Prestack depth migration has been used for decades to derive velocity distributions in depth. Numerous tools and methodologies have been developed to reach this goal. Exploration in geologically more complex areas exceeds the abilities of existing methods. New data-acquisition and data-processing methods are required to answer these new challenges effectively. The recently introduced wide-azimuth data acquisition method offers better illumination and noise attenuation as well as an opportunity to more accurately determine velocities for imaging. One of the most advanced tools for depth imaging is full-waveform inversion. Prestack seismic full-waveform inversion is very challenging because of the nonlinearity and nonuniqueness of the solution. Combined with multiple iterations of forward modeling and residual wavefield back propagation, the method is computer intensive, especially for 3D projects. We studied a time-domain, plane-wave implementation of 3D waveform inversion. We found that plane-wave gathers...

3D prestack plane-wave, full-waveform inversion

Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. Conventional acoustic reverse time migration (RTM) and least-squares reverse time migration (LSRTM) do not account for this distortion, which can lead to defocusing of migration images in highly attenuative geologic environments. To correct for this distortion, we used a linearized inversion method, denoted as Qp-LSRTM. During the leastsquares iterations, we used a linearized viscoacoustic modeling operator for forward modeling. The adjoint equations were derived using the adjoint-state method for back propagating the residual wavefields. The merit of this approach compared with conventional RTM and LSRTM was that Qp-LSRTM compensated for the amplitude loss due to attenuation and could produce images with better balanced amplitudes and more resolution below highly attenuative layers. Numerical tests on synthetic and field data illustrated the advantages of Qp-LSRTM over RTM and LSRTM when the recorded data had strong attenuation effects. Similar to standard LSRTM, the sensitivity tests for background velocity and Qp errors revealed that the liability of this method is the requirement for smooth and accurate migration velocity and attenuation models.

/pdf/attenuation-compensation-for-least-squares-reverse-time-2adz9rq5i9.pdf

Attenuation compensation for least-squares reverse time migration using the viscoacoustic-wave equation

PSDM has been in place for decades with numerous tools to derive velocity fields in depth, particularly in mature areas such as the Gulf of Mexico. The existing methods have reached their limits to further define and/or fine-tune the velocity models. With the new wide azimuth acquisitions where better illumination is foreseeable, velocities can be more accurately determined. One of the most advanced tools is to use full waveform inversion. Pre-stack seismic full waveform inversion is a highly challenging task due to non-linearity and nonuniqueness. Combined with compute intensive forward modeling and residual wavefield back propagation, the method makes the technique computer intensive, especially for 3D projects. For PSDM, forward modeling and reverse time migration are widely used in the industry. Even in the 3D sense the focus has become what sort of methods could be used to achieve higher resolution velocity models. The answer is full waveform inversion. Here we examine the time domain plane wave implementation of 3D waveform inversion supported with synthetic and field data examples.

3D Pre-Stack Plane Wave Full Waveform Inversion

Anelastic properties of the earth cause frequency dependent energy attenuation and phase distortion in seismic wave propagation. These unwanted effects are preferred to be corrected in a prestack depth migration. Based on the dispersion relation under a linear attenuation assumption, we derive a visco-acoustic wave equation in the time domain and apply it in a prestack reverse time migration to compensate for the anelastic effects in the seismic data. The equation is defined by a pseudo-differential operator, and the energy increases with frequencies when back propagating the seismic data in migration. Using a regularization process, we show that our method provides stable and amplitude balanced reverse time migration images.

Compensating for Visco-Acoustic Effects in TTI Reverse Time Migration

Full-waveform inversion (FWI) has become a popular method to estimate elastic earth properties from seismograms. It is formulated as a data-fitting least-squares minimization problem that iteratively updates an initial velocity model with the scaled gradient of the misfit until a satisfactory match between the real and synthetic data is obtained. However, such a local optimization approach can converge to a local minimum if the starting model used is not close enough to an optimal model. We have developed a two-step process in which we first estimate a starting model using a global optimization method. Unlike local optimization methods, a global optimization method starts with a random starting model and is not generally susceptible to be trapped in a local minimum. The starting model for FWI that we aim to estimate is sparsely parameterized and contains a set of interfaces and velocities that are used to represent the entire velocity model. We have obtained the depth of the interfaces and the vel...

Estimating a starting model for full-waveform inversion using a global optimization method

We introduce a new viscoacoustic Wave Equation Migration (WEM) for media with attenuation. Our solution is based on a Fourier Finite-Difference (FFD) scheme for migration by wavefield continuation. Similarly to the acoustic solution, the viscoacoustic migration consists of three terms: a phase-shift extrapolation, a thin-lens correction, and a finite-differences operation. The viscoacoustic migration is also extended to account for anisotropy (VTI and TTI). The anisotropic effects are incorporated in the migration by using odd and even rational function terms in the finite differences solution. The dispersion relation, in presence of attenuation, includes both real and imaginary terms. While the real part controls the kinematics of the image, the imaginary part recovers the high vertical wave numbers in the seismic image; therefore improving resolution and amplitude balance. The implementation is stable, efficient, and very flexible. In absence of attenuation or anisotropy, the solution reduces to the familiar isotropic acoustic case. Results from synthetic example and two dual sensor field surveys from the North Sea and the Gulf of Mexico demonstrate the importance of incorporating the attenuation effects in isotropic and anisotropic migration algorithms.

Wave Equation Migration With Attenuation And Anisotropy Compensation

Shaoping Lu, Dan Whitmore, Alejandro Valenciano and Nizar Chemingui present applications of separated wavefield imaging to a deepwater wide-azimuth survey in the Gulf of Mexico and to a narrow azimuth data set from offshore Malaysia.

Enhanced subsurface illumination from separated wavefield imaging

SWIM increases the surface coverage and subsurface illumination by turning each receiver into a “virtual” source. This principle is independent of the wave equation propagation algorithm, which can be based on one-way or two-way solutions. SWIM with reverse time migration (RTM) better images the steep dips of the data. On the other hand, SWIM using one-way wave equation migration (WEM) provides an efficient alternative for high-resolution high-frequency imaging.

Imaging complex structures with separated Up- and Down-going wavefields

Accurate sub-surface image reconstruction from prestack depth migration of surface seismic wavefields requires precise knowledge of the local propagation velocities between the recording location and the image location at depth. Such velocity information has traditionally been derived by tomographically inverting residual
moveout information of common image gathers, which have been computed using an initial velocity field. This methodology proves to be challenging in shallow water environments, particularly when strong and rapid velocity variations in the very shallow overburden need to be recovered, while moveout information from reflected arrivals is very sparse or not available.

High-fidelity complete wavefield velocity model building and imaging in shallow water environments - A North Sea case study

3D RTM Angle Gathers Using an Inverse Scattering Imaging Condition

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