Linearized inversion of amplitude versus offset (AVO) from multi-offset data consists of weighted... more Linearized inversion of amplitude versus offset (AVO) from multi-offset data consists of weighted stacking. It yields the elastic parameters as traces in terms of bandlimited relative contrasts. (Smith and Gidlow 1987; Lortzer and Berkhout 1989). The weighted stacking results are displayed as seismie traces. These traces may be considered as spiky relative contrasts convolved with the seismic wavelet.
The Journal of the Acoustical Society of America, 1997
A method is proposed to calculate and measure impulse responses in an enclosure along closely spa... more A method is proposed to calculate and measure impulse responses in an enclosure along closely spaced receiver arrays. Hence, instead of using a sparse distribution of receiver positions with single microphones, as is common practice now, arrays of microphones are applied to register the complex sound fields within enclosures. This way, there is a strong spatial correlation between adjacent responses, enabling one to analyze individual reflected wavefronts. It is shown that visualization of the recorded data in a two-dimensional domain, defined by detector position and travel time, gives a significantly improved insight in the structure of complex sound fields. This insight is further increased by applying the linear Radon transform (plane wave decomposition), yielding a representation of the data in the so-called ray parameter versus intercept time domain.
SEG Technical Program Expanded Abstracts 1997, 1997
In this paper we extend the Common Focus Point (CFP) processing technique [2] to mode-converted d... more In this paper we extend the Common Focus Point (CFP) processing technique [2] to mode-converted data. We show that, by introducing minor simplifications, the different data types can be migrated independently in exactly the same manner as in the acoustic situation. WRW-model for multi-component data It has been shown that the ¡ £ ¢ ¤ ¡-model for compressional waves [1] can be logically extended to converted and shear waves [3], according to
SEG Technical Program Expanded Abstracts 2014, 2014
A method is proposed that provides new insight in the separability of blended shot records. The p... more A method is proposed that provides new insight in the separability of blended shot records. The principle is that we don’t look at the detector side only, but we look at the source side as well. This is done by full wavefield reverse modeling: blended measurements are reversely extrapolated down to the deepest depth level and back to the surface, showing the source signals of the blended source array. Analysis of these source signals reveals what actually happened at the source side during acquisition. This extension to the blending theory leads to a new deblending concept that involves both the blended measurements and the blended source array signals.
SEG Technical Program Expanded Abstracts 1997, 1997
In this paper, the generation of 3-D pseudo VSP data is discussed and illustrated on a dataset. W... more In this paper, the generation of 3-D pseudo VSP data is discussed and illustrated on a dataset. We start with a 3-D shot record This shot record has been transformed to a pseudo VSP dataset The result is compared with a modeled VSP and integrated in combination with the slices from the 3-O migrated volume of data. In combination, the integration of different datasets yields a better insight and understanding of the wave propagation and the various events originating from the complex subsurface model. Some 3-D snapshots are shown to improve the data interpretation, further showing the wave propagation at different times. The model contains three layers where the uppermost layer is a water layer on top of an irregular layer and a dipping plane. Absorbing boundaries have been applied around the entire model. In Fig. 1 the volume of the 3-D model is depicted (3 axes x.y.z are indicated). The dimensions of the model are x max =1000m, y max =500m and z max 800m including a 50m = wide absorbing frame around the cube (see fig. 2a; note that the absorbing frame around the model is not shown). The distance between the gridpoints is 5m in all directions. Notice that the model as depicted in Fig. 1 and 2 is displayed with a coarser grid than 5m. Fig. 2b shows the model with the uppermost water layer removed.
SEG Technical Program Expanded Abstracts 1991, 1991
Multi-component seismic data is required to obtain information on the angle-dependent P-P, P-S, S... more Multi-component seismic data is required to obtain information on the angle-dependent P-P, P-S, S-P and S-S reflectivity of the subsurface. It is generally accepted that wave field decomposition should form part of the multi-component processing sequence, aiming at retrieving this reflectivity information. However, the question whether decomposition should take place before or after downward extrapolation has not yet been unambiguously solved. In this paper we argue that, although both procedures are theoretically equivalent, decomposition before downward extrapolation has a number of practical advantages, one of the reasons being the robustness with respect to macro model errors.
