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Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 1983 SEG Annual Meeting, September 11–15, 1983

Paper Number: SEG-1983-0395

... to

**Frequency**-**Domain****Migration**R. E. DuBroff, Phillips Petroleum There are two main points in this report. The first is a definition of**migration**as a process of finding surfaces upon which boundary conditions are satisfied. The second main point is that the process of finding these surfaces can be done...
Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, April 30–May 3, 1979

Paper Number: OTC-3659-MS

... concentrated on finite difference techniques. Now, however, the approach to

**migration**based on the**frequency****domain**has become a viable alternative. This is founded on the wave equation, and so includes diffractions and other effects. This paper seeks to motivate and illuminate**frequency****domain****migration**using...
Abstract

ABSTRACT Migration of seismic data has been important for some time. Graphical methods were employed first to accomplish correct positioning of seismic data. These procedures were succeeded by statistical methods using Kirchoff integral methods. Most of the recent work in migration has concentrated on finite difference techniques. Now, however, the approach to migration based on the frequency domain has become a viable alternative. This is founded on the wave equation, and so includes diffractions and other effects. This paper seeks to motivate and illuminate frequency domain migration using straightforward geometric techniques. INTRODUCTION Migration of seismic data is a process of mapping one time section onto a second time section, or a depth section in which events are repositioned under the appropriate surface location and at the correct time. That is, a migration output should be a time section of the geological depth section. No current migration technique perfectly handles all the difficulties of noise, rapidly varying velocities, steep dips, and other problems. Techniques vary greatly in performance relative to these problems. Three of the major techniques of migration are diffraction, finite difference, and frequency domain migration. Diffraction migration also is known as Kirchoff integral migration. The finite-difference approach commonly is known as time domain or wave equation migration. Frequency domain migration also may be referred to as FK migration, or Fourier transform migration. The diffraction stack process is a statistical approach. This procedure treats data that might have originated from certain subsurface locations. All such possible origins are treated as equally likely. The major advantage of diffraction migration is good performance with steep dip. One disadvantage is poor performance under low signal-to-noise ratio conditions. Finite-difference migration is a deterministic approach. The migration procedure is modeled by the wave equation. This partial differential equation then is approximated by a simpler type of equation appropriate for migration. This last equation then is approximated as a finite-difference scheme. An advantage of the finite-difference method is its good performance with a low signal-to-noise ratio. Disadvantages of this method include a relatively long running time and difficulty in handling steep dip data. Frequency domain migration is based also on a deterministic approach via the wave equation. Instead of utilizing finite-difference approximations, the two-dimensional Fourier transform is the fundamental technique of this method. The advantages of this method include fast running time, good performance under low signal-to-noise ratio conditions, and excellent performance for steep dip. Disadvantages include difficulties with widely varying velocity functions. This article is meant to serve as an overview to those working in the geophysical industry who wish to know more about migration. In particular, the authors hope to provide some new insights into the fundamental aspects of migration with a major emphasis on frequency migration. There will be much reliance on the geometry behind the usual physical and mathematical treatments of migration. The intimate geometric relations between the migration of a dipping event in time and the counterpart migration in the frequency domain will be explained.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, April 30–May 3, 1979

Paper Number: OTC-3660-MS

...

**migration**plane plane abcd three-dimensional**migration**upstream oil & gas fourier transform diffracted plane abcd perpendicular modeling technique**frequency****domain****migration**reservoir characterization modeling & simulation two-dome model**migrated**plane seismic line...
Abstract

