| 1. |
- Borcea, Liliana, et al.
(författare)
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Waveform inversion via reduced order modeling
- 2023
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Ingår i: Geophysics. - : Society of Exploration Geophysicists. - 0016-8033 .- 1942-2156. ; 88:2, s. R175-R191
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a novel approach to waveform inversion, based on a data driven reduced order model (ROM) of the wave operator. The presentation is for the acous- tic wave equation, but the approach can be extended to elastic or electromagnetic waves. The data are time resolved measurements of the pressure wave gathered by an acquisition system which probes the unknown medium with pulses and measures the generated waves. We propose to solve the inverse problem of velocity es- timation by minimizing the square misfit between the ROM computed from the recorded data and the ROM computed from the modeled data, at the current guess of the velocity. We give the step by step computation of the ROM, which depends nonlinearly on the data and yet can be obtained from them in a non-iterative fash- ion, using efficient methods from linear algebra. We also explain how to make the ROM robust to data inac- curacy. The ROM computation requires the full array response matrix gathered with colocated sources and receivers. However, we show that the computation can deal with an approximation of this matrix, obtained from towed-streamer data using interpolation and reci- procity on-the-fly.While the full-waveform inversion approach of nonlin- ear least-squares data fitting is challenging without low frequency information, due to multiple minima of the data fit objective function, we show that the ROM mis- fit objective function has a better behavior, even for a poor initial guess. We also show by an explicit com- putation of the objective functions in a simple setting that the ROM misfit objective function has convexity properties, whereas the least squares data fit objective function displays multiple local minima.
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| 2. |
- Borcea, Liliana, et al.
(författare)
-
Waveform Inversion with a Data Driven Estimate of the Internal Wave
- 2023
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Ingår i: SIAM Journal on Imaging Sciences. - : Society for Industrial and Applied Mathematics. - 1936-4954. ; 16:1, s. 280-312
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Tidskriftsartikel (refereegranskat)abstract
- We study an inverse problem for the wave equation, concerned with estimating the wave speed from data gathered by an array of sources and receivers that emit probing signals and measure the resulting waves. The typical approach to solving this problem is a nonlinear least squares minimization of the data misfit, over a search space. There are two main impediments to this approach, which manifest as multiple local minima of the objective function: The nonlinearity of the mapping from the wave speed to the data, which accounts for multiple scattering effects, and poor knowledge of the kinematics (smooth part of the wave speed), which causes cycle skipping. We show that the nonlinearity can be mitigated using a data driven estimate of the wave field at points inside the medium, also known as the "internal wave field." This leads to improved performance of the inversion for a reasonable initial guess of the kinematics.
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| 3. |
- De Hoop, Maarten V, et al.
(författare)
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Inverse problem for Love waves in a layered, elastic half-space
- 2024
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Ingår i: Inverse Problems. - : Institute of Physics Publishing (IOPP). - 0266-5611 .- 1361-6420. ; :045013, s. 1-44
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study Love waves in a layered, elastic half-space. We first address the direct problem and we characterize the existence of Love waves through the dispersion relation. We then address the inverse problem and we show how to recover the parameters of the elastic medium from the empirical knowledge of the frequency–wavenumber couples of the Love waves.
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