Velocity estimation via registration-guided least-squares inversion

This paper introduces an iterative scheme for acoustic model inversion where the notion of proximity of two traces is not the usual least-squares distance, but instead involves registration as in image processing. Observed data are matched to predicted waveforms via piecewise-polynomial warpings, obtained by solving a nonconvex optimization problem in a multiscale fashion from low to high frequencies. This multiscale process requires defining low-frequency augmented signals in order to seed the frequency sweep at zero frequency. Custom adjoint sources are then defined from the warped waveforms. The proposed velocity updates are obtained as the migration of these adjoint sources, and cannot be interpreted as the negative gradient of any given objective function. The new method, referred to as RGLS, is successfully applied to a few scenarios of model velocity estimation in the transmission setting. We show that the new method can converge to the correct model in situations where conventional least-squares inversion suffers from cycle-skipping and converges to a spurious model.Comment: 20 pages, 13 figures, 1 tabl

The failure mode of correlation focusing for model velocity estimation

We analyze the correlation focusing objective functional introduced by van Leeuwen and Mulder to avoid the cycle-skipping problem in full waveform inversion. While some encouraging numerical experiments were reported in the transmission setting, we explain why the method cannot be expected to work for general reflection data. We characterize the form that the adjoint source needs to take for model velocity updates to generate a time delay or a time advance. We show that the adjoint source of correlation focusing takes this desired form in the case of a single primary reflection, but not otherwise. Ultimately, failure owes to the specific form of the normalization present in the correlation focusing objective

Registration-guided least-squares waveform inversion

Full waveform inversion with frequency sweeping cannot start from zero frequency because of the lack of low-frequency data, requiring a good starting model. We study a di fferent iterative scheme where the notion of proximity of two traces is not the usual least-squares distance, but instead involves registration as in image processing. In order to create transported data, we introduce a nonconvex optimization problem and solve it in a multiscale fashion from low to high frequencies. This process requires defining low-frequency augmented signals in order to seed the frequency sweep at zero frequency. Successful registrations of noisy data, and application of the new method to model velocity estimation are demonstrated. In a crosshole seismic inversion example (transmission setting), we show that the new method decreases the model velocity error while conventional least-squares inversion converges to a spurious model

Image registration guided wavefield tomography for shear-wave velocity model building

Multicomponent acquisitions offer the opportunity to form elastic migration images and to estimate elastic parameters of the subsurface. Compared with better constrained P-wave velocity inversions, it is more difficult to estimate the S-wave velocity due to strong nonlinearities introduced by converted S-waves. We have developed an iterative S-wave velocity inversion method guided by image registration. Given an accurate P-wave velocity and a simple initial S-wave model, we form P-P and P-S images using elastic reverse time migration. We use image registration to find the shifts between the P-S and P-P images. The S-wave velocity model could be updated iteratively by minimizing the differences between the original and the fractionally warped P-S images. A simple layered model and a modified Marmousi model are used to demonstrate the viability of the new method. In both examples, high-quality P-S images, as well as smooth S-wave velocity models, are inverted efficiently with a homogeneous S-wave initial model

A New Method for Detecting the Time-Varying Nonlinear Damping in Nonlinear Oscillation Systems: Nonparametric Identification

This paper presents an original method that can be used for identifying time-varying nonlinear damping characteristics of a nonlinear oscillation system. The method developed involves the nonparametric identification, in which only the system responses, namely, displacement and velocity need to be known for the identification. However, the method is concerned with a Volterra-type integral equation of the first kind, which leads to an instability of numerical solutions. That is, the solutions identified lack stability properties. In order to overcome the difficulty, a stabilization technique is applied to the identification process. A numerical example comprising a highly nonlinear system is examined to demonstrate the workability of the proposed method for the time-varying damping identification

A spectral element method for fluid -structure interaction: New algorithm and applications to intracranial aneurysms

