Campos Basin field has been continuously character¬ised at the Reservoir Characterization Project... more Campos Basin field has been continuously character¬ised at the Reservoir Characterization Project (RCP) in Colorado School of Mines. Past research includes poststack and prestack joint inversions of PP and PS data which increased the reservoir resolution and could predict a porosity map. To further improve characterisation of the Campos Basin field, waveform tomography (WT), or full waveform inversion (FWI), is performed for a 2D line from the 2010 ocean bottom cable (OBC) data under a 2D acoustic isotropic medium assumption. The goal is to bring high resolution and accuracy to the P wave veloc¬ity model for better-quality reservoir imaging. In order to achieve the best results the application of WT to the 2D dataset required defining the suitable parameters to these data, where the main options in the inversion are the type of objective function, the time domain damping, and the fre¬quency discretisation. Waveform inversion has improved the final velocity model, as verified by migrated images showing more continuous and focused horizons at the reservoir depth. The improved seismic image and velocity model are possible inputs, respectively, to a new geological interpretation and to acoustic/elastic attributes inversion. Waveform tomography (WT), or Full Waveform Inversion (FWI), has been the subject of studies and conceptual devel-opment over the past 30 years (Virieux and Operto, 2009). Furthermore, research groups and the oil industry around the world have shown the improvement that WT can bring to the velocity model, especially in terms of high resolution in comparison with conventional techniques, such as traveltime tomography (TT) or migration velocity analysis (MVA). These techniques can only build a smoothed version of the velocity model, containing the kinematics of the wavefield, even though they are able to generate a good quality seismic image. WT represents a more advanced approach that attempts to completely describe the complex interaction of the propagating waves and the earth, in which the phase of the whole waveform is used in the model reconstruction (Pratt, 2013).
Mauricio Pedrassi, Jyoti Behura, Thomas L. Davis, Esteban Diaz y Satyan Singh presentan la invers... more Mauricio Pedrassi, Jyoti Behura, Thomas L. Davis, Esteban Diaz y Satyan Singh presentan la inversion de la forma de onda del OBC del campo de la cuenca de Campos definiendo la mejor parametrizacion para obtener una version mejorada del modelo de velocidad de la zona.
London 2013, 75th eage conference en exhibition incorporating SPE Europec, 2013
Waveform inversion (FWI) requires a good starting model and/or data at very low frequency (< 1Hz)... more Waveform inversion (FWI) requires a good starting model and/or data at very low frequency (< 1Hz) for convergence. However, this is not a necessary condition, but an artifact of the objective function defined using differences of observed and simulated data. Image-domain tomographic methods using the same wavefields and wave-equations can converge to a reasonable solution from poor starting models and without long offset and/or low frequency data. Cascading image-domain and data-domain wavefield tomography eliminates the need for extremely low-frequency in the acquired data.
SEG Technical Program Expanded Abstracts 2016, 2016
Multiple-scattered waves contain information that is commonly disregarded during imaging and tomo... more Multiple-scattered waves contain information that is commonly disregarded during imaging and tomography. Marchenko wavefields are superior to time-reverse wavefields by handling primaries together with internal and surface-related multiples. Using all types of waves for imaging can greatly improve the illumination and augment the sensitivity of the data to errors in the background velocity model. We compare extended images computed with reverse time and Marchenko wavefields, and investigate the potential of using multidimensional deconvolution for extended images in order to obtain higher image resolution. Our experiments show that the Marchenko wavefields are sensitive to errors in the background model in a way that is similar to the sensitivity of time-reverse wavefields. The main difference between these imaging strategies is the improved angle illumination with the Marchenko wavefields due to the correct use of multiples; this improvement can eliminate the bias of tomography operators towards lower velocities when the data are contaminated with multiples.