SEG Technical Program Expanded Abstracts 1991, 1991
Nowadays, it is well appreciated that the seismic inversion problem is seriously ill-posed. This ... more Nowadays, it is well appreciated that the seismic inversion problem is seriously ill-posed. This means a.o. that parametric estimation by matching model responses with field data (' model fitting') has many pitfalls. To make seismic inversion feasible in practice, a hierarchical subdivision of the subsurface parameters is required; it leads to a stepwise approach to seismic inversion. We have proposed to the industry a stepwise inversion scheme with three hierarchical steps, i.e. surface-relafed pre-processing, reflectivity imaging and target-related post-inversion. Using a systems formulation of the forward seismic model, the hierarchical stepwise approach can be easily explained.
The next generation seismic migration and inversion technology considers multiple scattering as v... more The next generation seismic migration and inversion technology considers multiple scattering as vital information, allowing the industry to derive significantly better reservoir models — with more detail and less uncertainty—while requiring a minimum of user intervention. Three new insights have been uncovered with respect to this fundamental transition. Unblended or blended multiple scattering can be included in the seismic migration process, and it has been proposed to formulate the imaging principle as a minimization problem. The resulting process yields angle-dependent reflectivity and is referred to as recursive full wavefield migration (WFM). The full waveform inversion process for velocity estimation can be extended to a recursive, optionally blended, anisotropic multiple-scattering algorithm. The resulting process yields angle-dependent velocity and is referred to as recursive full waveform inversion (WFI). The mathematical equations of WFM and WFI have an identical structur...
Most present day seismic migration schemes determine only the zero‐offset reflection coefficient ... more Most present day seismic migration schemes determine only the zero‐offset reflection coefficient for each grid point (depth point) in the subsurface. In matrix notation, the zero‐offset reflection coefficient is found on the diagonal of a reflectivity matrix operator that transforms the illuminating source‐wave field into a reflected‐wave field. However, angle dependent reflectivity information is contained in the full reflectivity matrix. Our objective is to obtain angle‐dependent reflection coefficients from seismic data by means of prestack migration (multisource, multioffset). After downward extrapolation of source and reflected wave fields to one depth level, the rows of the reflectivity matrix (representing angle‐dependent reflectivity information for each grid point at that depth level) are recovered by deconvolving the reflected wave fields with the related source wave fields. This process is carried out in the space‐frequency domain. In order to preserve the angle‐dependent...
Part I of this series starts with a brief review of the fundamental principles underlying wave fi... more Part I of this series starts with a brief review of the fundamental principles underlying wave field extrapolation. Next, the total wave field is split into downgoing and upgoing waves, described by a set of coupled one-way wave equations. In cases of limited propagation angles and weak inhomogeneities these one-way wave equations can be decoupled, describing primary waves only. For large propagation angles (up to and including 90") an alternative choice of subdivision into downgoing and upgoing waves is presented. It is shown that this approach is well suited for modeling as well as migration and inversion schemes for seismic data which include critical angle events.
In migration procedures, the velocity profile of the subsurface is the most important input infor... more In migration procedures, the velocity profile of the subsurface is the most important input information. Since, in general, this information is only approximately known, errors in the migration output due to errors in the velocity input occur in ail practical applications. In migration, velocity errors and depth errors can be interchanged. This interchange property is perfect in the paraxial approximation. From this result it follows that migration with incorrect velocities may still yield correctly migrated data if the imaging principle is modified. This attractive property can be used in the stripping version of migration (recursive migration).
