Dip-moveout Operator Research Articles

Elliptical dip moveout (EMO) for 3D seismic imaging in the presence of azimuthal anisotropy

Seismic images of the earth?s interior can be significantly distorted by complex wave propagation effects arising from 3D structural velocity variations, combined with the presence of azimuthal velocity anisotropy within some of the rock layers. Most image processing techniques attempt to separate and compensate for both of these phenomena sequentially; they rarely address both simultaneously. These approaches implicitly assume that the effects of 3D structural velocity and azimuthal anisotropy are separable, when in fact both effects are coupled together in the seismic data. The presence of strong azimuthal velocity anisotropy can lead to significant errors in estimated seismic velocity and degraded quality of subsurface images, especially for large source-receiver offsets, wide azimuths and steep geologic dips. Such imaging errors can greatly increase the uncertainty associated with exploring, characterizing, developing and monitoring subsurface geologic features for hydrocarbons, geothermal energy, CO2 sequestration, and other important geophysical imaging applications. Our approach is to simultaneously address velocity structure and azimuthal anisotropy by development of an elliptic dip moveout (DMO) operator. We combine the structural-velocity insensitivity of isotropic DMO with elliptic moveout representative of azimuthal velocity anisotropy. Forward and adjoint elliptical DMO operators are then cascaded together to form a single elliptical moveout (EMO) operation, which has a skewed saddle-like impulse response that resembles an isotropic azimuthal moveout operator. The EMO operator can be used as a prestack data conditioner, to estimate azimuthal anisotropy in a domain that is relatively insensitive to 3D velocity structure, or to compensate and map the data back to its original prestack domain in its approximately equivalent isotropic wavefield form. We show that EMO can reduce structural dip image errors of 10-20o or more for realistic azimuthal anisotropy values at far offsets.

Elliptical dip moveout for 3D seismic imaging in the presence of azimuthal anisotropy

Seismic images of the earth’s interior can be significantly distorted by complex wave propagation effects arising from 3D structural velocity variations, combined with the presence of azimuthal velocity anisotropy within some of the rock layers. Most image-processing techniques attempt to separate and compensate for both of these phenomena sequentially; they rarely address both simultaneously. These approaches implicitly assume that the effects of 3D structural velocity and azimuthal anisotropy are separable, whereas in fact, both effects are coupled together in the seismic data. In the presence of strong azimuthal velocity anisotropy, this can lead to significant errors in seismic velocity estimation and degraded quality of subsurface images, especially for large source-receiver offsets, wide azimuths, and steep geologic dips. Such imaging errors can greatly increase the uncertainty associated with exploring, characterizing, developing and monitoring subsurface geologic features for hydrocarbons, geothermal energy, [Formula: see text] sequestration, and other important geophysical imaging applications. Our approach simultaneously addressed velocity structure and azimuthal anisotropy by development of an elliptic dip moveout (DMO) operator. We combined the structural-velocity insensitivity of isotropic DMO with elliptic moveout representative of azimuthal velocity anisotropy. Forward and adjoint elliptical DMO operators were then cascaded together to form a single elliptical moveout (EMO) operation, which had a skewed saddle-like impulse response that resembles an isotropic azimuthal moveout operator. The EMO operator can be used as a prestack data conditioner, to estimate azimuthal anisotropy in a domain that is relatively insensitive to 3D velocity structure, or to compensate and map the data back to its original prestack domain in its approximately equivalent isotropic wavefield form. We demonstrated that EMO can reduce structural dip image errors of 10°–20° or more for realistic azimuthal velocity anisotropy values at far offsets.