SEG Technical Program Expanded Abstracts 2016, 2016
Two-way wavefields generated with the Marchenko method are able to reproduce complex wave phenome... more Two-way wavefields generated with the Marchenko method are able to reproduce complex wave phenomena that includes primaries, internal multiples and surfacerelated multiples. The wavefield contains reflections and information from the true model, but propagating with the kinematics of an input background velocity model. We design an inverse problem to find a model that explains the scattering phenomena present in the reconstructed wavefield. The two-way nature of the Marchenko wavefields allows us to use them with the homogeneous wave equation and obtain images that are indicative of subsurface model parameters. Unlike conventional imaging methods, where the image is indicative of the interfaces in the subsurface, our method inverts for the properties within the subsurface. Our tests show that one can invert for images indicative of the true model even when the background velocity model is partially inaccurate. Furthermore, we are able to image properties from the true model that are not part of the inputs used to generate the wavefield.
SEG Technical Program Expanded Abstracts 2016, 2016
Wavefield tomography can handle complex subsurface geology better than ray-based techniques and, ... more Wavefield tomography can handle complex subsurface geology better than ray-based techniques and, ultimately, provide a higher resolution. Here, we implement forward and adjoint wavefield extrapolation for VTI (transversely isotropic with a vertical symmetry axis) media using a pseudospectral operator that employes a separable approximation of the P-wave dispersion relation. This operator is employed to derive the gradients of the differential semblance optimization (DSO) and modified stack-power objective functions. We also obtain the gradient expressions for the data-domain objective function, which can incorporate borehole information necessary for stable VTI velocity analysis. These gradients are compared to the ones obtained with a space-time finite-difference (FD) scheme for a system of coupled wave equations. Whereas the kernels computed with the two wave-equation operators are similar, the pseudospectral method is not hampered by the imprint of the shear-wave artifact. Numerical examples also show that the modified stack-power objective function produces cleaner gradients than the more conventional DSO operator.
SEG Technical Program Expanded Abstracts 2015, 2015
We formulate the data domain tomography misfit criterion using local correlations. Correlation-ba... more We formulate the data domain tomography misfit criterion using local correlations. Correlation-based inversions are less sensitive to local minima than difference-based inversions. Correlations, however, are often contaminated with cross-talk between events; in addition, the global correlations give just a general idea of the kinematic errors of the model because of the summation along the entire time axis. Alternatively, local correlations with Gaussian windows, advocated in this paper, are able to extract the local kinematic errors in the misfit between modeled and observed data. Local correlations are also less sensitive to cross-talk of seismic events than global correlations because the summation is performed locally as a function of time. Less correlation cross-talk leads to cleaner adjoint sources and hence, cleaner gradients. We further improve the gradients using a penalty function that is consistent with the bandwidth of the seismic data, which is more realistic than linear penalty functions designed to annihilate infinite bandwidth data.
SEG Technical Program Expanded Abstracts 2013, 2013
Reverse time migration (RTM) backscattering contains kinematic information that can be used to co... more Reverse time migration (RTM) backscattering contains kinematic information that can be used to constrain velocity models. The backscattering results from the correlation between forward scattered and backscattered wavefields from sharp interfaces, i.e. sediment-salt interfaces. The synchronization between these wavefields depends on the velocity of the sediment section and the correct interpretation of the sharp boundary. Therefore, we can use these events along with reflection and diving waves to define a joint optimization problem for velocity model building. As in RTM images, in gradient computation the backscattering and diving information produces cross-talk. In order to avoid the cross-talk, we use a directional filter based on the Poynting vector which preserves the components of the wavefield that travel in the same direction. Using backscattered waves for constraining the velocity in the sediment section requires defining the top of salt in advance, which would imply a dynamic workflow for model building in salt environments where both sediment velocity and salt interface change iteratively during inversion.
For some acquisition geometries, the cost of Full Waveform Inversion (FWI) can be considerably re... more For some acquisition geometries, the cost of Full Waveform Inversion (FWI) can be considerably reduced by inverting simultaneously encoded shots. Encoded-shot strategies have the undesirable effect of leaving crosstalk noise in the final result. For FWI, changing the coding sequence periodically mitigates this effect. Another alternative is to use preconditioning, whereby the gradient is smoothed at every iteration along predefined directions. Preconditioning steers the solution towards accurate models while attenuating crosstalk artefacts. It also increases convergence speed and robustness to noise present in the data.
