We present an implementation of three-dimensional dynamic ray tracing in anisotropic elastic medi... more We present an implementation of three-dimensional dynamic ray tracing in anisotropic elastic media. The geometrical ray approximation is extended through Maslov uniform asymptotics, and is employed in the calculation of Maslov canonical operators describing the transmission of waves between two points in the background medium.
ABSTRACT We present a 3D contrast source inversion scheme for electromagnetic data in conductive ... more ABSTRACT We present a 3D contrast source inversion scheme for electromagnetic data in conductive media. We consider only contrasts in electric conductivity but allow the medium to be transversely isotropic in the vertical direction. This has applications in, for instance, inversion of marine controlled-source electromagnetic data. The contrast source inversion (CSI) method is based on the integral equation formulation of electromagnetic field propagation and solves the inverse problem of determining the conductivity structure of the subsurface. The method minimizes a cost functional that enforces both data fidelity and that the solution satisfy the Lippmann-Schwinger equation. Further regularization is introduced linearly into the cost functional to incorporate prior model information. Although the problem is nonlinear, the chosen strategy splits the minimization problem into two linear problems, which are solved alternatingly. To this end, contrast sources are introduced, which may be interpreted as sources emitting the scattered field from a scattering object. Two synthetic and two real field examples are inverted, which demonstrates the method and how the transversely isotropic in the vertical direction (TIV) inversion performs compared with isotropic inversion. The CSI method is found to be applicable to real field examples, and the results show that a TIV inversion is preferred over isotropic to identify weak anomalies in these examples. The reason for this is that both the horizontal and vertical conductivity affects the signal propagation in the overburden.
ABSTRACT We evaluated a joint contrast source inversion scheme for marine controlled-source elect... more ABSTRACT We evaluated a joint contrast source inversion scheme for marine controlled-source electromagnetic (mCSEM) and magnetotelluric (MT) data based on a scattered field formulation. The scheme considered only contrasts in electric conductivity, and it allowed the medium to be transversely isotropic with a vertical symmetry axis. The method was based on the integral equation formulation of electromagnetic field propagation, and we demonstrated how the method solved the inverse problem of determining the conductivity structure of the subsurface. The method did not consider MT impedances as data input to inversion, but instead explicitly the field components, and the consequences of this approach, were discussed. Although there are challenges associated with source estimation and data noise, we found it easier to make connections to CSEM and it simplified some computational issues. Three synthetic examples were considered to demonstrate the method: a reservoir below an anisotropic overburden, a salt diapir, and a reservoir near a salt diapir. MT and CSEM data were first treated sequentially, first inverting the MT data and using the result as the initial model and in the regularization in CSEM inversion. The result of this approach was then compared to a joint inversion. The same approach was finally applied to a real data set. We found that sequential inversions in some situations produced similar results as joint inversions, and hence, joint inversion may not be necessary in all situations. Nonetheless, joint inversion could be useful for imaging salt diapirs and eventually hydrocarbons near salt. In particular, it was useful to map the spatial extent of the salt diapirs. It was, moreover, a useful tool for checking data consistency in different models with respect to several data types.
ABSTRACT We present an integral equation framework for 2.5D frequency domain EM modelling in cond... more ABSTRACT We present an integral equation framework for 2.5D frequency domain EM modelling in conductive media, i.e. in media which are assumed invariant in one direction. Furthermore, we consider media which are transversely isotropic in the vertical direction (TIV), thus allowing the horizontal and vertical conductivities to differ. The integral equation framework allows for discretization of only a very limited area of the model, given a proper background model, thus leading to a small system of equations to be solved. The 2.5D integral equation method is suitable for studying the effect of localized resistivity anomalies efficiently and makes the generalization to real-world examples easier than for 1D modelling codes. We model three experiments to analyse and better understand the uncertainties of normalized amplitude and phase difference plots. Anisotropy has a significant effect on marine controlled source electromagnetic (mCSEM) data, and normalized amplitude graphs change both magnitude and position when changing the model to which one normalizes. It suggests that interpreters should be cautious when applying this to real data, where the model that caused the response at the reference receiver is unknown and may change along the line of receivers. Finally, we investigate whether mCSEM data are likely to be able to detect conductive inclusions in the stem of a salt diapir. When the models are exactly known, normalized amplitude plots can be used to check the sensitivity to perturbations.