Converted wave seismic imaging in the Flin Flon mining camp, Canada

Abstract Seismic imaging for mineral exploration in hardrock environment has typically relied on P-waves recorded using vertical component geophones. Here we demonstrate the potential of using P-to-S converted waves for mineral exploration by applying converted wave processing to high-resolution 3-component data acquired in the Flin Flon mining camp, Canada. Inferences regarding the relative value of PS data are made through comparison with corresponding PP images, interpretation with geological constraints, and by comparison with modeling results. Modeling results show that the horizontal component data provide a robust means of separating the PS conversions from the PP reflections in converted wave processing whereas contamination by PP energy is more severe if the vertical component data are used. A customized processing workflow has been developed in which horizontal component data are sorted into common-reflection point gathers by the application of the converted wave dip-moveout operator. The PS images are characterized by lower signal-to-noise ratios than the PP images due to the smaller S-wave impedance contrasts associated with the main lithologic units and the angular dependence of P-to-S conversion. An exception to this occurs for PS reflections from the ore zones which are accentuated on the PS images relative to the background host-rock reflectivity. There are discrepancies in the reflection dips and positions observed on corresponding PP and PS sections that are not fully explained. They can be partly attributed to the non-coincidence of subsurface spatial sampling associated with common-depth points versus common-conversion points, with an additional complication associated with the known 3D geology. Vp/Vs ratios determined by correlation of reflections observed on PP and PS images can provide a limited means of lithological discrimination.

Numerical analysis of the azimuth moveout operator for vertically inhomogeneous media

The azimuth‐moveout (AMO) operator, unlike the dip‐moveout (DMO) operator, has a 3D structure in homogeneous isotropic media, with an out‐of‐plane (crossline) component. In general, this component is concave downward, giving the operator an overall skewed‐saddle shape. The AMO operator, necessary for azimuth correction only, is typically smaller in size than conventional DMO operators, which corresponds to purely offset correction to zero offset. When velocity varies vertically, the operator shape changes depending on the degree of velocity variation. The general shape of the operator, however, remains saddlelike. In fact, for smooth velocity increases with depth, similar to those found in the Gulf of Mexico, the v(z) AMO operator does not differ much from its homogeneous counterpart. In this case, the residual AMO operator, constructed by cascading a forward homogeneous AMO operator with an inverse v(z) one, is extremely small, which suggests that the impact of such v(z) variations on the AMO operator is generally small. Complex vertical velocity variations, on the other hand, result in more complicated AMO operators that include, among other things, triplications at moderate angles. Regardless of the complexity of the model, the v(z) operator has the same first‐order behavior as its homogeneous counterpart. As a result, for small dip angles the homogeneous AMO, as a tool for partial stacking, often enhances the image. Moderate to steep dips in complex v(z) media requires the application of an algorithm that honors such velocity variations.

A fast sorting algorithm for large volume datasets

We introduce a new and efficient sorting technique, referred to as BT-Sort after the Bayer-balanced Tree (B-Tree) method. It is fast and parsimonious on usage of memory and scratch space, and is thus deemed very attractive for sorting very large datasets. One property of BT-Sort is that it minimizes the use of random I/O needed for accessing the scratch disk, regardless of the size of datasets being sorted. Furthermore, it uses sequential I/O to/from scratch disks in a very efficient way, and does not require large memory. For example, with such features, sorting 1.2 TB of input shot gathers into ordered common-midpoint gathers with BT-Sort would require only three days using four computing nodes (each of say 32 GB, 375 MHz RISC architecture), whereas the same exercise would typically require six to eight weeks to complete using conventional sorting techniques. From a seismic operational point of view, a rapid increase in seismic traces might result in altering some of the algorithms needed in the processing. Taking Saudi Aramco as an example, the current level of seismic-data acquisition there stands at 10 seismic crews, eight of which are 3D-seismic. The average count on these crews is about 2500 channels per crew. With an average daily production rate of some 2000 vibration points, the corresponding volume of seismic data flowing into processing is some 40 million traces per day. Consequently, some of the processing algorithms are being constantly updated in order to handle these massively increasing seismic volumes. Frequent sorting of seismic data into various domains (e.g. common-midpoint, common-receiver, etc.) has traditionally been avoided mainly because of the lack of efficient sorting algorithms. In the extreme case, sorting very large datasets with only limited computer resources (a few GB of memory) is a hugely inefficient task as the operation could take months to complete. As a compromise, geophysicists at times have opted to reformulate some existing processing algorithms such that seismic data would be kept in a certain preferred order throughout the processing sequence. One example was the reformulation of the dip-moveout operator by Biondi and Ronen (1987), so that it can be applied directly to recorded shot profiles instead of common-offset gathers if data cannot be sorted to common offsets (due to cost or other practical reasons), thereby avoiding the cost-prohibitive sorting process. Another, even worse shortcoming lies in the inability to apply some domain-specific processing algorithms, such as those for noise suppression and Radon multiple removal that require implementation in the common-receiver and common-midpoint (CMP) domains, respectively. In the case of (PRT) to normal-moveout-corrected CMP gathers, for example, geophysicists have attempted to speed up the process by optimizing the PRT operator (Kelamis and Chiburis 1992; Beylkin and Vassiliou 1998); this multiple elimination process in its entirety can benefit even further if data were sorted from shot to CMP gathers in a much faster way such as that proposed here. Unfortunately, lack of a fast sort may inevitably force the seismic data to suffer from unnecessary noisy contaminations if the expensive (slow) sort is to be avoided (Al Dossary et al. 1998). When using conventional (quick or heap) sorting algorithms, one may in theory estimate the cost (in terms of the number of operations to be performed) as N log2 N (Press et al. 1988), where N is the number of traces. On this basis, 500 million traces, for example, would require about 15 billion operations to sort them. In practice, however, such an implementation is more complicated than simply coping with a formidable number of operations. Specifically, the entire dataset should physically reside in memory (internal sorting) in a stand-alone system, a task most computer-hardware configurations cannot support.

