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ABSTRACT Dip moveout is presented as a data conditioning process in which a diffraction surface in midpoint-offset-time space is transformed into a surface of revolution. Pre-stack imaging operates on constant-time slices of the data, after dip moveout has been applied, in which diffractions appear as circles, adds data along these circles, and plots the sum at the largest offset point of each circle. After both operations, a standard velocity analysis and stacking algorithm produces a migrated section. Both operations are independent of velocity. INTRODUCTION Two problems commonly associated with CDP stacking are (1) a loss of resolution because the reflection point moves updip as the offset increases and (2) the stacking velocity depends on the dip angle of the reflector. The first problem is particularly severe if the reflection point moves across a fault as it moves updip, as indicated in Figure 1. The second problem means that stacking velocities are not appropriate for migration after stack. Dip moveout (DMO) helps with both problems, as first explained by Judson et al. (1976). There is less loss of resolution because the gathers, after DMO, have events with common reflection points. Also, the stacking velocity is not so dependent on the angle of dip and is more useful for selecting velocities to migrate the data after stack. However, the stacking velocity is estimated at the slant travel time T2 and not at the vertical travel time To, as one would wish. DMO can be followed by another processing step called pre-stack imaging (PSI). After PSI, the data are migrated but not yet stacked. In other words, gathers formed after DMO and PSI have been applied can be stacked using a standard velocity analysis and stack program. In this case, there is no loss of resolution, the stacking velocity gives the root-mean-square velocity at time To, and the stacked traces are fully migrated. Both DMO and PSI are independent of velocity. The processes do not have to be repeated if the velocity is changed. The selection of velocity is made at the last step when the migrated traces are being stacked. Thus the velocity analysis may be more robust because the traces used in the analysis have a better signal to noise ratio. This paper gives an overview of both processes and illustrates the algorithms by showing how a diffraction in multi-fold data is summed and plotted at a point. THREE-STEP PRE-STACK MIGRATION The first step is DMO. Viewing a 2D multi-fold line as a three-dimensional space with axes m (the midpoint coordinate), h (half the offset), and t (time), as shown in Figure 2, we can see that DMO operates on vertical sections with constant h. The original data cube is transformed into a new cube by processing the constant-offset sections one by one.

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ABSTRACT Dip moveout (DMO) provides a straightforward way to convert irregular three-dimensional data into regularly spaced offset-versus-time panels at regularly spaced spatial grid points without using any velocity information. An extension of this procedure is described which creates at each grid point an angle-of-incidence versus time panel in which reflection events are flattened and in which amplitude variations are related to reflection coefficients as a function of the angle of incidence. To obtain useful amplitudes after DMO, it is shown that the original data can be scaled by a ramp proportional to time, by a ramp inversely proportional to the shot-to-receiver offset, and by a ramp proportional to the square root of the time after the events are flattened. An algorithm is also given for estimating dip angle from common midpoint gathers after DMO. The methods are illustrated with in-line two-dimensional data but are applicable to irregular data. INTRODUCTION It is well known that velocity analysis is improved by using dip moveout (DMO) as a data-conditioning operation (Judson et al., 1978; Hale, 1981; Berg, 1984; French et al., 1984; Jacubowicz et al., 1981; Deregowski, 1986; Gardner et al., 1986); this paper describes a similar use for DMO to improve amplitude-versus-offset analysis. It is usual to investigate the variation of amplitude with offset by studying common midpoint (CMP) gathers, or averages of adjacent CMP gathers (Ostrander, 1984). DMO also combines adjacent CMPs, with the number of CMPs being proportional to the offset, but it also tends to remove any adverse effects caused by the dip of the structure. Since the amplitude variation with offset is difficult to preserve during any data-processing step it is not certain in advance that DMO will improve the interpretation. The results presented here were obtained using synthetic data and there are many effects such as attenuation and transmission losses that should be included before conclusions with regard to field data are made. For 2D multi-fold data, the most efficient DMO programs use Fourier transform or finite difference methods and rely on the data being regularly spaced. In three dimensions, regularity in the positioning of the shot and receiver is the exception and the usual two-dimensional algorithms lose their efficiency. An alternative processing procedure has been described by Forel (1986) in which each trace is added to an offset-versus-time panel at each grid point. This is the procedure followed in this paper. One difficulty with the procedure is that the amplitudes of traces resulting from the addition of the data depend on the weighting given to the data. The weighting needs to be selected so that the amplitudes of the events after processing have the characteristics desired. The goal is to construct a panel in which reflection events are aligned in the rows and in which the columns correspond to the angle of incidence with the normal to the reflector. Furthermore, the amplitude in each column should be proportional to the reflection coefficient for the corresponding angle.

Summary The processing of deep-offshore seismic data acquired with long streamers involves appropriate algorithms taking into account the non-hyperbolic shape of the reflection curves and the inadequacy of the standard DMO. The seismic signatures of the effects corresponding to bedding or VTI anisotropy are indistinguishable. Since the shifted hyperbola NMO equation seems to describe perfectly both effects, we propose to parameterize them with the VTI anisotropy parameter h. In the case of layered VTI model, our shifted hyperbola moveout correction using the actual effective values of V nmo and anellipticity h allows better result than Alkhalifah’s VTI NMO. The DMO operator derived from the anelliptic shifted hyperbola equation fits thoroughly to the monotonous part of Alkhalifah VTI DMO operators. This anelliptic dip moveout depends on effective h only. The outstanding effective h values seem to be linked up to the nonhyperbolic velocities analyses occurred at the same levels.

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Summary Moving from standard time processing means opening the focusing process to the anellipticity of the effective media. Short spread curvatures of reflection curves can not explain by themselves the seismic signatures of dipping and horizontal reflectors recorded with long streamers throughout layered strata containing shale sediments. We propose here a Dix-type effective medium, where two velocities could describe the full time processing. The ratio of these two velocities points out the anellipticity strength, which is represented by the well-known h parameter. Effective h encompasses two travel path effects: vertical inhomogeneity and transverse isotropy. In the case of anelliptic media the velocity pickings, sparse or dense, are extended on two parameters. Interpolated and filtered parameter fields could be estimated thanks to Dix properties of stacking and anelliptic velocities.

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Summary Converted wave (C-wave) dip moveout (DMO) is one of the main procedures for multi-component seismic data processing. In this work, we derive a C-wave DMO formula based upon a second-order approximate trajectory equation of conversion-points, and further propose a fast algorithm in frequency-wavenumber ( f-k ) domain. With Cwave DMO process, the common-conversion-point (CCP) migrates to the common-middle-point (CMP). Impuse responses and a real OBC data example are presented. Introduction Compared with traditional single-component seismic data, multi-component data, in which both P- and S-waves may exist, can provide much more valuable information of subsurface structure and lithology. Processing of multicomponent data is substantially more complex than P-wave processing (Tatham,1993).

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