ABSTRACT The frequency domain approach to migration extends to three dimensions. The application of a ray tracing approach to simple seismic events and the principle of superposition leads to the correct equation for the frequency domain migration and a further understanding of the basic migration procedure in three dimensions. Synthetic examples are used to illustrate the fact that two-dimensional migration of three-dimensional data will not result in a correct section. However, in the frequency domain, three-dimensional migration may be reduced to a series of two-dimensional migrations. The synthetics for this paper were generated by a particularly fast and straightforward technique. Such a fast three-dimensional seismic model can be generated for structures with certain symmetry. Starting from a two-dimensional synthetic, a three dimensional model can be constructed by rotation about the center of symmetry. Any line across the feature may then be synthesized from the basic data. Certain more complex three-dimensional models can also be developed using the superposition of simpler models. INTRODUCTION In recent years, there has been considerable interest in three-dimensional (3-D) data acquisition and true three-dimensional processing. In particular, J. Hagedorn (1954) and A. Musgrave (1961) discussed methods of three-dimensional migration. Hilterman (1970) and French (1974) published physically recorded sections from three-dimensional models. Hilterman compared the recorded data with calculated data. The calculated data was available for the models with true two-dimensional (2-D) structure. That is, these particular models may be generated by moving a 2-D cross-section in a straight line. French discussed the migration of the physically recorded model data with both 2-D and 3-D techniques. More recently, W. Schneider (1978) and R. Stolt (1978) have dealt with three-dimensional migration. Schneider considered the problem from an integral standpoint, while Stolt used the frequency domain approach. Stolt arrived at the basic equation for three-dimensional migration. In this paper, we have included a discussion of some of the fundamentals of three-dimensional migration in both the time and the frequency domain. This is primarily a tutorial approach based on a geometric or ray theory viewpoint. In order to relate these concepts to specifics, several synthetic examples will be considered. These were generated via a fast, simple technique described in this paper. THREE-DIMENSIONAL MIGRATION IN THE FREQUENCY DOMAIN Three-dimensional migration in the frequency domain is, at least conceptually, a natural extension of 2-D migration. Prior to discussing 3-D migration, we will review a few fundamental properties of the 3-D Fourier transform. Consider the infinite horizontal plane ABCD depicted in Figure la. In this figure, we will assume that the reflection coefficient is a constant throughout the plane. Suppose the Fourier transform is performed in the × direction. The plane will be transformed into a line as shown in Figure lb. Next, after the transform is performed in the y direction, the line will be transformed to a point as shown in Figure 1c.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2011 SEG Annual Meeting, September 18–23, 2011

Paper Number: SEG-2011-3419

... ABSTRACT Many researches based on wavefield separating

**migration**techniques have been suggested for processing multi-component data properly. Those works were carried out in the time**domain**, however. In this paper, we propose the**frequency**-**domain****migration**technique with wavefield separation...
Abstract

ABSTRACT Many researches based on wavefield separating migration techniques have been suggested for processing multi-component data properly. Those works were carried out in the time domain, however. In this paper, we propose the frequency-domain migration technique with wavefield separation. In the frequency domain, reverse-time migration can be implemented efficiently by the zero-lag convolution between virtual source and back-propagated wavefield. Our new migration can also be defined as the zero-lag convolution between the decomposed virtual source and the decomposed back-propagated wavefield derived by exploiting Helmholtz decomposition. P-and S-wave migration images can be obtained separately by defining the virtual source separately. We verify our new migration algorithm on synthetic seismic data generated from the Marmousi-2 model. We demonstrate that the results given by the new algorithm are more accurate than those of the conventional method without wavefield separation.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2009 SEG Annual Meeting, October 25–30, 2009

Paper Number: SEG-2009-2814

... enhances inversion results in

**frequency**-**domain**waveform inversion (Shin et al., 2007), which is one of the advantages of**frequency**-**domain**waveform inversion. We propose to use the source wavelet estimated by an inversion algorithm in reverse-time**migration**. The estimated source wavelet is used when we...
Abstract