3D F–K and finite‐difference dip moveout in cross‐spreads

ABSTRACTA 3D F–K dip‐moveout (DMO) is developed, which is applicable to data acquired in an elementary single‐fold cross‐spread. The key idea is that a 3D log‐stretch transform and the inherent regularity of the cross‐spread geometry make it possible to transform 3D Fourier DMO. The derived theory generalizes the 2D Fourier shot‐gather DMO in the log‐stretch domain; 2D turns out to be a special case. Similarly to 2D, the cross‐spread DMO becomes convolutional after multidimensional logarithmic stretch. The proposed method works for orthogonal and slanted acquisition geometries; the cross‐spread DMO relationships are found to be independent of the intersection angle of the shot and receiver lines. In contrast to integral (Kirchhoff‐style) methods, the cross‐spread F–K DMO does not degrade from the inevitable irregularity in 3D sampling of offsets in a CMP gather. The newly derived F–K DMO operator can be approximated by finite‐difference (FD) schemes; the low‐order FD cross‐spread DMO equation is shown to be the 3D extension of the Bolondi and Rocca offset continuation. It is shown that F–K and low‐order FD operators are effective in a synthetic case.

Least‐squares DMO and migration

Conventional processing, such as Kirchhoff dip moveout (DMO) and prestack full migration, are based on independent imaging of subsets of the data before stacking or amplitude variation with offset (AVO) analysis. Least‐squares DMO (LSDMO) and least‐squares migration (LSMig) are a family of developing processing methods which are based on inversion of reverse DMO and demigration operators. LSDMO and LSMig find the earth model that best fits the data and a priori assumptions which can be imposed as constraints. Such inversions are more computer intensive, but have significant advantages compared to conventional processing when applied to irregularly sampled data. Various conventional processes are approximations of the inversions in LSDMO and LSMig. Often, processing is equivalent to using the transpose of a matrix which LSDMO/LSMig inverts. Such transpose processing is accurate when the data sampling is adequate. In practice, costly survey design, real‐time coverage quality control, in‐fill acquisition, redundancy editing, and prestack interpolation, are used to create a survey geometry such that the transpose is a good approximation of the inverse. Normalized DMO and migration are approximately equivalent to following the application of the above transpose processing by a diagonal correction. However, in most cases, the required correction is not actually diagonal. In such cases LSDMO and LSMig can produce earth models with higher resolution and higher fidelity than normalized DMO and migration. The promise of LSMig and LSDMO is reduced acquisition cost, improved resolution, and reduced acquisition footprint. The computational cost, and more importantly turn‐around time, is a major factor in the commercialization of these methods. With parallel computing, these methods are now becoming practical.

