Modeling and inversion of seismic data using multiple scattering, renormalization and homotopy methods

Seismic scattering theory plays an important role in seismic forward modeling and is the theoretical foundation for various seismic imaging methods. Full waveform inversion is a powerful technique for obtaining a high-resolution model of the subsurface. One objective of this thesis is to develop convergent scattering series solutions of the Lippmann-Schwinger equation in strongly scattering media using renormalization and homotopy methods. Other objectives of this thesis are to develop efficient full waveform inversion methods of time-lapse seismic data and, to investigate uncertainty quantification in full waveform inversion for anisotropic elastic media based on integral equation approaches and the iterated extended Kalman filter. The conventional Born scattering series is obtained by expanding the Lippmann-Schwinger equation in terms of an iterative solution based on perturbation theory. Such an expansion assumes weak scattering and may have the problems of convergence in strongly scattering media. This thesis presents two scattering series, referred to as convergent Born series (CBS) and homotopy analysis method (HAM) scattering series for frequency-domain seismic wave modeling. For the convergent Born series, a physical interpretation from the renormalization prospective is given. The homotopy scattering series is derived by using homotopy analysis method, which is based on a convergence control parameter $h$ and a convergence control operator $H$ that one can use to ensure convergence for strongly scattering media. The homotopy scattering scattering series solutions of the Lippmann-Schwinger equation, which is convergent in strongly scattering media. The homotopy scattering series is a kind of unified scattering series theory that includes the conventional and convergent Born series as special cases. The Fast Fourier Transform (FFT) is employed for efficient implementation of matrix-vector multiplication for the convergent Born series and the homotopy scattering series. This thesis presents homotopy methods for ray based seismic modeling in strongly anisotropic media. To overcome several limitations of small perturbations and weak anisotropy in obtaining the traveltime approximations in anisotropic media by expanding the anisotropic eikonal equation in terms of the anisotropic parameters and the elliptically anisotropic eikonal equation based on perturbation theory, this study applies the homotopy analysis method to the eikonal equation. Then this thesis presents a retrieved zero-order deformation equation that creates a map from the anisotropic eikonal equation to a linearized partial differential equation system. The new traveltime approximations are derived by using the linear and nonlinear operators in the retrieved zero-order deformation equation. Flexibility on variable anisotropy parameters is naturally incorporated into the linear differential equations, allowing a medium of arbitrarily anisotropy. This thesis investigates efficient target-oriented inversion strategies for improving full waveform inversion of time-lapse seismic data based on extending the distorted Born iterative T-matrix inverse scattering to a local inversion of a small region of interest (e. g. reservoir under production). The target-oriented approach is more efficient for inverting the monitor data. The target-oriented inversion strategy requires properly specifying the wavefield extrapolation operators in the integral equation formulation. By employing the T-matrix and the Gaussian beam based Green’s function, the wavefield extrapolation for the time-lapse inversion is performed in the baseline model from the survey surface to the target region. I demonstrate the method by presenting numerical examples illustrating the sequential and double difference strategies. To quantify the uncertainty and multiparameter trade-off in the full waveform inversion for anisotropic elastic media, this study applies the iterated extended Kalman filter to anisotropic elastic full waveform inversion based on the integral equation method. The sensitivity matrix is an explicit representation with Green’s functions based on the nonlinear inverse scattering theory. Taking the similarity of sequential strategy between the multi-scale frequency domain full waveform inversion and data assimilation with an iterated extended Kalman filter, this study applies the explicit representation of sensitivity matrix to the the framework of Bayesian inference and then estimate the uncertainties in the full waveform inversion. This thesis gives results of numerical tests with examples for anisotropic elastic media. They show that the proposed Bayesian inversion method can provide reasonable reconstruction results for the elastic coefficients of the stiffness tensor and the framework is suitable for accessing the uncertainties and analysis of parameter trade-offs

Traveltime approximation for strongly anisotropic media using the homotopy analysis method

