendicular to the local direction of the survey line.

Seismic data processing for crooked line surveys requires an added emphasis on focusing seismic energy to capture the lateral continuity of subsurface reflectors, particularly along the sharp bends of the crooked segment. Since the first study was conducted by Larner et al. (1979), various solutions to travel time anomalies arising from reflector crossdip and variations in the transverse offset (cross-line offset) of the CMP have been proposed by Bois et al. (1990), Wang and West (1991), Kim et al. (1992), Wu (1996), Nedimovi et al. (2003), Nedimovi and West (2003), Malehmir et al. (2009), and Singh et al. (2010). However, the geometrical relationship between a CMP bin and its reflector for achieving the best signal focusing was not intensively studied. In this paper, synthetic seismic data generated from simple two- and three-layer models were tested and processed in an attempt to the improve the resolution of the stacked traces by designing the optimal slalom-line (i.e., rearranging the CMP bin) for a given dipping reflector. In addition, meaningful 3-D reflector attributes (e.g., the true crossdip angle and degree of lateral continuity) were estimated as a by-product of the crossdip correction.

 

Scattered common midpoints

For a straight line, there is no midpoint scattering effect in the cross-line direction (Fig. 1(a)). Although stacked traces have improved signal focusing after NMO correction, information on the crossdip angle ζ for a dipping reflector in the cross-line direction cannot be extracted from the CMP gathers (Fig. 1(b)). However, on a crooked line, the midpoints are scattered in both the in-line and cross-line directions (Fig. 2(a)), and the reflection event in a CMP gather appears incoherent with respect to offset (Fig. 2(b)). The effect of ζ is indicated on the transverse-offset sorted gather with the NMO correction applied, where the progressive misalignments of reflection signals with increasing transverse offset are a function of ζ. Thus, the crossdip of subsurface reflectors can introduce amplitude smearing, as well as travel time errors, which can strongly impair the stacking process. This focusing effect from the crossdip correction is shown schematically with a stacked trace in Fig. 2(b), while the stacked energy without the crossdip correction is broadly smeared, resulting in a defocused image of the reflector. The true crossdip of the reflector is also estimated as a by-product of the correction process.

Fig. 1.Straight-line geometry and CMP gather for a crossdipping reflector: (a) CMPs between the shots and receivers are multifold. ζ is the crossdip angle of the reflector; (b) CMP gather, before and after NMO correction.

Fig. 2.Schematic diagram of the crossdip effects along a crooked survey line: (a) the CMPs are scattered across the survey line; (b) the stack energy is focused after transverseoffset sorting, NMO correction, and crossdip correction (modified from Kim and Moon, 1994).

 

Estimation of crossdip attitudes

When the survey line is crooked, the crossdip information can be locally extracted from a CMP gather, since each trace contains information on both the transverse offset Y and in-line offset X of the corresponding midpoint. The conventional stacking process assumes that the travel time equation for the CMP gather is as follows (Sheriff and Geldart, 1982):

where T is the travel time from source to receiver, XD is the source-to-receiver offset for the CMP, V is the NMO velocity, and TO,D is the zero-offset two-way travel time for the CMP. However, Equation 1 is not satisfied if the survey line is not straight.

Departures in CMP positions from the center of the CMP bin introduce transverse offset into the travel time equation; thus, reflector crossdip across the profile becomes important. In this paper, the term “transverse offset” is defined as the distance between each CMP and center of the CMP bin. A new travel time equation for each CMP with respect to the center of the CMP bin can be given by (Fig. 3):

Fig. 3.Schematic diagram of a crossdipping reflector and a given CMP bin.

where YD,M is the transverse offset between the CMP and the center of the CMP bin, and XM is the source-toreceiver offset for the CMP. This equation specifies that there is residual moveout in the CMP gather after NMO correction, that is:

where TO,M is the zero-offset two-way travel time for the CMP. The travel time difference between a given CMP (TO,M) and the center of the CMP bin (TO,D) is then:

By generalizing the residual moveout for shot i and receiver j, the travel time difference ΔT attributable to the crossdip error can be expressed as (Fig. 3):

where ΔTi,j is the crossdip correction, Vk is the velocity of the reflector at CMP k, ζk is the crossdip angle at the CMP k, Yi,j is the transverse offset between the midpoint and corresponding CMP point, and p is the crossdip slowness for a given k (Kim et al., 1992). Therefore, the crossdip correction can be carried out through a slant stack transformation (Yilmaz, 2001), with respect to transverse offset, on the NMO-corrected CMP gathers.

 

Enhancing the stack energy near bends

The effectiveness of the crossdip correction

Synthetic seismic data were generated from an inclined two-layer model (Fig. 4(a)) to examine how the crossdip correction enhances the stacking energy of a dipping reflector. The velocities for the upper and lower layers were set at 2 and 4 km/sec, respectively, with a density of 2400 kg/m3 for both layers. The crossdip was set at 5° for the dipping reflector.

Fig. 4.Effect of crossdip correction for a two-layer model: (a) crossdipping reflector with ζ = 5° and a selected CMP bin (#340); (b) dipping feature indicated after transverse-offset sorting; (c) slant stack test with varying ζ (i.e., horizontal slowness).