Dip moveout in the Radon domain

I consider a new dip‐moveout (DMO) processing technique in the Radon domain called Radon DMO. The Radon DMO operator directly maps data from the NMO-corrected time domain to the DMO wavefield in the Radon domain. The method is built upon a process that transforms a single NMO-corrected trace into multiple traces spread along hyperbolas in the Radon domain. These hyperbolas are a linear Radon map of the DMO ellipses in the time domain. In this paper, I introduce the amplitude‐preserving Radon DMO and compare some examples of Radon DMO and Fourier DMO for both synthetic and real data. I also show the better frequency preservation properties of the Radon DMO method. Three‐dimensional data are often irregularly sampled with respect to fold, azimuth, and offset. Population deficiencies are exaggerated in the common‐offset domain. Radon DMO does not require that input traces belong to one common‐offset bin as does the Fourier method. Input traces can be organized from multiple offset bins grouping to perform Radon DMO, which is well used in 3-D surveys. Some synthetic and real data examples show these properties.

Spatial dealiasing of 3-D DMO

The construction of a 3-D Kirchhoff dip moveout (DMO) operator for the constant‐velocity case is remarkably simple in concept. First, generate the 2-D DMO operator between the source and receiver and then place it in the desired output 3-D volume along the trajectory between the source and receiver. Most of the literature concerning the design of such operators addresses the first step in the process, i.e., generation of the 2-D DMO operator. This paper treats the second part: sampling the 2-D DMO operator into the 3-D volume.

Kinematics of 3-D DMO operators in transversely isotropic media

The 3-D dip‐moveout (DMO) operator in homogeneous transversely isotropic media with vertical symmetry axis (VTI media), unlike that in homogeneous isotropic media, has an out‐of‐plane (cross‐line) component. In general, this component has a shape that is opposite to that of the cross‐line component of the isotropic v(z) saddle‐shaped operator. The width of the cross‐line component of the VTI operator is also smaller overall than that associated with isotropic v(z) media. When both typical anisotropy and inhomogeneity are combined, the net result is an operator with a smaller cross‐line component and a shape that is influenced more by the v(z) behavior. The large cost of a 3-D DMO operator, as well as the generally small cross‐line components associated with the DMO operator in VTI media, suggests the possibility, as is usually done for isotropic v(z) media, of just ignoring the contribution of the out‐of‐plane portion of the operator.

Dip‐moveout processing by Fourier transform in anisotropic media

Conventional dip‐moveout (DMO) processing is designed for isotropic media and cannot handle angle‐dependent velocity. We show that Hale's isotropic DMO algorithm remains valid for elliptical anisotropy but may lead to serious errors for nonelliptical models, even if velocity anisotropy is moderate. Here, Hale's constant‐velocity DMO method is extended to anisotropic media. The DMO operator, to be applied to common‐offset data corrected for normal moveout (NMO), is based on the analytic expression for dip‐dependent NMO velocity given by Tsvankin. Since DMO correction in anisotropic media requires knowledge of the velocity field, it should be preceded by an inversion procedure designed to obtain the normal‐moveout velocity as a function of ray parameter. For transversely isotropic models with a vertical symmetry axis (VTI media), P‐wave NMO velocity depends on a single anisotropic coefficient (η) that can be determined from surface reflection data. Impulse responses and synthetic examples for typical VTI media demonstrate the accuracy and efficiency of this DMO technique. Once the inversion step has been completed, the NMO-DMO sequence does not take any more computing time than the genetic Hale method in isotropic media. Our DMO operator is not limited to vertical transverse isotropy as it can be applied in the same fashion in symmetry planes of more complicated anisotropic models such as orthorhombic.

DMO in the Radon Domain

A new dip-moveout (DMO) processing technique is proposed. The method is based on an integral DMO method in the Radon domain called Radon DMO, which is especially applicable to irregularly sampled 3-D datasets. Radon DMO offers several advantages for processing surveys with irregularly sampled design or acquisition characteristics, common problems for land and Ocean Bottom Cable 3-D surveys in particular. First, the Radon DMO operator is nonaliased and dealiasing. Missing traces do not cause spatial aliasing, precursor noise, or unbearable distortions of phase and amplitude. Second, Radon DMO does not require that input traces belong to one offset bin. Input traces can be organised from multiple offset bins in the same azimuth grouping to perform Radon DMO. Third, the DMO-corrected output can be either stacked or unstacked, which enables the full range of post-DMO processing including post-DMO velocity analysis.The Radon DMO operator directly maps data from the NMO-corrected time domain to the DMO wavefield in the Radon domain. The impulse responses of Radon DMO are hyperbolas. The method is built upon a process that transforms a single, NMO-corrected trace into multiple traces spread along hyperbolas in the Radon domain. Most integral methods include the application of a 45° phase shift, as well as offset, time, and frequency-dependent gain factors when spreading the traces along ellipses. Such compensations are generally unnecessary with Radon DMO, which greatly simplifies program development and reduces the number of critical elements to control. By eliminating costs associated with gain factor application, the added costs for inverse Radon transform are alleviated. Total costs compare well with conventional integral DMO methods.