SEG Technical Program Expanded Abstracts 2012, 2012
Reverse time migration (RTM) backscattered events are produced by the cross-correlation between w... more Reverse time migration (RTM) backscattered events are produced by the cross-correlation between waves reflected from sharp interfaces (e.g. the top of salt bodies). Commonly, these events are seen as a drawback for the RTM method because they obstruct the image of the geologic structure. Many strategies have been developed to filter out the artifacts from the conventional image. However, these events contain information that can be used to analyze kinematic synchronization between source and receiver wavefields reconstructed in the subsurface. Numeric and theoretical analysis indicate the sensitivity of the backscattered energy to velocity accuracy: an accurate velocity model maximizes the backscattered artifacts. The analysis of RTM extended images can be used as a quality control tool and as input to velocity analysis designed to constrain salt models and sediment velocity. The analysis in this thesis suggest that we can use backscattering events along with reflection data to define a joint optimization problem for velocity model building. The gradient required for model optimization suffers from cross-talk, similar to the more conventional RTM images. In order to avoid the cross-talk, I use a directional filter based on Poynting vectors which preserves the components of the wavefield traveling in the same direction. Using backscattered waves for constraining the velocity in the sediment section requires defining the top of salt in advance, which implies a dynamic workflow for model building in salt environments where both sediment velocity and salt interface change iteratively during inversion.
Image-domain wavefield tomography (WT) exploits focusing characteristics of extended images for u... more Image-domain wavefield tomography (WT) exploits focusing characteristics of extended images for updating the velocity field. To make good use of this information, one must understand how such images behave if the migration velocity is accurate. This is not trivial because focusing depends on not only the model error, but also on the acquisition setup, the data bandwidth, and illumination variation caused by the overburden. We address this problem by constructing penalty functions based on the point spread functions of the imaging operator that characterize focusing in extended images. Moreover, instead of sampling the extended images at preset distances along the surface, we sample the image by constructing common-image-point gathers, which are more economical from a computational point of view and also measure the spatial and temporal focusing of the wavefield. Coupled with image residuals exploiting illumination-based penalty functions, we construct robust wavefield tomographic up...
One of the main challenges for full-waveform inversion (FWI) is taking into account both anisotro... more One of the main challenges for full-waveform inversion (FWI) is taking into account both anisotropy and elasticity. Here, we perform elastic FWI for a synthetic 2D VTI (transversely isotropic with a vertical symmetry axis) model based on the geologic section at Valhall field in the North Sea. Multicomponent surface data are generated by a finite-difference code. We apply FWI in the time domain using a multiscale approach with three frequency bands. An approximate inverse Hessian matrix, computed using the L-BFGS-B algorithm, is employed to scale the gradients of the objective function and improve the convergence. In the absence of significant diving-wave energy in the deeper part of the section, the model is updated primarily with reflection data. An oblique displacement source, which excites sufficiently intensive shear waves in the conventional offset range, helps provide more accurate updates in the Shear-wave vertical velocity, especially in the shallow layers. We test three mod...
Wavefield tomography can handle complex subsurface geology better than ray-based techniques and, ... more Wavefield tomography can handle complex subsurface geology better than ray-based techniques and, ultimately, provide a higher resolution. Here, we implement forward and adjoint wavefield extrapolation for VTI (transversely isotropic with a vertical symmetry axis) media using a generalized pseudospectral operator based on a separable approximation for the P-wave dispersion relation. This operator is employed to derive the gradients of the differential semblance optimization (DSO) and modified image-power objective functions. We also obtain the gradient expressions for a data-domain objective function that can more easily incorporate borehole information necessary for stable VTI velocity analysis. These gradients are similar to the ones obtained with a space-time finite-difference (FD) scheme for a system of coupled wave equations but the pseudospectral method is not hampered by the imprint of the shear-wave artifact. Numerical examples also show the potential advantages of the modified image-power objective function in estimating the anellipticity parameter η.