Synthetic data were computed using the OMNI 3D seismic modeling software (Schlumberger, 2012a), with the following parameters: 2 ms sampling interval, 120 channels, 50 m source interval, 50 m station spacing, and a Ricker wavelet with a dominant frequency of 30 Hz. Subsequent processing was done using the VISTA seismic processing package (Schlumberger, 2012b), with the core processing steps of CMP sorting, NMO correction, transverse-offset sorting, slant stack transformation, and crossdip correction.

A crooked segment (CMP bin#340; Fig. 4) was selected and tested for crossdip correction. Because the survey line is not straight, the midpoints are scattered in the cross-line direction. The NMO-corrected CMP gather shows a strong reflection at about 250-255 ms (Fig. 4(b)). The progressive misalignment of reflection energy with increasing transverse offset is clearly shown, as the reflector dips gently eastward (Fig. 4(b)), and the stacked energy is broadly smeared. A slant stack test applied with varying horizontal slowness p will identify the most focused reflection panel for CMP stacking when the assumed dip approaches the true crossdip of the reflector (Fig. 4(c)), since ζ is a function of p (where p = sinVk / Vk). The conventional stack corresponds to a stack with zero crossdip correction (p = 0, Fig. 4(a)). The reflection image is flattened and the stacked trace is focused through a downward shift in the negative transverse offsets, and an upward shift in the positive offsets, based on Equation 5. The greatest improvement in image focusing was obtained when p = 0.45 × 10−5 sec/m. This equates to a true crossdip of approximately 5.2°, using the input velocity of 2 km/sec, which is in strong agreement with the defined crossdip (ζ = 5°) of the reflector in the model (Fig. 4(a)).

Arrangement of the CMP bin

The effectiveness of the crossdip correction depends on the CMP-bin direction with respect to the attitude of the subsurface reflectors. For example, when imaging a NW-dipping structure, application of the crossdip correction is most effective with SE-directional CMP bin data, because most of the CMP bins transverse to the survey line are aligned in the dip direction of the reflector (Fig. 5).

Fig. 5.Schematic diagram highlighting the effect of crossdip correction with respect to the geometry of the reflector, slalom line, and CMP bin.

The crossdip of the reflector was set at ζ= 20° (Fig. 6). Two CMP bins (#408 and #480) were selected to investigate the effect of the crossdip correction with respect to the geometry of the slalom line, CMP bins, and reflector plane. After applying a crossdip correction with the true reflector dip of 20°, the trace events in CMP bin #408, perpendicular to the strike of the reflector, are well aligned and focused (Fig. 7(a)), whereas those events in CMP bin #480, parallel to the strike of reflector, are misaligned and defocused (Fig. 7b). Because the reflection points for CMP bin #480 were sampled along the strike of the reflector, the events were originally well aligned before crossdip correction. Therefore, the crossdip correction is more effective when CMP bins transverse to the slalom line are aligned in the dip direction of the reflector.

Fig. 6.Model of a crossdipping reflector with ζ = 20° and two selected CMP bins (#408 and #480), to demonstrate the effect of crossdip correction in relation to the geometry of the reflector, slalom line, and CMP bin.

Fig. 7.Effect of crossdip correction, with ζ = 20°: (a) CMP bin #408; (b) CMP bin #480.

Straight-line binning vs. slalom-line binning

Two CMP bins (Fig. 8(a)) for two different runs of data processing lines, one for slalom-line binning (CMP #310) and the other for straight-line binning (CMP #261), were selected to compare the degree of image focusing for the reflections in the corresponding gathers (Fig. 8(b)). These two CMP bins overlie each other in the vicinity of station #166. CMP bin #310, oriented perpendicular to the survey line (slalom-line binning), shows coherent (aligned) reflection events at the far sides, probably caused by approximately the same or small source-to-receiver offset. However, for CMP bin #261, which is oriented parallel to the survey line (straight-line binning), the event is approximately hyperbolic. As a result, straight-line binning enabled a better correlation of the seismic image. To investigate the focusing effect of an inclined third layer, the rootmean-squared (RMS) seismic velocity was used in the crossdip correction. Four crossdip scenarios (ζ = 10°, 15°, 20°, 25°) were tested using a three-layer model, and the resultant stack sections, both with and without cross correction applied, are shown in Fig. 9. As ζ increases, stacked events tend to be heavily smeared due to widely scattered reflection points (Fig. 9(b)). However, reflector focusing is improved when the appropriate crossdip correction and RMS velocity (~3200 m/sec) are applied; the true crossdip angle is determined as a by-product of this approach (Fig. 9(c)).

Fig. 8.(a) Map showing CMP scattering for slalom-line binning (left) and straight-line binning (right); (b) corresponding CMP gathers for straight-line binning (upper) and slalom-line binning (lower).

Fig. 9.(a) Models of a crossdipping reflector, for ζ = 10°, 15°, 20°, and 25°, and their resultant stack sections, (b) before crossdip correction and (c) after crossdip correction. The improvement in signal focusing from the crossdip correction is clearly shown, with the by-product of identifying the true crossdip angles.

 

Conclusions

In the processing of crooked-line seismic reflection data, crossdip correction improved the image of the dipping reflector, particularly along the sharp bends of the survey line. Furthermore, during the correction process, the true crossdip angle of the reflector was locally determined. Crossdip correction is more effective in focusing the stacking energy when CMP bins are set parallel to the dip direction of the reflector. Improved test results from the synthetic data suggest that the effect of widely scattered midpoints must be taken into account during crooked-line data processing. Straight-line binning is preferred to slalomline binning in imaging the reflection energy near bends.