We presents a technique for imaging both primaries and multiples using linearized inversion. Linearized full-wave inversion (LFWI) makes use of the multiple energy as signal while removing the crosstalk in the image. We demonstrate the concept and methodology in 2D with a synthetic Sigsbee2B model.
Tomographic Full waveform inversion (TFWI) provides a framework to invert the seismic data that is immune to cycle-skipping problems. This is achieved by extending the wave equation and adding an offset axis to the velocity model. However, this extension makes the propagation considerably more expensive because each multiplication by velocity becomes a convolution. We provide an alternative formulation which computes the backscattering and the forward scattering components of the gradient separately. To maintain high resolution results of TFWI, the two components of the gradient are first mixed and then separated based on a Fourier domain scale separation. This formulation is based on the born approximation where the medium parameters are broken into a long wavelength and short wavelength components. This approximation has an underlying assumption that the data contain primaries only without multiples. After deriving the equations, we test the theory with synthetic examples. The results of the Marmousi model show that convergence is possible even with large errors in the initial model that would have prevented convergence to conventional FWI.
We present an application of linearized joint inversion to time-lapse data sets from the Valhall field. By accounting for illumination mismatches—caused by differences in acquisition geometries—and for band-limited wave-propagation effects, our method provides more reliable estimates of production-related changes in reservoir properties than conventional time-lapse imaging methods. Using subsets of the Valhall Life of Field Seismic data sets, we demonstrate how this method attenuates artifacts in time-lapse seismic images that are caused by data gaps due to obstructions.
Combined ocean bottom nodes and streamer surveys offer the best of both methods: the economy of streamers and the ability of nodes to cover obstructed areas. In the past we shown that up-going and down-going (mirror) imaging can be combined in a joint inversion. We have now extend the method to joint-inversion of nodes and streamers data. Compared to conventional post-imaging merging, the joint inversion enhances resolution, suppresses migration artifacts, and more importantly, bring up the relative amplitude of true reflectors in the subfurface. We present a linearized inversion scheme for imaging narrow-azimuth (NAZ) and ocean-bottom data. Linearized inversion can enhance the resolution of the image, suppress migration artifacts, and increase the relative amplitude of true reflectors in the subsurface. We show that joint inversion can coherently combines the information from the two surveys and improve the image substantially. We demonstrate the concept and methodology in 2D with a synthetic Marmousi model.
The extension of the velocity-model domain to subsurface offsets solves the local-minima problem of data-fitting waveform inversion. By regularizing the extended-model data-fitting inversion with the addition of an image-focusing term to the objective function, we achieve robust global convergence of the waveform inversion problem. The method shares with full waveform inversion the advantage of simultaneously solving for all the wavelengths of the model, but it also has the global convergence characteristics of wave-equation migration velocity analysis. The numerical implementation of the proposed inversion method requires the solution of an extended wave-equation where velocity is a convolutional, instead of scalar, operator. The resulting method is therefore computationally intensive, and more computationally efficient approximations would be beneficial. Numerical tests performed on synthetic data modeled assuming a modified Marmousi model demonstrate the global convergence as well the high-resolution potential of the method.
We propose a new method to perform wave-equation migration velocity analysis by maximizing the flatness of the angle-domain common image gathers. Instead of maximizing the image-stack-power objective function directly with respect to the slowness, we link the objective function to the slowness indirectly through an intermediate moveout parameter. This approach is immune to the cycle-skipping problem, and it produces high-quality gradients. In addition, the proposed method does not require explicit picking of the moveout parameters. Our numerical examples demonstrate the great potential of this method: in the first example where there is a Gaussian-shaped anomaly slowness error, our method produces well-behaved gradient; from our test on the Marmousi models, the proposed method converges to a high-quality model that uniformly flattens the angle-domain common image gathers.