SEG Technical Program Expanded Abstracts 2015, 2015
One of the main challenges for full-waveform inversion (FWI) is taking into account both anisotro... more One of the main challenges for full-waveform inversion (FWI) is taking into account both anisotropy and elasticity. Here, we perform FWI for a synthetic 2D elastic VTI (transversely isotropic with a vertical symmetry axis) model based on the geologic section at Valhall field in the North Sea. Multicomponent data are generated by a finitedifference code for surface acquisition. The model is parameterized in terms of the P-and S-wave vertical velocities (V P 0 and V S0) and the P-wave NMO and horizontal velocities (V nmo and V hor). We apply FWI in the time domain using a multiscale approach with three frequency bands. An approximate Hessian matrix, computed using the L-BFGS algorithm, is employed to scale the gradients of the objective function and improve the convergence. In the absence of significant diving-wave energy, FWI allows us to update the model primarily using reflection data. The largest and most accurate updates are obtained for the velocities V P 0 and V hor. The vertical velocities V P 0 and V S0 are updated both in the shallow and deeper parts of the model, whereas V nmo and V hor change primarily in the near-surface horizons. Further improvement is expected after extending the frequency range for the inversion.
SEG Technical Program Expanded Abstracts 2014, 2014
Wavefield-based tomographic methods are idoneous for recovering velocity models from seismic data... more Wavefield-based tomographic methods are idoneous for recovering velocity models from seismic data. The use of wavefields rather than rays is more consistent with the bandlimited nature of seismic data. Image domain methods seek to improve the focusing in extended images, thus producing better seismic images. However, image domain methods produce low resolution models due to the fact their objective functions are smooth, particularly in the vicinity of the global minimum. In contrast, data-domain methods produce high resolution models but suffer from strong non-linearity causing cycle skipping if certain conditions are not met. By combining the characteristics of each method, we can obtain models that produce better images and contain high resolution features at the same time. We demonstrate the strength of the workflow that combines both methods with an application to a marine 2D dataset with variable streamer depth.
Reverse time migration backscattering contains kinematic information that can be used to constrai... more Reverse time migration backscattering contains kinematic information that can be used to constrain velocity models. The backscattering results from the correlation between forward scattered and backscattered wavefields from sharp interfaces, i.e., sediment-salt interfaces. The synchronization between these wavefields depends on the velocity of the sediment section and the correct interpretation of the sharp boundary. We have developed an optimization workflow in which the sediment velocity and the sharp boundary are updated iteratively. The presence of sharp boundaries in the model lead to high-and lowwavenumber components in the objective function gradient; the high-wavenumber components correspond to the correlation of wavefields traveling in opposite directions, whereas the low-wavenumber components correspond to the correlation of wavefields traveling in the same direction. This behavior is similar to reverse time migration in which the high-wavenumber components represent the reflectors (the signal) and the low-wavenumber components represent backscattering (noise). The opposite is true in tomography: The low wavenumber components represent changes to the velocity model, and the high-wavenumber components are noise that needs to be filtered out. We use a directional filter based on Poynting vectors during the gradient computation to preserve the smooth components of the gradient, thus spreading information away from the sharp boundary. Our tests indicated that velocity models are better constrained when we include the sharp boundaries (and the associated backscattering) in wavefield tomography.
W aveform inversion (FWI) requires a good starting model and/or data at low frequency (<1 Hz) for... more W aveform inversion (FWI) requires a good starting model and/or data at low frequency (<1 Hz) for convergence. However, this is not a necessary condition, but an artifact of the objective function defined using differences of observed and simulated data. Image-domain tomographic methods using the same wavefields and wave equations can converge to a reasonable solution from poor starting models and without long-offset and/or low-frequency data. Cascading imagedomain and data-domain wavefield tomography eliminates the need for extremely low-frequency in the acquired data.
