Albertin, Uwe (Chevron Energy Technology Company) | Shen, Peng (Chevron) | Sekar, Anusha (Chevron) | Johnsen, Thor (Chevron) | Wu, Chunling (Chevron) | Nihei, Kurt (Lawrence Berkeley Laboratory) | Bube, Ken (University of Washington)
We formulate the theory of 3D orthorhombic full-waveform inversion using adjoint state techniques for recovery of shear and p-wave elastic stiffness coefficients from acquired pressure data. In formulating the adjoint of forward Born scattering, we use a novel transformation of wavefields that allows us to use the same high performance elastic propagation kernel for the adjoint that we use for forward elastic modeling. We further derive inversion equations suitable for recovery of p-wave and shear velocities in fixed inhomogeneous density media with fixed inhomogeneous anisotropic coefficients, through the use of a chain rule formulation. We demonstrate that for a simple model with a strong Class 2 AVO signature involving phase reversal, a sequence of short-offset p-wave elastic stiffness recovery (equivalently velocity or impedance) folllowed by long offset shear elastic stiffness recovery produces a significant uplift in data fitting when compared to simple acoustic inversion for p-wave velocity. We also demonstrate effective recovery in 2D using similar techniques, for a more complex model with thin sands exhibiting strong AVO behavior.
Presentation Date: Tuesday, October 18, 2016
Start Time: 8:00:00 AM
Presentation Type: ORAL
We show an explicit scheme that separates seismic source and receiver wave-fields individually into up- and down- going components. The main challenge of the work is generating wavefields that correspond to positive or negative temporal frequencies in space-time 4D volume. This difficulty arises because the seismic propagators we typically employ store wave-fields with slowest dimension in time but the Fourier transform operates most efficiently on data that are stored contiguously. We solve this issue by a temporal Hilbert transform of the source term of the wave-equation followed by the conventional propagations. The pair of wave-fields, namely, the wave-field propagated without a Hilbert transformed source and the wave-field generated by the Hilbert transformed source, constitute the desired positive or negative temporal components in real and imaginary parts, respectively and separately. The down-going and up-going wave components can then be conveniently obtained by applying 1D Fourier filters in depth. We pursue a causal imaging condition that correlates the down-going source component with the up-going receiver component for subsurface imaging. We demonstrate that by applying the causal imaging condition certain strong near-salt imaging artifacts are removed.
In the forward time axis, an incident source wave-field causally excites the reflected source wave-field at the boundary between two mediums. In this work, we refer to the causal reflection imaging condition as the correlation between the incident source wave-field and the wave-field that kinematically agrees with the reflected source wave-field. The latter can be produced as part of the receiver wave-field which propagates along the reversed time axis using the receiver data acquired on some boundary (Lions, 1972). Let the word, incident, be used to indicate the state “before” reflections occur in time, forward or reversed, in which source and receiver wave-field, respectively, is computationally propagated. It then makes sense to distinguish the incident receiver wave-field from the reflected receiver wave-field at the boundary of velocity contrast. With the terminologies laid above, we can restate the causal reflection imaging condition as the correlation between the incident source wave-field and the incident receiver wave-field, and this is consistent with the survey sinking concept introduced in Claerbout (1985).
An RTM, reverse-time migration, involves propagation of source wave-field, adjoint-state propagation of receiver wave-field, and correlation of source and receiver wave-field along the forward time axis at zero lag (Baysal et al., 1983; Loewenthal and Mufti, 1983; McMechan, 1983; Whitmore, 1983). The “two-way” propagator engineered in RTM does not separate incident from reflected, neither refractions from reflections. A conventional imaging condition implemented as a straight forward correlation between source and receiver wave-field thus produces many types of artifacts. A practical approach that removes most of the large angle imaging artifacts is to apply the Laplacian filter to the stacks (Zhang and Sun, 2009).
A great deal of salt-related model building cycle-time is devoted to fine-tuning the small-scale details of the salt geometry, especially along the top and bottom of salt, in order to get an optimal subsalt imaging. Recovering these short wavelength features is very challenging in velocity model building and is beyond the capability of traditional migration velocity analysis tools. In this study, we incorporate the adjustment of short-wavelength salt geometry into the seismic imaging procedure. Our approach enhances subsalt imaging by first correcting the salt geometry by estimating time delays from reverse time migration (RTM) time-lag gathers, and then updating the top of salt automatically by local time-to-depth mapping and surface warping. The effectiveness of our new implementation is demonstrated using the 2004 BP velocity benchmark 2D synthetic dataset and a Gulf of Mexico (GOM) 3D field data example.