Traveltime approximation plays an important role in seismic data processing, for example, anisotropic parameter estimation and seismic imaging. By exploiting seismic traveltimes, it is possible to improve the accuracy of anisotropic parameter estimation and the resolution of seismic imaging. Conventionally, the traveltime approximations in anisotropic media are obtained by expanding the anisotropic eikonal equation in terms of the anisotropic parameters and the elliptically anisotropic eikonal equation based on perturbation theory. Such an expansion assumes a small perturbation and weak anisotropy. In a realistic medium, however, the assumption of small perturbation likely breaks down. We present a retrieved zero-order deformation equation that creates a map from the anisotropic eikonal equation to a linearized partial differential equation system based on the homotopy analysis method. By choosing the linear and nonlinear operators in the retrieved zero-order deformation equation, we develop new traveltime approximations that allow us to compute the traveltimes for a medium of arbitrarily strength anisotropy. A comparison of the traveltimes and their errors from the homotopy analysis method and from the perturbation method suggests that the traveltime approximations provide a more reliable result in strongly anisotropic media.publishedVersio

Homotopy analysis of the Lippmann-Schwinger equation for seismic wavefield modeling in strongly scattering media

We present an application of the homotopy analysis method for solving the integral equations of the Lippmann-Schwinger type, which occurs frequently in acoustic and seismic scattering theory. In this method, a series solution is created which is guaranteed to converge independent of the scattering potential. This series solution differs from the conventional Born series because it contains two auxiliary parameters ε and h and an operator H that can be selected freely in order to control the convergence properties of the scattering series. The ε-parameter which controls the degree of dissipation in the reference medium (that makes the wavefield updates localized in space) is known from the so-called convergent Born series theory; but its use in conjunction with the homotopy analysis method represents a novel feature of this work. By using H = I (where I is the identity operator) and varying the convergence control parameters h and ε, we obtain a family of scattering series which reduces to the conventional Born series when h = −1 and ε = 0. By using H = γ where γ is a particular preconditioner and varying the convergence control parameters h and ε, we obtain another family of scattering series which reduces to the so-called convergent Born series when h = −1 and ε ≥ εc where εc is a critical dissipation parameter depending on the largest value of the scattering potential. This means that we have developed a kind of unified scattering series theory that includes the conventional and convergent Born series as special cases. By performing a series of 12 numerical experiments with a strongly scattering medium, we illustrate the effects of varying the (ε, h, H)-parameters on the convergence properties of the new homotopy scattering series. By using (ε, h, H) = (0.5, −0.8, I) we obtain a new scattering series that converges significantly faster than the convergent Born series. The use of a non-zero dissipation parameter ε seems to improve on the convergence properties of any scattering series, but one can now relax on the requirement ε ≥ εc from the convergent Born series theory, provided that a suitable value of the convergence control parameter h and operator H is used.publishedVersio

A complex point-source solution of the acoustic eikonal equation for Gaussian beams in transversely isotropic media

The complex traveltime solutions of the complex eikonal equation are the basis of inhomogeneous plane-wave seismic imaging methods, such as Gaussian beam migration and tomography. We present the analytic approximations for complex traveltime in transversely isotropic media with a titled symmetry axis (TTI), which is defined by a Taylor series expansion over the anisotropy parameters. The formulation for complex traveltime is developed using perturbation theory and the complex point source method. The real part of the complex traveltime describes the wavefront and the imaginary part of the complex traveltime describes the decay of amplitude of waves away from the central ray. We derive the linearized ordinary differential equations for the coefficients of the Taylor-series expansion 2 using perturbation theory. The analytical solutions for the complex traveltimes are determined by applying the complex point source method to the background traveltime formula and subsequently obtaining the coefficients from the linearized ordinary differential equations. We investigate the influence of the anisotropy parameters and of the initial width of the ray tube on the accuracy of the computed traveltimes. The analytical formulas, as outlined, are efficient methods for the computation of complex traveltimes from the complex eikonal equation. In addition, those formulas are also effective methods for benchmarking approximated solutions.acceptedVersio