Campos Basin field has been continuously character¬ised at the Reservoir Characterization Project... more Campos Basin field has been continuously character¬ised at the Reservoir Characterization Project (RCP) in Colorado School of Mines. Past research includes poststack and prestack joint inversions of PP and PS data which increased the reservoir resolution and could predict a porosity map. To further improve characterisation of the Campos Basin field, waveform tomography (WT), or full waveform inversion (FWI), is performed for a 2D line from the 2010 ocean bottom cable (OBC) data under a 2D acoustic isotropic medium assumption. The goal is to bring high resolution and accuracy to the P wave veloc¬ity model for better-quality reservoir imaging. In order to achieve the best results the application of WT to the 2D dataset required defining the suitable parameters to these data, where the main options in the inversion are the type of objective function, the time domain damping, and the fre¬quency discretisation. Waveform inversion has improved the final velocity model, as verified by migrated images showing more continuous and focused horizons at the reservoir depth. The improved seismic image and velocity model are possible inputs, respectively, to a new geological interpretation and to acoustic/elastic attributes inversion. Waveform tomography (WT), or Full Waveform Inversion (FWI), has been the subject of studies and conceptual devel-opment over the past 30 years (Virieux and Operto, 2009). Furthermore, research groups and the oil industry around the world have shown the improvement that WT can bring to the velocity model, especially in terms of high resolution in comparison with conventional techniques, such as traveltime tomography (TT) or migration velocity analysis (MVA). These techniques can only build a smoothed version of the velocity model, containing the kinematics of the wavefield, even though they are able to generate a good quality seismic image. WT represents a more advanced approach that attempts to completely describe the complex interaction of the propagating waves and the earth, in which the phase of the whole waveform is used in the model reconstruction (Pratt, 2013).
Mauricio Pedrassi, Jyoti Behura, Thomas L. Davis, Esteban Diaz y Satyan Singh presentan la invers... more Mauricio Pedrassi, Jyoti Behura, Thomas L. Davis, Esteban Diaz y Satyan Singh presentan la inversion de la forma de onda del OBC del campo de la cuenca de Campos definiendo la mejor parametrizacion para obtener una version mejorada del modelo de velocidad de la zona.
London 2013, 75th eage conference en exhibition incorporating SPE Europec, 2013
Waveform inversion (FWI) requires a good starting model and/or data at very low frequency (< 1Hz)... more Waveform inversion (FWI) requires a good starting model and/or data at very low frequency (< 1Hz) for convergence. However, this is not a necessary condition, but an artifact of the objective function defined using differences of observed and simulated data. Image-domain tomographic methods using the same wavefields and wave-equations can converge to a reasonable solution from poor starting models and without long offset and/or low frequency data. Cascading image-domain and data-domain wavefield tomography eliminates the need for extremely low-frequency in the acquired data.
SEG Technical Program Expanded Abstracts 2016, 2016
Multiple-scattered waves contain information that is commonly disregarded during imaging and tomo... more Multiple-scattered waves contain information that is commonly disregarded during imaging and tomography. Marchenko wavefields are superior to time-reverse wavefields by handling primaries together with internal and surface-related multiples. Using all types of waves for imaging can greatly improve the illumination and augment the sensitivity of the data to errors in the background velocity model. We compare extended images computed with reverse time and Marchenko wavefields, and investigate the potential of using multidimensional deconvolution for extended images in order to obtain higher image resolution. Our experiments show that the Marchenko wavefields are sensitive to errors in the background model in a way that is similar to the sensitivity of time-reverse wavefields. The main difference between these imaging strategies is the improved angle illumination with the Marchenko wavefields due to the correct use of multiples; this improvement can eliminate the bias of tomography operators towards lower velocities when the data are contaminated with multiples.
