3,315 research outputs found
Full Waveform Inversion for Time-Distance Helioseismology
Inferring interior properties of the Sun from photospheric measurements of
the seismic wavefield constitutes the helioseismic inverse problem. Deviations
in seismic measurements (such as wave travel times) from their fiducial values
estimated for a given model of the solar interior imply that the model is
inaccurate. Contemporary inversions in local helioseismology assume that
properties of the solar interior are linearly related to measured travel-time
deviations. It is widely known, however, that this assumption is invalid for
sunspots and active regions, and likely for supergranular flows as well. Here,
we introduce nonlinear optimization, executed iteratively, as a means of
inverting for the sub-surface structure of large-amplitude perturbations.
Defining the penalty functional as the norm of wave travel-time
deviations, we compute the the total misfit gradient of this functional with
respect to the relevant model parameters %(only sound speed in this case) at
each iteration around the corresponding model. The model is successively
improved using either steepest descent, conjugate gradient, or quasi-Newton
limited-memory BFGS. Performing nonlinear iterations requires privileging
pixels (such as those in the near-field of the scatterer), a practice not
compliant with the standard assumption of translational invariance.
Measurements for these inversions, although similar in principle to those used
in time-distance helioseismology, require some retooling. For the sake of
simplicity in illustrating the method, we consider a 2-D inverse problem with
only a sound-speed perturbation.Comment: 24 pages, 10 figures, to appear in Ap
Full waveform inversion with extrapolated low frequency data
The availability of low frequency data is an important factor in the success
of full waveform inversion (FWI) in the acoustic regime. The low frequencies
help determine the kinematically relevant, low-wavenumber components of the
velocity model, which are in turn needed to avoid convergence of FWI to
spurious local minima. However, acquiring data below 2 or 3 Hz from the field
is a challenging and expensive task. In this paper we explore the possibility
of synthesizing the low frequencies computationally from high-frequency data,
and use the resulting prediction of the missing data to seed the frequency
sweep of FWI. As a signal processing problem, bandwidth extension is a very
nonlinear and delicate operation. It requires a high-level interpretation of
bandlimited seismic records into individual events, each of which is
extrapolable to a lower (or higher) frequency band from the non-dispersive
nature of the wave propagation model. We propose to use the phase tracking
method for the event separation task. The fidelity of the resulting
extrapolation method is typically higher in phase than in amplitude. To
demonstrate the reliability of bandwidth extension in the context of FWI, we
first use the low frequencies in the extrapolated band as data substitute, in
order to create the low-wavenumber background velocity model, and then switch
to recorded data in the available band for the rest of the iterations. The
resulting method, EFWI for short, demonstrates surprising robustness to the
inaccuracies in the extrapolated low frequency data. With two synthetic
examples calibrated so that regular FWI needs to be initialized at 1 Hz to
avoid local minima, we demonstrate that FWI based on an extrapolated [1, 5] Hz
band, itself generated from data available in the [5, 15] Hz band, can produce
reasonable estimations of the low wavenumber velocity models
Seismic full waveform inversion in archaeological prospecting
Seismic full waveform inversion is introduced as novel high-resolution imaging tool in archaeological prospection. The full waveform inversion approach allows the high-resolution characterization of low-contrast sedimentary layers, high-contrast stone wall structures and air-filled cavities
Chapter 5 • Full waveform inversion
In the geophysics of oil exploration and reservoir studies, the surface seismic method is the most commonly used method to obtain a subsurface model in 2 or 3 dimensions. This method plays an increasingly important role in soil investigations for geotechnical, hydrogeological and site characterization studies regarding seismic hazard issues. The goal of this book is to provide a practical guide, using examples from the field, to the application of seismic methods to surface imaging. After reviewing the current state of knowledge in seismic wave propagation, refraction and reflection seismic methods, the book aims to describe how seismic tomography and fullwave form inversion methods can be used to obtain seismic images of the subsurface. Through various synthetic and field examples, the book highlights the benefit of combining different sets of data: refracted waves with reflected waves, and body waves with surface waves. With field data targeting shallow structures, it shows how more accurate geophysical models can be obtained by using the proposed hybrid methods. Finally, it shows how the integration of seismic data (3D survey and VSP), logging data (acoustic logging) and core measurements, combined with a succession of specific and advanced processing techniques, enables the development of a 3D high resolution geological model in depth. In addition to these examples, the authors provide readers with guidelines to carry out these operations, in terms of acquisition, as well as processing and interpretation. In each chapter, the reader will find theoretical concepts, practical rules and, above all, actual application examples. For this reason, the book can be used as a text to accompany course lectures or continuing education seminars. This book aims to promote the exchange of information among geologists, geophysicists, and engineers in geotechnical fields
Anisotropic Waveform Tomography: Application to Crosshole data for Transversely Isotropic Media
Anisotropic Traveltime Tomography and Full Waveform Inversion were applied first to synthetic and then to real data following the development of a transversely isotropic model for handling anisotropy. Best-fitting models of seismic velocity and Thomsen\u27s anisotropy parameters were initially obtained from traveltime tomography, and then used as the starting models for Full Waveform Inversion. The use of a Laplace transform approach effectively damps late arriving S-wave artifacts that introduce errors into the modelling process. The results of the synthetic study highlights the tradeoffs in resolution between the two parameter classes, but verify anisotropic traveltime tomography as a valid method for generating starting models for Full Waveform Inversion. The joint technique was then applied to field gathers from Western Canada and compared to a similar analyses that used a simpler anisotropy model. The transversely isotropic approach yielded a Full Waveform Inversion model with superior resolution that better predicted the true data
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