Co-attention Propagation Network for Zero-Shot Video Object Segmentation

Zero-shot video object segmentation (ZS-VOS) aims to segment foreground objects in a video sequence without prior knowledge of these objects. However, existing ZS-VOS methods often struggle to distinguish between foreground and background or to keep track of the foreground in complex scenarios. The common practice of introducing motion information, such as optical flow, can lead to overreliance on optical flow estimation. To address these challenges, we propose an encoder-decoder-based hierarchical co-attention propagation network (HCPN) capable of tracking and segmenting objects. Specifically, our model is built upon multiple collaborative evolutions of the parallel co-attention module (PCM) and the cross co-attention module (CCM). PCM captures common foreground regions among adjacent appearance and motion features, while CCM further exploits and fuses cross-modal motion features returned by PCM. Our method is progressively trained to achieve hierarchical spatio-temporal feature propagation across the entire video. Experimental results demonstrate that our HCPN outperforms all previous methods on public benchmarks, showcasing its effectiveness for ZS-VOS.Comment: accepted by IEEE Transactions on Image Processin

Numerical Simulation of the Dynamics of Water Droplet Impingement on a Wax Surface

The impact of droplets on solid surfaces is important for a wide range of engineering applications, such as ink-jet printing, spray cooling of hot surfaces, spray coating and painting, solder-drop deposition, blood spattering for criminal forensics and disease detection, etc. This paper simulated the dynamic process of a water droplet impinging onto a wax substrate in COMSOL, using the Phase Field method for tracking the free surface. The predicted spreading factor and apex height were validated against experimental results, showing good agreement during the dynamic impingement process. The effect of contact angles on the impingement process was also studied. The initial inertia driven spreading process is not affected by the contact angle, but the later spreading process and recoil process are significantly affected by the contact angle. The simulation results can provide a good understanding of the dynamic impingement process and provide insights on how surface wettability can affect the droplet spreading and rebounding process

Linking ethylene to nitrogen-dependent leaf longevity of grass species in a temperate steppe

Author's manuscript made available in accordance with the publisher's policy.Background and Aims Leaf longevity is an important plant functional trait that often varies with soil nitrogen supply. Ethylene is a classical plant hormone involved in the control of senescence and abscission, but its role in nitrogen-dependent leaf longevity is largely unknown. Methods Pot and field experiments were performed to examine the effects of nitrogen addition on leaf longevity and ethylene production in two dominant plant species, Agropyron cristatum and Stipa krylovii, in a temperate steppe in northern China. Key Results Nitrogen addition increased leaf ethylene production and nitrogen concentration but shortened leaf longevity; the addition of cobalt chloride, an ethylene biosynthesis inhibitor, reduced leaf nitrogen concentration and increased leaf longevity. Path analysis indicated that nitrogen addition reduced leaf longevity mainly through altering leaf ethylene production. Conclusions These findings provide the first experimental evidence in support of the involvement of ethylene in nitrogen-induced decrease in leaf longevity

Removing multiple types of noise of distributed acoustic sensing seismic data using attention-guided denoising convolutional neural network

In recent years, distributed optical fiber acoustic sensing (DAS) technology has been increasingly used for vertical seismic profile (VSP) exploration. Even though this technology has the advantages of high spatial resolution, strong resistance to high temperature and pressure variations, long sensing distance, DAS seismic noise has expanded from random noise to optical abnormal noise, fading noise and horizontal noise, etc. This seriously affects the quality of the seismic data and brings huge challenges to subsequent imaging, inversion and interpretation. Moreover, the noise is more complex and more difficult to simultaneously suppress using traditional methods. Therefore, for the purpose of effectively improving the signal-to-noise ratio (SNR) of DAS seismic data, we introduce a denoising network named attention-guided denoising convolutional neural network (ADNet). The network is composed of four blocks, including a sparse block (SB), a feature enhancement block (FEB), an attention block (AB) and a reconstruction block (RB). The network uses different kinds of convolutions alternately to enlarge the receptive field size and extract global feature of the input. Meanwhile, the attention mechanism is introduced to extract the hidden noise information in the complex background. The network predicts the noise, and denoised data are obtained by subtracting the predicted results from the noisy inputs. In addition, we uniquely construct a large number of complex forward models for pure seismic data training set to enhance the network suitability. The combination design improves the denoising performance and reduces computational cost and memory consumption. The results obtained from both synthetic- and field data illustrate that the network has the ability to denoise the seismic images and retrieve weak effective signals better than conventional methods and common networks