SEG Technical Program Expanded Abstracts 2016, 2016
Two-way wavefields generated with the Marchenko method are able to reproduce complex wave phenome... more Two-way wavefields generated with the Marchenko method are able to reproduce complex wave phenomena that includes primaries, internal multiples and surfacerelated multiples. The wavefield contains reflections and information from the true model, but propagating with the kinematics of an input background velocity model. We design an inverse problem to find a model that explains the scattering phenomena present in the reconstructed wavefield. The two-way nature of the Marchenko wavefields allows us to use them with the homogeneous wave equation and obtain images that are indicative of subsurface model parameters. Unlike conventional imaging methods, where the image is indicative of the interfaces in the subsurface, our method inverts for the properties within the subsurface. Our tests show that one can invert for images indicative of the true model even when the background velocity model is partially inaccurate. Furthermore, we are able to image properties from the true model that are not part of the inputs used to generate the wavefield.
SEG Technical Program Expanded Abstracts 2016, 2016
Wavefield tomography can handle complex subsurface geology better than ray-based techniques and, ... more Wavefield tomography can handle complex subsurface geology better than ray-based techniques and, ultimately, provide a higher resolution. Here, we implement forward and adjoint wavefield extrapolation for VTI (transversely isotropic with a vertical symmetry axis) media using a pseudospectral operator that employes a separable approximation of the P-wave dispersion relation. This operator is employed to derive the gradients of the differential semblance optimization (DSO) and modified stack-power objective functions. We also obtain the gradient expressions for the data-domain objective function, which can incorporate borehole information necessary for stable VTI velocity analysis. These gradients are compared to the ones obtained with a space-time finite-difference (FD) scheme for a system of coupled wave equations. Whereas the kernels computed with the two wave-equation operators are similar, the pseudospectral method is not hampered by the imprint of the shear-wave artifact. Numerical examples also show that the modified stack-power objective function produces cleaner gradients than the more conventional DSO operator.
SEG Technical Program Expanded Abstracts 2015, 2015
We formulate the data domain tomography misfit criterion using local correlations. Correlation-ba... more We formulate the data domain tomography misfit criterion using local correlations. Correlation-based inversions are less sensitive to local minima than difference-based inversions. Correlations, however, are often contaminated with cross-talk between events; in addition, the global correlations give just a general idea of the kinematic errors of the model because of the summation along the entire time axis. Alternatively, local correlations with Gaussian windows, advocated in this paper, are able to extract the local kinematic errors in the misfit between modeled and observed data. Local correlations are also less sensitive to cross-talk of seismic events than global correlations because the summation is performed locally as a function of time. Less correlation cross-talk leads to cleaner adjoint sources and hence, cleaner gradients. We further improve the gradients using a penalty function that is consistent with the bandwidth of the seismic data, which is more realistic than linear penalty functions designed to annihilate infinite bandwidth data.
SEG Technical Program Expanded Abstracts 2013, 2013
Reverse time migration (RTM) backscattering contains kinematic information that can be used to co... more Reverse time migration (RTM) backscattering contains kinematic information that can be used to constrain velocity models. The backscattering results from the correlation between forward scattered and backscattered wavefields from sharp interfaces, i.e. sediment-salt interfaces. The synchronization between these wavefields depends on the velocity of the sediment section and the correct interpretation of the sharp boundary. Therefore, we can use these events along with reflection and diving waves to define a joint optimization problem for velocity model building. As in RTM images, in gradient computation the backscattering and diving information produces cross-talk. In order to avoid the cross-talk, we use a directional filter based on the Poynting vector which preserves the components of the wavefield that travel in the same direction. Using backscattered waves for constraining the velocity in the sediment section requires defining the top of salt in advance, which would imply a dynamic workflow for model building in salt environments where both sediment velocity and salt interface change iteratively during inversion.
For some acquisition geometries, the cost of Full Waveform Inversion (FWI) can be considerably re... more For some acquisition geometries, the cost of Full Waveform Inversion (FWI) can be considerably reduced by inverting simultaneously encoded shots. Encoded-shot strategies have the undesirable effect of leaving crosstalk noise in the final result. For FWI, changing the coding sequence periodically mitigates this effect. Another alternative is to use preconditioning, whereby the gradient is smoothed at every iteration along predefined directions. Preconditioning steers the solution towards accurate models while attenuating crosstalk artefacts. It also increases convergence speed and robustness to noise present in the data.