Velocity-independent seismic data processing requires information about the local slope in the da... more Velocity-independent seismic data processing requires information about the local slope in the data. From estimates of local time and space derivatives of the data, a total least-squares algorithm gives an estimate of the local slope at each data point. Total least squares minimizes the orthogonal distance from the data points (the local time and space derivatives) to the fitted straight line defining the local slope. This gives a more consistent estimate of the local slope than standard least squares because it takes into account uncertainty in the temporal and spatial derivatives. The total least-squares slope estimate is the same as the one obtained from using the structure tensor with a rectangular window function. The estimate of the local slope field is used to extrapolate all traces in a seismic gather to the smallest recorded offset without using velocity information. Extrapolation to zero offset is done using a hyperbolic traveltime function in which slope information replaces the knowledge of the normal moveout (NMO) velocity. The new data processing method requires no velocity analysis and there is little stretch effect. All major reflections and diffrac-tions that are present at zero offset will be reproduced in the output zero-offset section. Therefore, if multiple reflections are undesired in the output, they should be removed before data extrapolation to zero offset. The automatic method is sensitive to noise, so for poor signal-to-noise ratios, standard NMO velocities for primary reflections can be used to compute the slope field. Synthetic and field data examples indicate that compared with standard seismic data processing (velocity analysis, mute, NMO correction, and stack), our method provides an improved zero-offset section in complex data areas.
ABSTRACT A combination of prestack elastic inversion with gravity modeling has been applied to a ... more ABSTRACT A combination of prestack elastic inversion with gravity modeling has been applied to a shallow seismic anomaly in the southern Barents Sea. The anomaly is crosscutting dipping layers of late Paleocene age. Earlier seismic interpretations indicate a possible origin in gas-hydrated sediments trapping underlying free gas. Our interpretation includes seismic inversion of a seismic model which consists of a stack of isotropic, homogeneous, and anelastic layers. The unknown parameters are the P- and S-wave velocities, density, and thickness for each layer. As densities are poorly determined by this method, we included gravity modeling, which improved the density estimates. The resulting para meters have been integrated by rock physics calculations and the knowledge of typical attributes of gas hydrate occurrences. The top of the seismic anomaly is interpreted as a reflection from the base of a gas-hydrated sediment trapping underlying free gas. The base of the anomaly is the gas-water contact, which deviates from a flat spot due to capillary pressure differences related to lithology and the generation process of gas hydrate. The estimated density has been interpreted together with well results and indicates a significant amount of gas filling the pore volume.
SEG Technical Program Expanded Abstracts 1992, 1992
... The nonlinear objective function (3) can be decoupled (Cad-zow, 1990) to give a simplified no... more ... The nonlinear objective function (3) can be decoupled (Cad-zow, 1990) to give a simplified nonlinear optimization prob-lem for the coefficient vector r. When introducing matrix notation the moveout corrected data window for a single event consisting of ... 2 Robust AVO analysis ...
We present an implementation of three-dimensional dynamic ray tracing in anisotropic elastic medi... more We present an implementation of three-dimensional dynamic ray tracing in anisotropic elastic media. The geometrical ray approximation is extended through Maslov uniform asymptotics, and is employed in the calculation of Maslov canonical operators describing the transmission of waves between two points in the background medium.
ABSTRACT We present a 3D contrast source inversion scheme for electromagnetic data in conductive ... more ABSTRACT We present a 3D contrast source inversion scheme for electromagnetic data in conductive media. We consider only contrasts in electric conductivity but allow the medium to be transversely isotropic in the vertical direction. This has applications in, for instance, inversion of marine controlled-source electromagnetic data. The contrast source inversion (CSI) method is based on the integral equation formulation of electromagnetic field propagation and solves the inverse problem of determining the conductivity structure of the subsurface. The method minimizes a cost functional that enforces both data fidelity and that the solution satisfy the Lippmann-Schwinger equation. Further regularization is introduced linearly into the cost functional to incorporate prior model information. Although the problem is nonlinear, the chosen strategy splits the minimization problem into two linear problems, which are solved alternatingly. To this end, contrast sources are introduced, which may be interpreted as sources emitting the scattered field from a scattering object. Two synthetic and two real field examples are inverted, which demonstrates the method and how the transversely isotropic in the vertical direction (TIV) inversion performs compared with isotropic inversion. The CSI method is found to be applicable to real field examples, and the results show that a TIV inversion is preferred over isotropic to identify weak anomalies in these examples. The reason for this is that both the horizontal and vertical conductivity affects the signal propagation in the overburden.