Inversion of multicomponent seismic data can be subdivided in three main processes : (1) Surface-... more Inversion of multicomponent seismic data can be subdivided in three main processes : (1) Surface-related preprocessing (decomposition of the multicomponent data into ' primary ' Pand S-wave responses). (2) Prestack migration of the primary P-and S-wave responses, yielding the (angle-dependent) P-P, P-s, s-P and s-S reflectivity of the subsurface. (3) Targetrelated post-processing (transformation of the reflectivity into the rock and pore parameters in the target). This paper deals with the theoretical aspects of surface-related preprocessing. In a multicomponent seismic data set the P-and S-wave responses of the subsurface are distorted by two main causes: (1) The seismic vibrators always radiate a mixture of P-and S-waves into the subsurface. Similarly, the geophones always measure a mixture of Pand S-waves. (2) The free surface reflects any upgoing wave fully back into the subsurface. This gives rise to strong multiple reflections, including conversions. Therefore, surface-related preprocessing consists of two steps : (1) Decomposition of the multicomponent data (pseudo Pand S-wave responses) into true Pand S-wave responses. In practice this procedure involves (a) decomposition per common shot record of the particle velocity vector into scalar upgoing P-and S-waves, followed by (b) decomposition per common receiver record of the traction vector into scalar downgoing P-and S-waves. (2) Elimination of the surface-related multiple reflections and conversions. In this procedure the free surface is replaced by a reflection-free surface. The effect is that we obtain 'primary' Pand S-wave responses, that contain internal multiples only.
A unifying scientific framework is proposed that connects the different worlds of active and pass... more A unifying scientific framework is proposed that connects the different worlds of active and passive seismic methods. The involved seismic sources may be man-made or natural, they may be situated at the surface or in the subsurface, they may be impulsive or dispersive, the firing times may be user-controlled or unknown and the measured wavefields may contain any complexity. A link is made between the method of incoherent shooting (man-made blending) and the recording of passive data (natural blending). We particularly focus on the growing field of microseismics. The proposed framework leads to a three-step inversion scheme that uses both primary and multiple scattering as carriers of subsurface information (double illumination). Results of the scheme indicate that the double illumination concept is very attractive for micro-earthquake imaging.
Linearized inversion of amplitude versus offset (AVO) from multi-offset data consists of weighted... more Linearized inversion of amplitude versus offset (AVO) from multi-offset data consists of weighted stacking. It yields the elastic parameters as traces in terms of bandlimited relative contrasts. (Smith and Gidlow 1987; Lortzer and Berkhout 1989). The weighted stacking results are displayed as seismie traces. These traces may be considered as spiky relative contrasts convolved with the seismic wavelet.
The Journal of the Acoustical Society of America, 1997
A method is proposed to calculate and measure impulse responses in an enclosure along closely spa... more A method is proposed to calculate and measure impulse responses in an enclosure along closely spaced receiver arrays. Hence, instead of using a sparse distribution of receiver positions with single microphones, as is common practice now, arrays of microphones are applied to register the complex sound fields within enclosures. This way, there is a strong spatial correlation between adjacent responses, enabling one to analyze individual reflected wavefronts. It is shown that visualization of the recorded data in a two-dimensional domain, defined by detector position and travel time, gives a significantly improved insight in the structure of complex sound fields. This insight is further increased by applying the linear Radon transform (plane wave decomposition), yielding a representation of the data in the so-called ray parameter versus intercept time domain.
SEG Technical Program Expanded Abstracts 1997, 1997
In this paper we extend the Common Focus Point (CFP) processing technique [2] to mode-converted d... more In this paper we extend the Common Focus Point (CFP) processing technique [2] to mode-converted data. We show that, by introducing minor simplifications, the different data types can be migrated independently in exactly the same manner as in the acoustic situation. WRW-model for multi-component data It has been shown that the ¡ £ ¢ ¤ ¡-model for compressional waves [1] can be logically extended to converted and shear waves [3], according to
SEG Technical Program Expanded Abstracts 2014, 2014
A method is proposed that provides new insight in the separability of blended shot records. The p... more A method is proposed that provides new insight in the separability of blended shot records. The principle is that we don’t look at the detector side only, but we look at the source side as well. This is done by full wavefield reverse modeling: blended measurements are reversely extrapolated down to the deepest depth level and back to the surface, showing the source signals of the blended source array. Analysis of these source signals reveals what actually happened at the source side during acquisition. This extension to the blending theory leads to a new deblending concept that involves both the blended measurements and the blended source array signals.