SEG Technical Program Expanded Abstracts 2012, 2012
Reverse time migration (RTM) backscattered events are produced by the cross-correlation between w... more Reverse time migration (RTM) backscattered events are produced by the cross-correlation between waves reflected from sharp interfaces (e.g. the top of salt bodies). Commonly, these events are seen as a drawback for the RTM method because they obstruct the image of the geologic structure. Many strategies have been developed to filter out the artifacts from the conventional image. However, these events contain information that can be used to analyze kinematic synchronization between source and receiver wavefields reconstructed in the subsurface. Numeric and theoretical analysis indicate the sensitivity of the backscattered energy to velocity accuracy: an accurate velocity model maximizes the backscattered artifacts. The analysis of RTM extended images can be used as a quality control tool and as input to velocity analysis designed to constrain salt models and sediment velocity. The analysis in this thesis suggest that we can use backscattering events along with reflection data to define a joint optimization problem for velocity model building. The gradient required for model optimization suffers from cross-talk, similar to the more conventional RTM images. In order to avoid the cross-talk, I use a directional filter based on Poynting vectors which preserves the components of the wavefield traveling in the same direction. Using backscattered waves for constraining the velocity in the sediment section requires defining the top of salt in advance, which implies a dynamic workflow for model building in salt environments where both sediment velocity and salt interface change iteratively during inversion.
Image-domain wavefield tomography (WT) exploits focusing characteristics of extended images for u... more Image-domain wavefield tomography (WT) exploits focusing characteristics of extended images for updating the velocity field. To make good use of this information, one must understand how such images behave if the migration velocity is accurate. This is not trivial because focusing depends on not only the model error, but also on the acquisition setup, the data bandwidth, and illumination variation caused by the overburden. We address this problem by constructing penalty functions based on the point spread functions of the imaging operator that characterize focusing in extended images. Moreover, instead of sampling the extended images at preset distances along the surface, we sample the image by constructing common-image-point gathers, which are more economical from a computational point of view and also measure the spatial and temporal focusing of the wavefield. Coupled with image residuals exploiting illumination-based penalty functions, we construct robust wavefield tomographic up...
One of the main challenges for full-waveform inversion (FWI) is taking into account both anisotro... more One of the main challenges for full-waveform inversion (FWI) is taking into account both anisotropy and elasticity. Here, we perform elastic FWI for a synthetic 2D VTI (transversely isotropic with a vertical symmetry axis) model based on the geologic section at Valhall field in the North Sea. Multicomponent surface data are generated by a finite-difference code. We apply FWI in the time domain using a multiscale approach with three frequency bands. An approximate inverse Hessian matrix, computed using the L-BFGS-B algorithm, is employed to scale the gradients of the objective function and improve the convergence. In the absence of significant diving-wave energy in the deeper part of the section, the model is updated primarily with reflection data. An oblique displacement source, which excites sufficiently intensive shear waves in the conventional offset range, helps provide more accurate updates in the Shear-wave vertical velocity, especially in the shallow layers. We test three mod...
Wavefield tomography can handle complex subsurface geology better than ray-based techniques and, ... more Wavefield tomography can handle complex subsurface geology better than ray-based techniques and, ultimately, provide a higher resolution. Here, we implement forward and adjoint wavefield extrapolation for VTI (transversely isotropic with a vertical symmetry axis) media using a generalized pseudospectral operator based on a separable approximation for the P-wave dispersion relation. This operator is employed to derive the gradients of the differential semblance optimization (DSO) and modified image-power objective functions. We also obtain the gradient expressions for a data-domain objective function that can more easily incorporate borehole information necessary for stable VTI velocity analysis. These gradients are similar to the ones obtained with a space-time finite-difference (FD) scheme for a system of coupled wave equations but the pseudospectral method is not hampered by the imprint of the shear-wave artifact. Numerical examples also show the potential advantages of the modified image-power objective function in estimating the anellipticity parameter η.