Summary We propose to introduce source wavelet estimation in reverse-time migration. Numerical examples show that we can enhance reverse-time migration images using an estimated source wavelet. In an effort to obtain higher-resolution migrated images, we scale the migrated results by the diagonal of the pseudo-Hessian matrix and then multiply the resulting images by the amplitude spectrum of the source wavelet. The latter gives an effect of weighting frequency components around the dominant frequency of the source wavelet. Introduction Reverse-time migration using two-way wave equations has the advantages that it can preserve real amplitudes of seismic wavefields and handle steep-dip reflectors. The rapid growth of computer technology has increased the popularity of reverse-time migration among geophysicists and applied mathematicians who want to obtain high-fidelity subsurface images to find reservoirs containing oil and gas. Reverse-time migration is performed by back-propagating field data, which is based on the adjoint state of the wave equation. Tarantola (1984) showed that reverse-time migration is tantamount to performing the first iteration of full waveform inversion, which allows us to share the same algorithm as full waveform inversion (Shin et al., 2003). While waveform inversion is accomplished by back-propagating the residuals between observed data and modeled data and then convolving the back-propagated residuals with virtual sources (which are obtained from forward-modeled data), reverse-time migration back-propagates field data rather than residuals and then convolves the back-propagated field data with virtual sources. This is the main difference between waveform inversion and reverse-time migration. In other words, we can perform reverse-time migration by replacing the modeled data with null data in the waveform inversion, which transforms the residual into the observed data (Shin et al., 2003) in waveform inversion. Especially, using a smoothed model for an initial model in waveform inversion also has an effect of reducing the residuals to observed data, because smoothed models do not generate any reflections in their model response. Although we can obtain velocity information through waveform inversion, we usually obtain subsurface images rather than velocity information from the reverse-time migration. It has been proven that source wavelet estimation enhances inversion results in frequency-domain waveform inversion (Shin et al., 2007), which is one of the advantages of frequency-domain waveform inversion. We propose to use the source wavelet estimated by an inversion algorithm in reverse-time migration. The estimated source wavelet is used when we compute forward-modeled data to obtain virtual sources. To obtain high-fidelity two-way reverse-time migration images, we also multiply migrated images by the amplitude spectrum of the estimated source wavelet, which has an effect of weighting frequency components of migrated results. Consequently, frequency components around the dominant frequency will influence the migration results more than other lower or higher frequency components do. Reverse-time migration algorithm Migration can generally be expressed as a zero lag of cross-correlation between the partial derivative wavefields with respect to an earth parameter (such as velocity, density or impedance) and the measured data on the receivers in the time domain (Shin et al., 2003):

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2014 SEG Annual Meeting, October 26–31, 2014

Paper Number: SEG-2014-1566

... Summary The

**frequency**sampling of**frequency**-**domain**reverse-time**migration**is defined by the Nyquist-Shannon theorem. An integration (summation) of the images over all**frequencies**during imaging condition corresponds to zero-lag cross-correlation in the time**domain**. We propose a method...
Abstract

Summary The frequency sampling of frequency-domain reverse-time migration is defined by the Nyquist-Shannon theorem. An integration (summation) of the images over all frequencies during imaging condition corresponds to zero-lag cross-correlation in the time domain. We propose a method to interpolate images between sparse-frequency samples in order to achieve frequency-domain two-way migration with reduced cost in wave modeling. Using a high-frequency asymptotic expression of the image, we show numerically that this assumption applies to a wide range of frequencies that contribute to the significant part of the final image. The image interpolation is then carried out by fitting the asymptotic coefficients at sparse-frequency samples in the least-squares sense. We employ a regularized nonstationary autoregression to determine the traveltime and amplitude terms. The choice of sparse-frequency samples can be made according to the frequency spectrum of the source wavelet and/or data. Several synthetic examples demonstrate the validity of the proposed approach.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the SEG International Exposition and Annual Meeting, September 15–20, 2019

Paper Number: SEG-2019-3215854

... reverse time

**migration**(RTM) with the rough topography have been proposed in the time**domain**. Compared with the time-**domain**seismic imaging methods, the**frequency**-**domain**seismic imaging methods provide more straightforward estimation of model parameters and direct implementation of multiple sources. Here...
Abstract

ABSTRACT Considering the fact that most inland seismic surveys are carried out in basin and mountain areas, the development of seismic imaging techniques with the presence of rough topography is very important for seismic data processing and interpretation. Numerous researches on seismic reverse time migration (RTM) with the rough topography have been proposed in the time domain. Compared with the time-domain seismic imaging methods, the frequency-domain seismic imaging methods provide more straightforward estimation of model parameters and direct implementation of multiple sources. Here, we proposed a frequency-domain finite-difference prestack RTM with the presence of irregular rough topography in the curvilinear coordinate system. The boundary-conforming method is used to discretize the model with the surface topography. In the frequency domain, we transform the second-order elastic wave equations from the Cartesian coordinate system to the curvilinear coordinate system. The zero-lag cross-correlation is used as the imaging condition. Numerical studies show that our RTM algorithm can accurately provide the velocity structure of subsurface. Presentation Date: Tuesday, September 17, 2019 Session Start Time: 9:20 AM Presentation Start Time: 9:20 AM Location: Poster Station 11 Presentation Type: Poster

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2017 SEG International Exposition and Annual Meeting, September 24–29, 2017

Paper Number: SEG-2017-17685570

... : 53rd Annual International Meeting, SEG, Expanded Abstracts , 382 – 385 , 10.1190/1.1893867 .