ABSTRACT We evaluated a joint contrast source inversion scheme for marine controlled-source elect... more ABSTRACT We evaluated a joint contrast source inversion scheme for marine controlled-source electromagnetic (mCSEM) and magnetotelluric (MT) data based on a scattered field formulation. The scheme considered only contrasts in electric conductivity, and it allowed the medium to be transversely isotropic with a vertical symmetry axis. The method was based on the integral equation formulation of electromagnetic field propagation, and we demonstrated how the method solved the inverse problem of determining the conductivity structure of the subsurface. The method did not consider MT impedances as data input to inversion, but instead explicitly the field components, and the consequences of this approach, were discussed. Although there are challenges associated with source estimation and data noise, we found it easier to make connections to CSEM and it simplified some computational issues. Three synthetic examples were considered to demonstrate the method: a reservoir below an anisotropic overburden, a salt diapir, and a reservoir near a salt diapir. MT and CSEM data were first treated sequentially, first inverting the MT data and using the result as the initial model and in the regularization in CSEM inversion. The result of this approach was then compared to a joint inversion. The same approach was finally applied to a real data set. We found that sequential inversions in some situations produced similar results as joint inversions, and hence, joint inversion may not be necessary in all situations. Nonetheless, joint inversion could be useful for imaging salt diapirs and eventually hydrocarbons near salt. In particular, it was useful to map the spatial extent of the salt diapirs. It was, moreover, a useful tool for checking data consistency in different models with respect to several data types.
ABSTRACT We present an integral equation framework for 2.5D frequency domain EM modelling in cond... more ABSTRACT We present an integral equation framework for 2.5D frequency domain EM modelling in conductive media, i.e. in media which are assumed invariant in one direction. Furthermore, we consider media which are transversely isotropic in the vertical direction (TIV), thus allowing the horizontal and vertical conductivities to differ. The integral equation framework allows for discretization of only a very limited area of the model, given a proper background model, thus leading to a small system of equations to be solved. The 2.5D integral equation method is suitable for studying the effect of localized resistivity anomalies efficiently and makes the generalization to real-world examples easier than for 1D modelling codes. We model three experiments to analyse and better understand the uncertainties of normalized amplitude and phase difference plots. Anisotropy has a significant effect on marine controlled source electromagnetic (mCSEM) data, and normalized amplitude graphs change both magnitude and position when changing the model to which one normalizes. It suggests that interpreters should be cautious when applying this to real data, where the model that caused the response at the reference receiver is unknown and may change along the line of receivers. Finally, we investigate whether mCSEM data are likely to be able to detect conductive inclusions in the stem of a salt diapir. When the models are exactly known, normalized amplitude plots can be used to check the sensitivity to perturbations.
Velocity-independent seismic data processing requires information about the local slope in the da... more Velocity-independent seismic data processing requires information about the local slope in the data. From estimates of local time and space derivatives of the data, a total least-squares algorithm gives an estimate of the local slope at each data point. Total least squares minimizes the orthogonal distance from the data points (the local time and space derivatives) to the fitted straight line defining the local slope. This gives a more consistent estimate of the local slope than standard least squares because it takes into account uncertainty in the temporal and spatial derivatives. The total least-squares slope estimate is the same as the one obtained from using the structure tensor with a rectangular window function. The estimate of the local slope field is used to extrapolate all traces in a seismic gather to the smallest recorded offset without using velocity information. Extrapolation to zero offset is done using a hyperbolic traveltime function in which slope information replaces the knowledge of the normal moveout (NMO) velocity. The new data processing method requires no velocity analysis and there is little stretch effect. All major reflections and diffrac-tions that are present at zero offset will be reproduced in the output zero-offset section. Therefore, if multiple reflections are undesired in the output, they should be removed before data extrapolation to zero offset. The automatic method is sensitive to noise, so for poor signal-to-noise ratios, standard NMO velocities for primary reflections can be used to compute the slope field. Synthetic and field data examples indicate that compared with standard seismic data processing (velocity analysis, mute, NMO correction, and stack), our method provides an improved zero-offset section in complex data areas.
ABSTRACT A combination of prestack elastic inversion with gravity modeling has been applied to a ... more ABSTRACT A combination of prestack elastic inversion with gravity modeling has been applied to a shallow seismic anomaly in the southern Barents Sea. The anomaly is crosscutting dipping layers of late Paleocene age. Earlier seismic interpretations indicate a possible origin in gas-hydrated sediments trapping underlying free gas. Our interpretation includes seismic inversion of a seismic model which consists of a stack of isotropic, homogeneous, and anelastic layers. The unknown parameters are the P- and S-wave velocities, density, and thickness for each layer. As densities are poorly determined by this method, we included gravity modeling, which improved the density estimates. The resulting para meters have been integrated by rock physics calculations and the knowledge of typical attributes of gas hydrate occurrences. The top of the seismic anomaly is interpreted as a reflection from the base of a gas-hydrated sediment trapping underlying free gas. The base of the anomaly is the gas-water contact, which deviates from a flat spot due to capillary pressure differences related to lithology and the generation process of gas hydrate. The estimated density has been interpreted together with well results and indicates a significant amount of gas filling the pore volume.