SEG Technical Program Expanded Abstracts 1997, 1997
In this paper, the generation of 3-D pseudo VSP data is discussed and illustrated on a dataset. W... more In this paper, the generation of 3-D pseudo VSP data is discussed and illustrated on a dataset. We start with a 3-D shot record This shot record has been transformed to a pseudo VSP dataset The result is compared with a modeled VSP and integrated in combination with the slices from the 3-O migrated volume of data. In combination, the integration of different datasets yields a better insight and understanding of the wave propagation and the various events originating from the complex subsurface model. Some 3-D snapshots are shown to improve the data interpretation, further showing the wave propagation at different times. The model contains three layers where the uppermost layer is a water layer on top of an irregular layer and a dipping plane. Absorbing boundaries have been applied around the entire model. In Fig. 1 the volume of the 3-D model is depicted (3 axes x.y.z are indicated). The dimensions of the model are x max =1000m, y max =500m and z max 800m including a 50m = wide absorbing frame around the cube (see fig. 2a; note that the absorbing frame around the model is not shown). The distance between the gridpoints is 5m in all directions. Notice that the model as depicted in Fig. 1 and 2 is displayed with a coarser grid than 5m. Fig. 2b shows the model with the uppermost water layer removed.
SEG Technical Program Expanded Abstracts 1991, 1991
Multi-component seismic data is required to obtain information on the angle-dependent P-P, P-S, S... more Multi-component seismic data is required to obtain information on the angle-dependent P-P, P-S, S-P and S-S reflectivity of the subsurface. It is generally accepted that wave field decomposition should form part of the multi-component processing sequence, aiming at retrieving this reflectivity information. However, the question whether decomposition should take place before or after downward extrapolation has not yet been unambiguously solved. In this paper we argue that, although both procedures are theoretically equivalent, decomposition before downward extrapolation has a number of practical advantages, one of the reasons being the robustness with respect to macro model errors.
SEG Technical Program Expanded Abstracts 1991, 1991
Nowadays, it is well appreciated that the seismic inversion problem is seriously ill-posed. This ... more Nowadays, it is well appreciated that the seismic inversion problem is seriously ill-posed. This means a.o. that parametric estimation by matching model responses with field data (' model fitting') has many pitfalls. To make seismic inversion feasible in practice, a hierarchical subdivision of the subsurface parameters is required; it leads to a stepwise approach to seismic inversion. We have proposed to the industry a stepwise inversion scheme with three hierarchical steps, i.e. surface-relafed pre-processing, reflectivity imaging and target-related post-inversion. Using a systems formulation of the forward seismic model, the hierarchical stepwise approach can be easily explained.
The next generation seismic migration and inversion technology considers multiple scattering as v... more The next generation seismic migration and inversion technology considers multiple scattering as vital information, allowing the industry to derive significantly better reservoir models — with more detail and less uncertainty—while requiring a minimum of user intervention. Three new insights have been uncovered with respect to this fundamental transition. Unblended or blended multiple scattering can be included in the seismic migration process, and it has been proposed to formulate the imaging principle as a minimization problem. The resulting process yields angle-dependent reflectivity and is referred to as recursive full wavefield migration (WFM). The full waveform inversion process for velocity estimation can be extended to a recursive, optionally blended, anisotropic multiple-scattering algorithm. The resulting process yields angle-dependent velocity and is referred to as recursive full waveform inversion (WFI). The mathematical equations of WFM and WFI have an identical structur...
