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Abstract The Simulating eXtreme Spacetimes Collaboration's code \texttt{SpEC} can now routinely simulate binary black hole mergers undergoing $$\sim25$$ orbits, with the longest simulations undergoing nearly $$\sim180$$ orbits. While this sounds impressive, the mismatch between the highest resolutions for this long simulation is $$\mathcal{O}(10^{-1})$$. Meanwhile, the mismatch between resolutions for the more typical simulations tends to be $$\mathcal{O}(10^{-4})$$, despite the resolutions being similar to the long simulations'. In this note, we explain why mismatch alone gives an incomplete picture of code---and waveform---quality, especially in the context of providing waveform templates for LISA and 3G detectors, which require templates with $$\mathcal{O}(10^{3}) - \mathcal{O}(10^{5})$$ orbits. We argue that to ready the GW community for the sensitivity of future detectors, numerical relativity groups must be aware of this caveat, and also run future simulations with at least three resolutions to properly assess waveform accuracy.
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A Procedure to Infer Lightning Return-Stroke Current Waveform From Far-Field Waveform for the Case of Lossy Ground
- Award ID(s):
- 2055178
- PAR ID:
- 10499798
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Transactions on Electromagnetic Compatibility
- ISSN:
- 0018-9375
- Page Range / eLocation ID:
- 1 to 7
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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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 acoustic 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 that probes the unknown medium with pulses and measures the generated waves. We propose to solve the inverse problem of velocity estimation 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 a step by step computation of the ROM, which depends nonlinearly on the data and yet can be obtained from them in a noniterative fashion, using efficient methods from linear algebra. We also explain how to make the ROM robust to data inaccuracy. The ROM computation requires the full array response matrix gathered with colocated sources and receivers. However, we find that the computation can deal with an approximation of this matrix, obtained from towed-streamer data using interpolation and reciprocity on-the-fly. Although the full-waveform inversion approach of nonlinear least-squares data fitting is challenging without low-frequency information, due to multiple minima of the data fit objective function, we find that the ROM misfit objective function has better behavior, even for a poor initial guess. We also find by explicit computation 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.more » « less
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Abstract Objective. Arterial viscosity is emerging as an important biomarker, in addition to the widely used arterial elasticity. This paper presents an approach to estimate arterial viscoelasticity using shear wave elastography (SWE).Approach. While dispersion characteristics are often used to estimate elasticity from SWE data, they are not sufficiently sensitive to viscosity. Driven by this, we develop a full waveform inversion (FWI) methodology, based on directly matching predicted and measured wall velocity in space and time, to simultaneously estimate both elasticity and viscosity. Specifically, we propose to minimize an objective function capturing the correlation between measured and predicted responses of the anterior wall of the artery.Results. The objective function is shown to be well-behaving (generally convex), leading us to effectively use gradient optimization to invert for both elasticity and viscosity. The resulting methodology is verified with synthetic data polluted with noise, leading to the conclusion that the proposed FWI is effective in estimating arterial viscoelasticity.Significance. Accurate estimation of arterial viscoelasticity, not just elasticity, provides a more precise characterization of arterial mechanical properties, potentially leading to a better indicator of arterial health.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/TEMC.2023.3325280