**Frequency**-**domain**reverse-time**migration**using generalized multiscale forward modeling Yongchae Cho*, Richard L. Gibson Jr., and Shubin Fu, Texas A&M University SUMMARY Reverse time**migration**(RTM...
Abstract

ABSTRACT Reverse time migration (RTM) is widely used due to its ability to recover complex geological structures that might not imaged correctly with methods based on ray theory. However, RTM incurs a considerable computational cost. For this reason, we applied a model reduction technique that solves local spectral problems on a fine-grid to simulate wave propagation rapidly on a coarser-grid. We can also greatly reduce the computation cost by applying a frequency-domain implementation that requires only a one-time matrix inversion for wave simulation. The multiscale model reduction, a fundamental aspect of the generalized multiscale finite element method (GMsFEM), is obtained by utilizing a set of basis functions determined from a spectral problem. We can tune the accuracy and computational speed by varying these number of functions. Applying RTM with fewer basis functions provides results more rapidly, though the usable frequency band will decrease. However, we can still clearly interpret large-scale structures from the multiscale RTM result. This is useful when the velocity model needs to be updated, as it allows faster generation of trail images. In addition, multiscale RTM with a larger number basis functions can provide faster imaging than current approaches without sacrificing accuracy. Presentation Date: Wednesday, September 27, 2017 Start Time: 3:30 PM Location: 371A Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015

Paper Number: SEG-2015-5909496

...

**Frequency****domain**least-squares reverse time**migration**with a modified scattering-integral approach Jizhong Yang*, Yuzhu Liu and Liangguo Dong, State Key Laboratory of Marine Geology, Tongji University Summary Least-squares reverse time**migration**(LSRTM) is an iterative inversion-based imaging...
Abstract

Summary Least-squares reverse time migration (LSRTM) is an iterative inversion-based imaging process, which can suppress migration artefacts, balance reflector amplitudes, and enhance spatial resolution compared with standard reverse time migration (RTM). The widely accepted approach for gradient calculation in LSRTM is the adjoint-state method, where the forward propagated source wavefields are zero-lag cross-correlated with the back-propagated receiver wavefields. In this study, we propose a practical alternative for implementing frequency domain RTM (FRTM) and LSRTM (FLSRTM) with a modified scattering-integral approach. The gradient of the misfit function with respect to model parameters is formulated as matrix-vector products, which are calculated with vector operations through the accumulation of decomposed vector-scalar products without explicitly building the kernel matrix. With such a matrix-based scattering-integral approach, we can guarantee that the migration operator is the exact adjoint (conjugate transpose) of the forward Born modeling operator while with reduced memory requirement. At the meantime, the Gauss-Newton normal equation is iteratively solved with a matrix-free conjugate gradient algorithm. The Hessian-vector products are calculated based on a demigration/migration procedure, which are implemented with two nested kernel-vector products. Thus, no additional forward simulations are required any more. The numerical example proves the feasibility of our method. Introduction Seismic migration is an important imaging process in exploration seismology, through which we can build an image of the Earth’s interior from recorded field data, by back locating these data into their ‘true’ geological position in the subsurface. The classic imaging principle for shot-based migration states that reflectors exist where the first-arrival downward wavefield is coincident with the up-going wavefield in time (Claerbout, 1971). Theoretically speaking, migration algorithms under the framework of this classic imaging principle are just performed as the adjoint of the forward Born modeling operator rather than the inverse applied to the observed seismic data. However, the adjoint operator is not a good approximation to the inverse operator (Claerbout, 1992), especially when the data is imperfect in cases with limited acquisition aperture, irregular and sparse spatial sampling, and poor illumination. The final migrated image will be degraded in resolution with distorted amplitudes and blurred reflectivity.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2014 SEG Annual Meeting, October 26–31, 2014