Most present day seismic migration schemes determine only the zero‐offset reflection coefficient ... more Most present day seismic migration schemes determine only the zero‐offset reflection coefficient for each grid point (depth point) in the subsurface. In matrix notation, the zero‐offset reflection coefficient is found on the diagonal of a reflectivity matrix operator that transforms the illuminating source‐wave field into a reflected‐wave field. However, angle dependent reflectivity information is contained in the full reflectivity matrix. Our objective is to obtain angle‐dependent reflection coefficients from seismic data by means of prestack migration (multisource, multioffset). After downward extrapolation of source and reflected wave fields to one depth level, the rows of the reflectivity matrix (representing angle‐dependent reflectivity information for each grid point at that depth level) are recovered by deconvolving the reflected wave fields with the related source wave fields. This process is carried out in the space‐frequency domain. In order to preserve the angle‐dependent...
Part I of this series starts with a brief review of the fundamental principles underlying wave fi... more Part I of this series starts with a brief review of the fundamental principles underlying wave field extrapolation. Next, the total wave field is split into downgoing and upgoing waves, described by a set of coupled one-way wave equations. In cases of limited propagation angles and weak inhomogeneities these one-way wave equations can be decoupled, describing primary waves only. For large propagation angles (up to and including 90") an alternative choice of subdivision into downgoing and upgoing waves is presented. It is shown that this approach is well suited for modeling as well as migration and inversion schemes for seismic data which include critical angle events.
In migration procedures, the velocity profile of the subsurface is the most important input infor... more In migration procedures, the velocity profile of the subsurface is the most important input information. Since, in general, this information is only approximately known, errors in the migration output due to errors in the velocity input occur in ail practical applications. In migration, velocity errors and depth errors can be interchanged. This interchange property is perfect in the paraxial approximation. From this result it follows that migration with incorrect velocities may still yield correctly migrated data if the imaging principle is modified. This attractive property can be used in the stripping version of migration (recursive migration).
Inversion of multicomponent seismic data can be subdivided in three main processes : (1) Surface-... more Inversion of multicomponent seismic data can be subdivided in three main processes : (1) Surface-related preprocessing (decomposition of the multicomponent data into ' primary ' Pand S-wave responses). (2) Prestack migration of the primary P-and S-wave responses, yielding the (angle-dependent) P-P, P-s, s-P and s-S reflectivity of the subsurface. (3) Targetrelated post-processing (transformation of the reflectivity into the rock and pore parameters in the target). This paper deals with the theoretical aspects of surface-related preprocessing. In a multicomponent seismic data set the P-and S-wave responses of the subsurface are distorted by two main causes: (1) The seismic vibrators always radiate a mixture of P-and S-waves into the subsurface. Similarly, the geophones always measure a mixture of Pand S-waves. (2) The free surface reflects any upgoing wave fully back into the subsurface. This gives rise to strong multiple reflections, including conversions. Therefore, surface-related preprocessing consists of two steps : (1) Decomposition of the multicomponent data (pseudo Pand S-wave responses) into true Pand S-wave responses. In practice this procedure involves (a) decomposition per common shot record of the particle velocity vector into scalar upgoing P-and S-waves, followed by (b) decomposition per common receiver record of the traction vector into scalar downgoing P-and S-waves. (2) Elimination of the surface-related multiple reflections and conversions. In this procedure the free surface is replaced by a reflection-free surface. The effect is that we obtain 'primary' Pand S-wave responses, that contain internal multiples only.
A unifying scientific framework is proposed that connects the different worlds of active and pass... more A unifying scientific framework is proposed that connects the different worlds of active and passive seismic methods. The involved seismic sources may be man-made or natural, they may be situated at the surface or in the subsurface, they may be impulsive or dispersive, the firing times may be user-controlled or unknown and the measured wavefields may contain any complexity. A link is made between the method of incoherent shooting (man-made blending) and the recording of passive data (natural blending). We particularly focus on the growing field of microseismics. The proposed framework leads to a three-step inversion scheme that uses both primary and multiple scattering as carriers of subsurface information (double illumination). Results of the scheme indicate that the double illumination concept is very attractive for micro-earthquake imaging.
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Papers by A. Berkhout