An accurate formulation of log‐stretch dip moveout in the frequency‐wavenumber domain

Dip moveout (DMO) processing is a partial prestack migration procedure that has been widely used in seismic data processing. The DMO process has been described in Deregowski (1986), Hale (1991) and Liner (1990). Many different DMO algorithms have been developed over the past decade. These algorithms have been designed to improve either the accuracy or the computational speed of the DMO process. Hale (1984) developed a method for performing DMO via Fourier transforms that is accurate for all reflector dips (assuming constant velocity). Hale’s method is computationally expensive because his DMO operator is temporally nonstationary, but its accuracy and simplicity have made it an industry standard. It has become a benchmark by which results from other DMO algorithms are judged. Of all the methods used to make the frequency‐domain DMO computationally efficient, the technique of logarithmic time stretching, first suggested in Bolondi et al. (1982), is widely used. After logarithmic stretching of the time axis, the DMO operator becomes temporally stationary which enables replacement of the slow temporal Fourier integration with a fast Fourier transform combined with a simple phase shift. Bale and Jakubowicz (1987) presented a log‐stretch DMO operator (hereafter referred to as Bale’s DMO) in the frequency‐wavenumber (F-K) domain without approximations, while Notfors and Godfrey (1987) suggested an approximate version of log‐stretch DMO operator (hereafter referred to as Notfors’s DMO). Surprisingly, Bale’s full log‐stretch DMO operator produces a less satisfactory impulse response than Notfors’s approximate log‐stretch DMO scheme (see Liner, 1990). Liner (1990) attributed this characteristic to the fact that Bale’s DMO derivation implicitly assumes that the Fourier transform frequency in the log‐stretch domain is not time‐dependant. He presented an exact log‐stretch DMO operator (hereafter referred to as Liner’s DMO) which was derived by transforming the time log‐stretched Hale’s (t, x) DMO impulse response into the Fourier domain. Its derivation is relatively complicated, but Liner has shown that his DMO does generate good DMO impulse responses.

Accurate and efficient shot‐gather dip moveout processing in the log‐stretch domain1

AbstractAn accurate analytical expression for shot‐gather dip‐moveout (DMO) in the timespace log‐stretch domain has until now not been published. We present a simpler, alternative derivation of the exact DMO relationships of Black et al. which correctly take account of the repositioning of the midpoint. A new computationally efficient frequency‐wavenumber (F‐K) DMO operator for shot profiles is then derived, based on these DMO relationships in the time‐space log‐stretch domain. The newly derived DMO operator is, unlike most other log‐stretch DMO operators) accurate for the full range of reflector dips. Along with other schemes which are performed in the log‐stretch domain, it offers considerable time savings over conventional DMO processing. We have compared numerically the impulse response of the new operator with those of a number of other shot‐gather DMO operators, and found it to be superior and well match to the theoretical elliptical DMO response.

A partial DMO Operator for use with the Stacking Velocity Function

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.

Squeezing dip moveout for depth‐variable velocity

In dip‐moveout (DMO) processing, velocity variations with depth can be handled approximately by squeezing a constant‐velocity DMO operator to narrow its impulse response. This squeezed DMO approximation provides a computationally efficient and reasonably accurate method of DMO correction for depth‐variable velocity. DMO is squeezed by two modifications to constant‐velocity DMO. One modification is a squeezing function of time that depends only on simple time averages of velocity that are likely to be known before DMO is applied. This squeeze function ensures that squeezed DMO accurately handles moderately steep reflections and can be incorporated with simple time stretching before and after DMO, without any changes to existing constant‐velocity DMO methods. The second modification is a constant squeezing factor, which may be used to tune squeezed DMO to better handle steep reflections. This factor requires only trivial changes to constant‐velocity DMO methods. Tests with both synthetic and recorded seismic data suggest that squeezed DMO is an effective method for handling velocity variations with depth. These tests also show that the differences between constant‐velocity DMO and squeezed DMO can be significant.