Paper Number: SEG-2014-1641

..., flexibility and accuracy. For areas of complex subsurface geology, the reverse time

**migration**(RTM) is the preferred option. Here we propose a new RTM procedure in the**frequency****domain**for the DPW data. For the DPW in the**frequency****domain**, the shot gathers are fully decomposed from shots, receivers and time...
Abstract

Summary Double plane wave (DPW) downward continuation integral provides a strategy for migrating seismic data slant stacked into the DPW domain. Previous works on migration procedure for DPW data using Kirchhoff-integral migration demonstrates that the DPW migration has high efficiency, flexibility and accuracy. For areas of complex subsurface geology, the reverse time migration (RTM) is the preferred option. Here we propose a new RTM procedure in the frequency domain for the DPW data. For the DPW in the frequency domain, the shot gathers are fully decomposed from shots, receivers and time into source plane wave components, receiver or offset plane wave components and frequencies. We can select any part from this volume to carry out migration using DPW RTM, which makes the algorithm flexible. It has the potential to speed up the calculation and maintain reasonable resolution at the same time. DPW RTM requires only a limited number of synthetic forward propagation for the source plane waves. It can reduce the calculation and that is important for the large dataset. DPW RTM can generate ray parameter CIGs at the end of migration providing us with an easy tool for velocity analysis. We demonstrate effectiveness of our algorithm with application to a synthetic dataset.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2013 SEG Annual Meeting, September 22–27, 2013

Paper Number: SEG-2013-0132

...

**migration**artifacts while still keep reasonable efficiency. crosswell rtm imaging wavefield artifact**frequency**-**domain**crosswell reverse time**migration**geophysics**migration**seismic data seg houston 2013 reservoir characterization annual international meeting upstream oil & gas wave...
Abstract

Summary Crosswell reverse time migration (RTM) with up and downgoing wave separation can greatly reduce artifacts usually seen in the conventional RTM without wave separation. However, the up and downgoing wave separation cannot be efficiently conducted in space-time domain algorithms because the upper/lower half space images are indistinguishable. In order to tackle this problem, we propose a frequency-domain algorithm with up and downgoing wave decomposition for the crosswell RTM. The numerical experiments and field data example demonstrate that the proposed method can greatly attenuate migration artifacts while still keep reasonable efficiency.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2012 SEG Annual Meeting, November 4–9, 2012

Paper Number: SEG-2012-0531

... in the wavefield. Thus, we consider the application of the logarithm and the L 1 -norm to wavefields, as several earlier studies on waveform inversion applied the logarithm and the L 1 -norm to the objective functions. In this study, we propose an algorithm for

**frequency**-**domain**reverse time**migration**using...
Abstract

Summary To obtain a reverse time migration image, we can display subsurface image by using a zero-lag cross-correlation between modeled and observed wavefields. However, reverse time migration based on the cross-correlation imaging condition can produce a distorted image when noise exists in the wavefield. Thus, we consider the application of the logarithm and the L 1 -norm to wavefields, as several earlier studies on waveform inversion applied the logarithm and the L 1 -norm to the objective functions. In this study, we propose an algorithm for frequency-domain reverse time migration using the logarithm and the L 1 -norm of a wavefield. We test our proposed algorithm on a synthetic dataset generated by the Marmousi model. After verifying the experiment with the synthetic data, we demonstrate the proposed algorithm on a real exploration dataset obtained from an area in the Gulf of Mexico. Through these numerical simulations, we verify the feasibility of the proposed algorithm. Moreover, we expect that the use of the proposed algorithm will reduce the effort of preprocessing procedures.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2011 SEG Annual Meeting, September 18–23, 2011

Paper Number: SEG-2011-3169

... of the objective function. For this reason, the L, 1, -norm is used as an objective function, which shows the robustness against outliers in waveform inversion. In this study, we propose the introduction of the L, 1, -norm into 2D reverse time