The first part of the thesis presents the surface representation of blood vessel walls extracted from medical images, sensitivity to the inlet/outlet boundary conditions, and a hp-refinement study. Our study shows that flow instability in supraclinoid aneurysms is not affected by flow division at downstream branches. However, inlet boundary condition is recommended to be specified upstream of the cavernous segment. The hp-refinement study shows that our spectral element code captures velocity and wall shear stress (WSS) fluctuations. The second part describes the development and implementation of new fluid solvers with better stability properties than the standard NEKTAR. Due to the strict CFL condition in semi-implicit scheme, the standard NEKTAR over-resolves solutions in time. The semi-implicit scheme is stabilized by sub-iterations with relaxation at each time step. The stability and accuracy of the scheme has been tested with analytic steady solutions, unsteady flows past a cylinder, and pulsatile flows in straight/bend pipes. We also develop a high-order spectral/hp element method for fluid-structure interaction which couples solvers in a partitioned way. Fictitious mass and damping terms introduced to the elastodynamics equation are shown to enhance the stability and reduce the number of sub-iterations. A new boundary condition with spring supports is proposed and its effect on the displacement and stability is investigated. In the last part of the thesis, we report on flow instabilities and WSS distributions in funnel-shaped bifurcations and aneurysms. Our simulations also show that pulsatile flows in aneurysms are subject to a hydrodynamic instability during the decelerating systolic phase, resulting in high-frequency oscillations in the range of 20–50 Hz. When the aneurysmal flow becomes unstable, both the magnitude and the directions of WSS vectors fluctuate at the aforementioned high frequencies. Impingement regions coincide with the locations of the rupture of infundibulae or progression to aneurysms

A new method for measuring nonharmonic periodic excitation forces in nonlinear damped systems

The purpose of this study is to identify an external loading of long time duration, which is nonharmonic but periodic, acting on a nonlinear dynamic system with nonlinear restoring as well as nonlinear damping. A new procedure is proposed for the force identification through an inverse formalism. However, this involves a Volterra-type nonlinear integral equation of the first kind, which lacks solution stability. Therefore, the nonlinear dynamic system under investigation is transformed into a linear relation between forces and pseudo-displacements. The lack of solution stability is resolved by applying available regularization methods. The feasibility of the force identification is demonstrated through a numerical example. (C) 2011 Elsevier Ltd. All rights reserved.Jang TS, 2010, MECH SYST SIGNAL PR, V24, P1665, DOI 10.1016/j.ymssp.2010.01.003Jang TS, 2010, WAVE MOTION, V47, P146, DOI 10.1016/j.wavemoti.2009.10.002Jang TS, 2009, INT J NONLIN MECH, V44, P801, DOI 10.1016/j.ijnonlinmec.2009.05.001Worden K, 2009, MECH SYST SIGNAL PR, V23, P104, DOI 10.1016/j.ymssp.2007.11.031Lu ZR, 2007, MECH SYST SIGNAL PR, V21, P2099, DOI 10.1016/j.ymssp.2006.11.004Jang TS, 2007, OCEAN ENG, V34, P676, DOI 10.1016/j.oceaneng.2006.06.011Feldman M, 2007, MECH SYST SIGNAL PR, V21, P943, DOI 10.1016/j.ymssp.2006.01.004CHARLES G, 2006, STABLE APPROXIMATE EChen J, 2004, COMPUT MECH, V33, P365, DOI 10.1007/s00466-003-0538-9JANG TS, 2001, J MARINE SCI TECHNOL, V5, P107JANG TS, 2000, J MAR SCI TECHNOL, V5, P16JANG TS, 2000, J MARINE SCI TECHNOL, V5, P181ZEN QH, 2000, IEEE T MAGN, V36, P2667Doyle JF, 1997, EXP MECH, V37, P403KIRSCH A, 1996, INTRO MATH THEOR INV, V10, P282DONOHO DL, 1995, APPL COMPUTATIONAL HMASRI SF, 1993, J APPL MECH-T ASME, V60, P123GROETSCH CW, 1993, INVERSE PROBLEMS MATHANSEN PC, 1992, SIAM REV, V34, P561BRAUN SC, 1991, MECH SYSTEMS SIGNAL, V58, P233MURDOCK JA, 1991, PERTURBATIONS THEORY, V16, P509FINK AM, 1974, SIAM J APPL MATH, V26, P26WHITHAM GB, 1974, LINEAR NONLINEAR WAV, V16, P636JORDAN TH, 1971, P NATL ACAD SCI USA, V68, P291ABRAMOWITZ M, 1964, HDB MATH FUNCTIONS F, V14, P1046TIKHONOV AN, 1963, SOV MATH DOKL, V4, P1035FRIDMAN VM, 1956, USP MAT NAUK, V11, P233LANDWEBER L, 1951, AM J MATH, V73, P615