Seismic depth imaging in subsalt areas remains a significant challenge due to the high velocity contrast between sediment and salt. Typical depth-imaging processing flows utilize a top-down approach to subsalt imaging. First, the sediment velocity above salt is estimated. A depth image is then obtained using the sediment velocities, followed by manual interpretation of the image to determine top-salt location. Salt velocity is then inserted into the model below top salt, followed by another depth migration using this salt-flooded velocity model. Manual interpretation of the image is then employed to determine base salt location. The model is finally modified to truncate salt velocities at base of salt, and the subsalt image is finally obtained after constructing a subsalt velocity model. Effective subsalt imaging therefore requires accurate positioning of both the top and the base salt events in the model. The processing step of interpreting salt boundaries is often a time consuming part of the depthimaging workflow, and correct interpretation of salt position is often difficult in highly complex areas. This leads to wrong salt geometries in the model, and subsequent loss of fidelity in the seismic image.
Previous efforts in solving this problem focus on using various techniques of reflection tomography (Stork, 1992) or wave-equation based migration velocity analysis (WEMVA) (Biondi and Sava, 1999; Shen and Symes, 2008; Shan et al. 2014) to invert velocity models in image or data domain using ray tracing, one-way or two-way propagators. Meanwhile, it has been proposed to use waveform inversion (Sirgue and Pratt, 2003) to update such imperfections in salt boundaries. However, it is difficult to get the inversion to high enough frequency to get a truly sharp boundary in practice, and Gibbs phenomena at the salt boundary also cause issues. Recently Hill (2014) used beam inversion to update the velocity model in interactive imaging platform. Etgen et al. (2014) proposed a seismic adaptive optics approach to analyze time or depth extrapolated wavefields for the tell-tale signature of high-contrast short-wavelength velocity structure.
We present a method based on wavefield decomposition to improve wave equation migration velocity analysis. We decompose the gradient into long wavelength and short wavelength components. At early stage of the inversion, we only use the long wavelength component of the gradient. When the long wavelength part of the velocity is well resolved, we start to add more and more short wavelength components of gradient into the inversion. We demonstrate that wavefield decomposition helps the inversion to converge to the correct velocity model starting from essentially a v(z) initial starting model.
We present a new elastic reverse time migration implementation. The elastic wave propagation is simulated using a nonsplit-field complex frequency-shifted (CFS) recursive integration perfectly matched layer (PML) implementation (RIPML) with the auxiliary differential equations (ADEs) for elastic wave modeling. Here, RIPML can overcome the spurious reflection for waves incident on the PML interface at near-grazing angles, and evanescent waves within PML where the classic PML algorithm fails. For the imaging condition, we use Poynting vectors as a means to attenuate low-frequency cross correlation noise. This approach has been widely studied by numerous authors in acoustic imaging. We calculate the Poynting vector for elastic waves with a least squares formulation based on an optical flow equation in local windows to improve robustness. The effectiveness of our new implementation is demonstrated using a two layer synthetic model and a complicated SEG/EAGE salt dome elastic model.
In the presence of complex scattering effects, such as those that may be encountered at rugose salt boundaries, the assumption of single scattering used by most true-amplitude production imaging algorithms may no longer apply. This may render true-amplitude imaging ineffective with regard to amplitude fidelity in complex areas. Often in these areas, complex scattering and wave behavior manifests itself as complex misalignment and wavelet distortion on partial image gathers, even when the velocity model is correct. Such misalignment affects the stack, and ultimately amplitude fidelity. Here we present a general optimization method for the alignment of partial images to mitigate the effects of complex scattering and complex wave behavior through salt. Although we do not claim that the method produces true amplitude fidelity, we have found that it can enhance migration images in complex shadow zones, and is an effective quality control tool to locate areas of complex partial-image misalignment that compromises amplitude fidelity.
We develop a gradient computation for recovering anisotropic parameters associated with tilted-transverse isotropy (TTI) in full-waveform inversion (FWI). Our treatment is based on adjoint state theory and pseudo-analytic TTI wave propagation. The method provides reasonable estimates for anisotropic parameter updates and we observe that the migrated images for both the synthetic and real data show improvements with the inverted anisotropic parameters. However, due to the huge null space associated with the inversion we occasionally obtain parameters that are not in line with our understanding of the geology. To overcome this, we introduce a priori information within our inversion via dip annihilation filters. The introduction of this model styling goal within our inversion not only makes the results aesthetically pleasing but also in accordance with our physical intuition about the model. We illustrate our method with the help of a synthetic 3D example.
Full bandwidth velocity recovery, or more generally, impedance recovery, is a central issue in seismic inversion, and in particular full-waveform inversion. Here we develop an adjoint theory of seismic inversion based on the scattering series that leads to an inversion method involving a cascade of inversions that can potentially recover velocity information at all wavelengths. A key aspect of our method is the separation of low and high frequency parts of the model, since model updates in inversion are typically more successful when longer wavelengths are updated first. Toward this end, we develop a gradient orthogonalization scheme between successive order gradients that helps to isolate the lower frequency components when carried out to second order. We illustrate our method in detail with a very simple single reflector model in a laterally invariant background velocity.