**migration**with**frequency**-**domain**modeling operator. We demonstrate our...
Abstract

ABSTRACT In full waveform inversion, the objective function using the L, 2, -norm is almost always used for obtaining subsurface information. However, the waveform inversion with the L, 2, -norm can give distorted results when outliers on seismograms are included in the calculation of the objective function. For this reason, the L, 1, -norm is used as an objective function, which shows the robustness against outliers in waveform inversion. In this study, we propose the introduction of the L, 1, -norm into 2D reverse time migration with frequency-domain modeling operator. We demonstrate our algorithm through numerical examples of synthetic Marmousi model and field data taken at the Gulf of Mexico.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2007 SEG Annual Meeting, September 23–28, 2007

Paper Number: SEG-2007-0594

... exploration. We extend the method and numerical algorithm of

**frequency****domain**(FD) 2-D EM**migration**, developed by Wan and Zhdanov (2005a, b) for full 3-D**migration**. We present several numerical examples of the practical application of this technique for fast imaging of a sea-bottom hydrocarbon (HC) reservoir...
Abstract

Summary In this paper we develop a fast 3-D electromagnetic (EM) migration method for marine geophysical exploration. The developed migration algorithm is based on downward extrapolation of the observed EM field using a special form of finite-difference equation for the migration field. It allows us to migrate within the sea-bottom formations the EM signals observed by the sea-bottom receivers. The migration field is subsequently transformed in the resistivity image of the sea-bottom geoelectrical structures. This technique is in an order faster than the conventional inversion. It can be used for fast imaging of the marine magnetotelluric (MT) and controlled-source electromagnetic (CSEM) data in off-shore hydrocarbon (HC) exploration. Introduction There is growing interest in developing fast interpretation methods for marine controlled-source electromagnetic (MCSEM) data. Over the last few years several papers have been published dedicated to imaging MCSEM data using EM migration (e.g., Tompkins, 2004; Mittet et al., 2005; Wan and Zhdanov, 2005a, b; Zhdanov et al., 2006). In this paper we present new results of developing a fast 3-D EM migration method for marine geophysical exploration. We extend the method and numerical algorithm of frequency domain (FD) 2-D EM migration, developed by Wan and Zhdanov (2005a, b) for full 3-D migration. We present several numerical examples of the practical application of this technique for fast imaging of a sea-bottom hydrocarbon (HC) reservoir. Finite difference migration of 3-D EM field Zhdanov et al., (1996) have developed an efficient algorithm for the finite-difference migration of the 2-D EM field. In this paper we extend this method for 3-D case. According to equation (6), one can find the migration field if the function Qm(x, y, z, w ) is known. This function can be calculated at different levels inside the sea bottom using a 3-D finite-difference technique similar to one developed by Zhdanov et al. (1996) for 2-D fields. Examples of EM migration and imaging of marine EM data We will present below the results of numerical application of the developed algorithm to synthetic and field marine MT and CSEM data. A simplified geoelectrical model of the TWGP survey area We consider first a synthetic model simulating the MCSEM survey in the Troll West Gas Province (TWGP), Offshore Norway (Amundsen et al., 2004). The survey consists of 24 receivers, deployed along a line crossing the Oil Province, the Western Gas Province, and the Eastern Gas Province of the Troll Field. First we consider a simplified geoelectrical model of the TWGP survey area. The gas reservoir is approximated by a 7,000 m x 10,000 m x 100 m prismatic body with a resistivity of 250 Ohm-m. It is located below the sea bottom at a depth of 1,100 m within conductive sediments with a resistivity of 1 Ohm-m. The sea layer has a 300 m depth with a resistivity of 0.2 Ohm-m. Forty-one receivers are located at the sea bottom at 500 m intervals along a 20,000 m profile.The operating frequencies are 1.75, 1.25, 0.75, and 0.25 Hz.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2005 SEG Annual Meeting, November 6–11, 2005

Paper Number: SEG-2005-0518

... Summary This paper discusses an application of electromagnetic (EM)

**migration**for sea-bottom EM imaging. We apply to marine EM data the method of**frequency****domain**EM**migration**developed by Zhdanov et al. (1996) for fast imaging of land EM data. We study a synthetic survey with electric...
Abstract