SEG Technical Program Expanded Abstracts 2015, 2015
One of the main challenges for full-waveform inversion (FWI) is taking into account both anisotro... more One of the main challenges for full-waveform inversion (FWI) is taking into account both anisotropy and elasticity. Here, we perform FWI for a synthetic 2D elastic VTI (transversely isotropic with a vertical symmetry axis) model based on the geologic section at Valhall field in the North Sea. Multicomponent data are generated by a finitedifference code for surface acquisition. The model is parameterized in terms of the P-and S-wave vertical velocities (V P 0 and V S0) and the P-wave NMO and horizontal velocities (V nmo and V hor). We apply FWI in the time domain using a multiscale approach with three frequency bands. An approximate Hessian matrix, computed using the L-BFGS algorithm, is employed to scale the gradients of the objective function and improve the convergence. In the absence of significant diving-wave energy, FWI allows us to update the model primarily using reflection data. The largest and most accurate updates are obtained for the velocities V P 0 and V hor. The vertical velocities V P 0 and V S0 are updated both in the shallow and deeper parts of the model, whereas V nmo and V hor change primarily in the near-surface horizons. Further improvement is expected after extending the frequency range for the inversion.
SEG Technical Program Expanded Abstracts 2014, 2014
Wavefield-based tomographic methods are idoneous for recovering velocity models from seismic data... more Wavefield-based tomographic methods are idoneous for recovering velocity models from seismic data. The use of wavefields rather than rays is more consistent with the bandlimited nature of seismic data. Image domain methods seek to improve the focusing in extended images, thus producing better seismic images. However, image domain methods produce low resolution models due to the fact their objective functions are smooth, particularly in the vicinity of the global minimum. In contrast, data-domain methods produce high resolution models but suffer from strong non-linearity causing cycle skipping if certain conditions are not met. By combining the characteristics of each method, we can obtain models that produce better images and contain high resolution features at the same time. We demonstrate the strength of the workflow that combines both methods with an application to a marine 2D dataset with variable streamer depth.
Reverse time migration backscattering contains kinematic information that can be used to constrai... more Reverse time migration backscattering contains kinematic information that can be used to constrain velocity models. The backscattering results from the correlation between forward scattered and backscattered wavefields from sharp interfaces, i.e., sediment-salt interfaces. The synchronization between these wavefields depends on the velocity of the sediment section and the correct interpretation of the sharp boundary. We have developed an optimization workflow in which the sediment velocity and the sharp boundary are updated iteratively. The presence of sharp boundaries in the model lead to high-and lowwavenumber components in the objective function gradient; the high-wavenumber components correspond to the correlation of wavefields traveling in opposite directions, whereas the low-wavenumber components correspond to the correlation of wavefields traveling in the same direction. This behavior is similar to reverse time migration in which the high-wavenumber components represent the reflectors (the signal) and the low-wavenumber components represent backscattering (noise). The opposite is true in tomography: The low wavenumber components represent changes to the velocity model, and the high-wavenumber components are noise that needs to be filtered out. We use a directional filter based on Poynting vectors during the gradient computation to preserve the smooth components of the gradient, thus spreading information away from the sharp boundary. Our tests indicated that velocity models are better constrained when we include the sharp boundaries (and the associated backscattering) in wavefield tomography.
W aveform inversion (FWI) requires a good starting model and/or data at low frequency (<1 Hz) for... more W aveform inversion (FWI) requires a good starting model and/or data at low frequency (<1 Hz) for convergence. However, this is not a necessary condition, but an artifact of the objective function defined using differences of observed and simulated data. Image-domain tomographic methods using the same wavefields and wave equations can converge to a reasonable solution from poor starting models and without long-offset and/or low-frequency data. Cascading imagedomain and data-domain wavefield tomography eliminates the need for extremely low-frequency in the acquired data.
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Papers by Esteban Díaz