James Rickett

SUMMARY: Full-waveform inversion (FWI) has demonstrated increasing success in estimating medium properties, but its computational cost still poses challenges in moving towards high-resolution imaging of targets at depth. Here, we propose a target-oriented FWI method that inverts for the medium parameters confined within an arbitrary region of interest. Our method is novel in terms of both local wavefield modelling and data redatuming, in order to build a target-oriented objective function which is sensitive to the target medium only without further assumptions about the medium outside. Based on the convolution-type representation theorem, our local forward modelling operator propagates wavefields within the target medium only while providing full acoustic coupling between the target medium and the surrounding geology. A key requirement of our local FWI method is that the subsurface wavefields surrounding and inside the target be as accurate as possible. As such, the subsurface wavefields are retrieved by the Marchenko method, which can redatum the single-sided surface reflection data to the target zone while preserving both primary and multiple reflections, with minimal a priori knowledge of the full-domain medium. Given a sufficiently accurate initial velocity macromodel, our numerical examples show that our local FWI method resolves the reservoir zone of a 2-D Barrett Unconventional P-wave velocity model much more efficiently than the conventional full-domain FWI without significantly sacrificing accuracy. Our method may further enable FWI approaches to high-resolution imaging of subsurface targets.

Planar waves events recorded in a seismic array can be represented as lines in the Fourier domain. However, in the real world, seismic events usually have curvature or amplitude variability, which means that their Fourier transforms are no longer strictly linear but rather occupy conic regions of the Fourier domain that are narrow at low frequencies but broaden at high frequencies where the effect of curvature becomes more pronounced. One can consider these regions as localised “signal cones”. In this work, we consider a space–time variable signal cone to model the seismic data. The variability of the signal cone is obtained through scaling, slanting, and translation of the kernel for cone‐limited (C‐limited) functions (functions whose Fourier transform lives within a cone) or C‐Gaussian function (a multivariate function whose Fourier transform decays exponentially with respect to slowness and frequency), which constitutes our dictionary. We find a discrete number of scaling, slanting, and translation parameters from a continuum by optimally matching the data. This is a non‐linear optimisation problem, which we address by a fixed‐point method that utilises a variable projection method with ℓ₁ constraints on the linear parameters and bound constraints on the non‐linear parameters. We observe that slow decay and oscillatory behaviour of the kernel for C‐limited functions constitute bottlenecks for the optimisation problem, which we partially overcome by the C‐Gaussian function. We demonstrate our method through an interpolation example. We present the interpolation result using the estimated parameters obtained from the proposed method and compare it with those obtained using sparsity‐promoting curvelet decomposition, matching pursuit Fourier interpolation, and sparsity‐promoting plane‐wave decomposition methods.

In order to deconvolve the ghost response from marine seismic data, an estimate of the ghost operator is required. Typically, this estimate is made using a model of in‐plane propagation, i.e., the ray path at the receiver falls in the vertical plane defined by the source and receiver locations. Unfortunately, this model breaks down when the source is in a crossline position relative to the receiver spread. In this situation, in‐plane signals can only exist in a small region of the signal cone.In this paper, we use Bayes' theory to model the posterior probability distribution functions for the vertical component of the ray vector given the known source–receiver azimuth and the measured inline component of the ray vector. This provides a model for the ghost delay time based on the acquisition geometry and the dip of the wave in the plane of the streamer. The model is fairly robust with regard to the prior assumptions and controlled by a single parameter that is related to the likelihood of in‐plane propagation.The expected values of the resulting distributions are consistent with the deterministic in‐plane model when in‐plane likelihood is high but valid everywhere in the signal cone. Relaxing the in‐plane likelihood to a reasonable degree radically simplifies the shape of the expected‐value surface, lending itself for use in deghosting algorithms. The model can also be extended to other plane‐wave processing problems such as interpolation.

The benefits of seismic imaging in areas of complex geology using a broad range of azimuths have been well documented for almost over a decade, and wide geometries (in various applications) have become the preferred acquisition style in the Gulf of Mexico. Helical (or “coil”) geometries using two or more vessels contain longer offsets and complete azimuth coverage, which is particularly valuable for deep subsalt targets. However, all wide-azimuth geometries pose additional challenges to single-component data-domain deghosting algorithms. In this paper, we demonstrate a data-adaptive deghosting algorithm on two data sets from the Gulf of Mexico: one acquired with a multivessel full-azimuth helical geometry, and another more conventional straight- and parallel-swath wide-azimuth geometry. Presentation Date: Wednesday, October 19, 2016 Start Time: 3:10:00 PM Location: 147/154 Presentation Type: ORAL

We found a data calibration scheme for frequency-domain full-waveform inversion (FWI). The scheme is based on the variable projection technique. With this scheme, the FWI algorithm can incorporate the data calibration procedure into the inversion process without introducing additional unknown parameters. The calibration variable for each frequency is computed using a minimum norm solution between the measured and simulated data. This process is directly included in the data misfit cost function. Therefore, the inversion algorithm becomes source independent. Moreover, because all the data points are considered in the calibration process, this scheme increases the robustness of the algorithm. Numerical tests determined that the FWI algorithm can reconstruct velocity distributions accurately without the source waveform information.

This paper compares three alternative algorithms for simultaneously estimating a source wavelet at the same time as an earth model in full‐waveform inversion: (i) simultaneous descent, (ii) alternating descent and (iii) descent with the variable projection method. The latter is a technique for solving separable least‐squares problems that is well‐known in the applied mathematics literature. When applied to full‐waveform inversion, it involves making the source wavelet an implicit function of the earth model via a least‐squares filter‐estimation process. Since the source wavelet becomes purely a function of medium parameters, it no longer needs to be treated as a separate unknown in the inversion. Essentially, the predicted data are projected onto the measured data in a least‐squares sense at every function evaluation, making use of the fact that the filter estimation problem is trivial when compared to the full‐waveform inversion problem. Numerical tests on a simple 1D model indicate that the variable projection method gives the best result; actually producing results in quality that are very similar to control experiments with a known, correct wavelet.