Summary This paper discusses an application of electromagnetic (EM) migration for sea-bottom EM imaging. We apply to marine EM data the method of frequency domain EM migration developed by Zhdanov et al. (1996) for fast imaging of land EM data. We study a synthetic survey with electric receivers measuring the natural telluric electric field at the sea bottom over a 3-D geoelectrical model of a sea-bottom petroleum reservoir. We also demonstrate that the EM migration can be applied for fast imaging of marine controlled-source electromagnetic data. The results of this modeling show that the migration method can be effectively used for fast sea-bottom imaging of resistive reservoir structures. Introduction The application of EM methods in petroleum exploration requires development of appropriate imaging techniques which provide the means for fast but accurate evaluation of the observed data. In seismic exploration, which is a leading method for oil and gas prospecting, the most widely used imaging technique is seismic migration (Tarantola, 1984; Claerbout, 1985). In a series of publications, Zhdanov and his co-authors have extended the method of seismic migration to the case of a low frequency diffusive EM field (Zhdanov, 1981; Zhdanov and Frenkel, 1983; Zhdanov et al., 1996; Zhdanov, 1999; and Zhdanov, 2002). The US patent for this technology was issued in 2001 (Zhdanov, 2001). The EM migration has important features in common with seismic migration, but differs in that, for geoelectrical problems, EM migration is done on the basis of Maxwell’s equations, while in the seismic case it is based on the wave equation. EM migration, similar to seismic migration, is based on a special form of downward continuation of the observed field or one of its components. This downward continuation is obtained as the solution of the boundary value problem in the lower half-space for the adjoint Maxwell’s equations, in which the boundary values of the migration field on the earth’s surface are determined by the observed EM data. It was shown in the original paper by Zhdanov and Traynin (1997) that EM migration can be treated as an approximate solution of the corresponding EM inverse problem. It was also demonstrated in subsequent publications (see, for example, Zhdanov, 2002) that EM migration can be applied iteratively, which results in a rigorous inverse EM problem solution. Tompkins (2004) has reported an application of this migration technique for fast imaging of Sea Bed Logging (SBL) EM data. In the present paper, we investigate a 3-D geoelectrical model of a sea-bottom petroleum reservoir. We extend the method and numerical algorithm of frequency domain (FD) EM migration, developed by Zhdanov et al. (1996) for processing land EM data, to be effectively used for seabottom imaging of resistive reservoir structures. Numerical study of a sea-bottom electrical field migration Migration of the sea-bottom telluric electric field We will analyze a model of a sea-bottom petroleum reservoir to illustrate seabed imaging with frequency domain EM migration. Figure 1 shows a 3-D view of a model with the corresponding system of Cartesian coordinates.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2002 SEG Annual Meeting, October 6–11, 2002

Paper Number: SEG-2002-1212

... formula type 3 reservoir characterization acquisition geometry velocity model approximation amplitude-preserving finite-difference

**migration**Amplitude-preserving finite-difference**migration**based on a least-squares formulation in the**frequency****domain**René-Edouard Plessix and Wim Mulder, Shell...
Abstract

Summary A migration algorithm based on the least-squares formulation will reconstruct the correct relative reflector amplitudes only if proper migration weights are applied. These migration weights should approximate the pseudo-inverse of the Hessian of the least-squares error functional that measures the difference between observed and modeled data. Common diagonal approximations are based on the assumption of continuous source and receiver coverage with infinite extent and may lead to poor amplitude estimates for deep reflectors. Here, two new amplitude-preserving migration formulae are derived from a Born approximation of the Hessian that avoids the assumption of infinite continuous coverage.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2002 SEG Annual Meeting, October 6–11, 2002

Paper Number: SEG-2002-1152

... Summary 3-D prestack

**migration**of constant-offset data can be formulated in the**frequency**-wavenumber**domain**as a stationary phase approximation to equivalent Kirchhoff expressions. This formulation constitutes a proof of Dubrulle''s (1983) heuristic algorithm. Numerical implementations are 3-D...
Abstract