SEG Technical Program Expanded Abstracts 1992, 1992
... The nonlinear objective function (3) can be decoupled (Cad-zow, 1990) to give a simplified no... more ... The nonlinear objective function (3) can be decoupled (Cad-zow, 1990) to give a simplified nonlinear optimization prob-lem for the coefficient vector r. When introducing matrix notation the moveout corrected data window for a single event consisting of ... 2 Robust AVO analysis ...
We present a fast and efficient frequency-domain
implementation of a modified parabolic Radon tr... more We present a fast and efficient frequency-domain
implementation of a modified parabolic Radon transform
(modified PRT) based on a singular value decomposition
with applications to multiple removal. With a change of
variable, the problem is transformed into a complex linear
system involving a single operator after merging the
curvature-frequency parameters into a new variable. A
complex singular value decomposition (SVD) can be
applied to this operator and the forward modified
parabolic Radon transform is computed for all frequency
components within the signal bandwidth by means of
complex back-substitution only.
The standard PRT can be obtained by interpolation in the
modified transform domain. The method is also able to
resolve the multiple energy from the primaries when they
interfere in a small time interval and resists well to AVO
effects in the data. The proposed modified PRT was
successfully applied to a deep-water seismic line at the
Gulf of Mexico to attenuate water-bottom multiples and
subsequent peg-legs originating from multiple paths in the
water column.
Apresentamos um método de atenuação do ground roll que utiliza a decomposição SVD. Esta é aplicad... more Apresentamos um método de atenuação do ground roll que utiliza a decomposição SVD. Esta é aplicada sobre os sismogramas de famílias de ponto de tiro comu corrigidas de normal move out (NMO). Esta transformação tem o objetivo de deixar as reflexões de interesse aproximadamente horizontais. O método SVD é aplicado sobre um conjunto de traços de uma janela móvel que se desloca desde o primeiro até o último traço da família de ponto de tiro comum. Apenas o traço central das primeiras autoimagens de cada janela é preservado. Estes traços contem os eventos de maior correlação horizontal, representados pelas reflexões de interesse. Ilustramos o método utilizando dados sísmicos terrestres de uma linha sísmica da bacia de Tacutu. Os resultados mostram que o novo método é mais eficaz que o método f-k e permite colocar em evidência reflexões que estavam mascaradas pelo ground roll.
SEG Technical Program Expanded Abstracts: pp. 1603-1606.; 01/1996
A simplified approach for the mixed-phase signal decomposition and deconvolution algorithm of Por... more A simplified approach for the mixed-phase signal decomposition and deconvolution algorithm of Porsani and Ursin (1995), is presented. In the present approach the solution of the extended Yule-Walker (EYW) system of equations is used to deconvolve the equivalent minimum-phase wavelet from its minimum-delay component, resulting in the maximum-delay component of the wavelet. By solving EYW system of equations for different lags of the auto-correlation function (ACF) on the diagonal of the coefficient matrix, a suite of mixed-phase inverse filters and wavelets is generated. To choose the best filter and corresponding wavelet, we have used the maximum value of the Lp norm of the filtered signal. The algorithm is applied to the mixedphase wavelet deconvolution using measured seismic reflection data and ground penetrating radar (GPR) data. Numerical examples show that a mixed-phase inverse filter based on the signal decomposition algorithm performs much better than minimum-phase deconvolution.
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Papers by Bjorn Ursin
implementation of a modified parabolic Radon transform
(modified PRT) based on a singular value decomposition
with applications to multiple removal. With a change of
variable, the problem is transformed into a complex linear
system involving a single operator after merging the
curvature-frequency parameters into a new variable. A
complex singular value decomposition (SVD) can be
applied to this operator and the forward modified
parabolic Radon transform is computed for all frequency
components within the signal bandwidth by means of
complex back-substitution only.
The standard PRT can be obtained by interpolation in the
modified transform domain. The method is also able to
resolve the multiple energy from the primaries when they
interfere in a small time interval and resists well to AVO
effects in the data. The proposed modified PRT was
successfully applied to a deep-water seismic line at the
Gulf of Mexico to attenuate water-bottom multiples and
subsequent peg-legs originating from multiple paths in the
water column.