Anti-Aliasing and Amplitude Preserving 2D and 3D DMO — some Practical Considerations

A practical definition of DMO (Dip Move-Out) is that it is a mapping to zero offset. In order to avoid the arbitrary attenuation of dipping events in this mapping process, Amplitude-Preserving or True-Amplitude DMO is needed. Such a DMO algorithm will be an invaluable tool in the study of AVO (Amplitude-Versus-Offset) effects. A method is described whereby both anti-aliasing and Amplitude-Preserving DMO can be implemented using the integral approach (also known as Kirchhoff DMO, Summation DMO, and (x-t) or space-time DMO). Anti-aliasing is accomplished by using band-limited sincfunction interpolators based upon local dip of the impulse response of the DMO operator. This enables the appropriate amplitude weighting along the DM0 impulse response to be applied. That gives rise to the so-called True-Amplitude and Amplitude-Preserving DMO algorithms. The F-K domain offers a useful platform for the comparison and implementation of various weighting factors for the DMO impulse response. F-K analyses of impulse responses can be used to illustrate the effects of anti-aliasing and amplitude properties of integral DMO. In 2D, where in general there is regular sampling in the common offset plane, the anti-aliasing and Amplitude-Preserving DMO algorithm improves the image quality in the mapping of pre-stack data to zero offset. In the 3D case the DMO ellipse is exactly the same as the 2D DMO ellipse, apart from the fact that for 3D DMO we must rotate the ellipse to lie in the direction given by the source-receiver axis with respect to the processing grid. This grid is usually organised in terms of 3D binline and 3D CMP (Common Mid-Point). In marine data, streamer feathering has the effect of spreading midpoints (3D CMPs), for a given sail line, over several 3D binlines. The result of this is to vary the distribution of source-receiver azimuths (feather angles) within a given bin. This leads to irregular sampling in the common offset-azimuth plane where 3D DMO is performed. Whilst Kirchhoff methods have the flexibility of dealing with irregularly sampled data, the desirability of regular sampling in this common offset-azimuth plane in order to preserve amplitudes is illustrated. Methods for data regularisation in offset and azimuth are not discussed here. Instead we question the need for 3D DMO in certain marine applications. A simple criterion for determining the condition under which cable feathering becomes a significant factor in determining the need for 3D DMO is presented in tabular form and its implications are discussed.

Ray‐geometrical analysis of dip moveout amplitude distribution

Amplitude analysis (such as for amplitude‐versus‐offset effects) requires a true‐amplitude correction at each process stage, including the dip moveout (DMO) process. The well known DMO operator is the “smile” smear, derived by Deregowski and Rocca (1981). In this note we continue their geometrical‐optics approach to obtain the amplitude on the operator they derived. The proposed solution is based on ray theory.

Shot dip moveout with logarithmic transformations

In a recent paper, Notfors and Godfrey (1987) presented an approximate analytical expression for a common‐offset dip moveout (DMO) operator in the space, logarithmic‐time domain. This operator yields an efficient frequency‐wavenumber DMO algorithm. In this note we extend Notfors and Godfrey’s work to obtain an approximate DMO operator in the logarithmic space and time domains and propose an efficient frequency‐wavenumber DMO algorithm that is applied to shot gathers. A synthetic example is presented.

DIP-moveout by Fourier transform

Seismic reflection survey is primarily designed to determine subsurface geological structures from the data recorded at the surface. Processing of seismic data undergoes several digital processing and beam forming steps, first to enhance the signal-to-noise ratio and then to construct the final digital image which is physically correct and geologically meaningful. Dip-moveout (prestack partial migration) is a processing step which corrects the dip filtering action of normal moveout (NMO) and stacking. Dip-moveout (DMO) eliminates the reflection point scattering associated with dipping reflectors by shifting the reflection event to its zero offset location. In recent years several dip-moveout methods have been discussed in literature. This paper presents a DMO program (FORTRAN) and its long write-up based on the “Dip-moveout by Fourier transform” by Hale [Geophysics 49 (1984) 741]. The program was tested with theoretical synthetic seismic data in which the expected DMO operator response was simulated.