Summary 3-D prestack migration of constant-offset data can be formulated in the frequency-wavenumber domain as a stationary phase approximation to equivalent Kirchhoff expressions. This formulation constitutes a proof of Dubrulle''s (1983) heuristic algorithm. Numerical implementations are 3-D extensions of his algorithms and lead to very efficient migration under the assumption of lateral invariance in velocity and acquisition geometry. Introduction Dubrulle (1983) presented a method for migrating 2-D common-offset data in the frequency-wavenumber domain. His algorithm for finite offset data is based on a heuristic extension of an algorithm devised for zero offset data. The phase shifts required to migrate the data are computed by the numerical solution of a pair of algebraic equations relating the traveltime and midpoint ray parameter of a diffraction event to the offset and migration displacement.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2002 SEG Annual Meeting, October 6–11, 2002

Paper Number: SEG-2002-1384

... inversion reflectivity approximation salt lake city

**migration**optimization problem reflector equation iteration finite-difference iterative**migration****frequency****domain**linearized waveform inversion Finite-difference iterative**migration**by linearized waveform inversion in the**frequency****domain**S...
Abstract

Summary We present an iterative migration technique for mapping seismic data to reflector amplitudes, obtained by formulating migration as an optimization problem. The method can be based on any kind of seismic modeling and provides true-amplitude images in a natural way. In this paper, we use a finite-difference solution of the linearized constant-density wave equation in the frequency domain. Because the constant-density acoustic equation cannot handle impedance contrasts, we use its linearized form, which is equivalent to the Born approximation. Examples are given for synthetic and real data and show that the iterative technique improves the amplitudes and resolution of reflectors.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2001 SEG Annual Meeting, September 9–14, 2001

Paper Number: SEG-2001-1103

....

**Migration**based on a finite difference scheme for the two-way wave equation does not suffer from these drawbacks but the computational cost is very high. However, if the wave equation is solved in the**frequency****domain**, the computational cost of the finite difference scheme is proportional to the number...
Abstract

Summary The migration of seismic data recorded over a complex subsurface structure requires accurate modeling of wave propagation. Ray tracing, based on a high-frequency approximation, and one-way wave equations assuming small velocity perturbations, often break down in complex models. Migration based on a finite difference scheme for the two-way wave equation does not suffer from these drawbacks but the computational cost is very high. However, if the wave equation is solved in the frequency domain, the computational cost of the finite difference scheme is proportional to the number of frequencies. After a Fourier transform of the time-domain seismic data, each frequency panel of the data carries information on the reflectivity. To make finite difference migration affordable, it is proposed to migrate only a few frequency panels and apply a regularization term to reduce the ringing in the migration image.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2018 SEG International Exposition and Annual Meeting, October 14–19, 2018

Paper Number: SEG-2018-2997917

... anisotropic media. We develop an computationally efficient vector elastic reverse-time

**migration**method in the hybrid time and**frequency****domains**to greatly improve the computational efficiency. This computational efficiency improvement results largely from reducing the high computational cost of qP/qS-wave...
Abstract

ABSTRACT Vector elastic reverse-time migration is an efficient tool to provide clear subsurface elastic images with correct polarities. However, the decomposition of elastic wavefields into vector Pand S-wavefields is computationally expensive, particularly in heterogeneous and complex anisotropic media. We develop an computationally efficient vector elastic reverse-time migration method in the hybrid time and frequency domains to greatly improve the computational efficiency. This computational efficiency improvement results largely from reducing the high computational cost of qP/qS-wave decomposition in anisotropic media. Rather than decomposing elastic wavefields in the time domain into vector qP and qS wavefields for each time step, we conduct the wavefield decomposition in the frequency domain for a few given frequencies. In general, the number of selected frequencies is much smaller than the number of time steps, leading to greatly reduced computational costs for wavefield decomposition in the frequency domain. We further combine an implicit directional wavefield separation into the vector elastic reverse-time migration to enhance the image quality. Numerical results demonstrate that our new method produces almost identical images for complex models using only approximately ten percent of the computational time of the conventional timedomain method. Presentation Date: Tuesday, October 16, 2018 Start Time: 1:50:00 PM Location: 207A (Anaheim Convention Center) Presentation Type: Oral

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