scholarly journals A Hybrid Method Applied to Improve the Efficiency of Full-Waveform Inversion for Pavement Characterization

Sensors ◽  
2018 ◽  
Vol 18 (9) ◽  
pp. 2916 ◽  
Author(s):  
Jingwei Zhang ◽  
Shengbo Ye ◽  
Li Yi ◽  
Yuquan Lin ◽  
Hai Liu ◽  
...  
Keyword(s):  
Hybrid Method ◽  
Optimization Algorithm ◽  
High Efficiency ◽  
Estimation Error ◽  
Waveform Inversion ◽  
Multilayer Perceptrons ◽  
Full Waveform Inversion ◽  
Inversion Algorithm ◽  
Full Waveform ◽  
Two Stages

Ground penetrating radar (GPR), as a nondestructive testing tool, is suitable for estimating the thickness and permittivity of layers within the pavement. However, it would become problematic when the layer is thin with respect to the probing pulse width, in which case overlapping between the reflected pulses occurs. In order to deal with this problem, a hybrid method based on multilayer perceptrons (MLPs) and a local optimization algorithm is proposed. This method can be divided into two stages. In the first stage, the MLPs roughly estimate the thickness and the permittivity of the GPR signal. In the second stage, these roughly estimated values are used as the initial solution of the full-waveform inversion algorithm. The hybrid method and the conventional global optimization algorithm are respectively used to perform the full-waveform inversion of the simulated GPR data. Under the same inversion precision, the objective function needs to be calculated for 450 times and 30 times for the conventional method and the hybrid method, respectively. The hybrid method is also applied to a measured data, and the thickness estimation error is 1.2 mm. The results show the high efficiency and accuracy of such hybrid method to resolve the problem of estimating the thickness and permittivity of a “thin layer”.

scholarly journals Application of an Improved Ultrasound Full-Waveform Inversion in Bone Quantitative Measurement

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 260
Author(s):  
Meng Suo ◽  
Dong Zhang ◽  
Yan Yang
Keyword(s):  
Nonlinear Equations ◽  
Waveform Inversion ◽  
Optimal Solution ◽  
Inversion Method ◽  
Full Waveform Inversion ◽  
Inversion Algorithm ◽  
Elastic Wave Equation ◽  
Full Waveform ◽  
Ultrasonic Propagation ◽  
Joint Velocity

Inspired by the large number of applications for symmetric nonlinear equations, an improved full waveform inversion algorithm is proposed in this paper in order to quantitatively measure the bone density and realize the early diagnosis of osteoporosis. The isotropic elastic wave equation is used to simulate ultrasonic propagation between bone and soft tissue, and the Gauss–Newton algorithm based on symmetric nonlinear equations is applied to solve the optimal solution in the inversion. In addition, the authors use several strategies including the frequency-grid multiscale method, the envelope inversion and the new joint velocity–density inversion to improve the result of conventional full-waveform inversion method. The effects of various inversion settings are also tested to find a balanced way of keeping good accuracy and high computational efficiency. Numerical inversion experiments showed that the improved full waveform inversion (FWI) method proposed in this paper shows superior inversion results as it can detect small velocity–density changes in bones, and the relative error of the numerical model is within 10%. This method can also avoid interference from small amounts of noise and satisfy the high precision requirements for quantitative ultrasound measurements of bone.

Application of the variable projection scheme for frequency-domain full-waveform inversion

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. R249-R257 ◽  
Author(s):  
Maokun Li ◽  
James Rickett ◽  
Aria Abubakar
Keyword(s):  
Frequency Domain ◽  
Waveform Inversion ◽  
Simulated Data ◽  
Calibration Procedure ◽  
Full Waveform Inversion ◽  
Inversion Algorithm ◽  
Unknown Parameters ◽  
Variable Projection ◽  
Full Waveform ◽  
Data Calibration

We found a data calibration scheme for frequency-domain full-waveform inversion (FWI). The scheme is based on the variable projection technique. With this scheme, the FWI algorithm can incorporate the data calibration procedure into the inversion process without introducing additional unknown parameters. The calibration variable for each frequency is computed using a minimum norm solution between the measured and simulated data. This process is directly included in the data misfit cost function. Therefore, the inversion algorithm becomes source independent. Moreover, because all the data points are considered in the calibration process, this scheme increases the robustness of the algorithm. Numerical tests determined that the FWI algorithm can reconstruct velocity distributions accurately without the source waveform information.

scholarly journals ML-descent: An optimization algorithm for full-waveform inversion using machine learning

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. R477-R492 ◽  
Author(s):  
Bingbing Sun ◽  
Tariq Alkhalifah
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Inverse Problem ◽  
Optimization Algorithm ◽  
Waveform Inversion ◽  
Slight Modification ◽  
Descent Method ◽  
Quadratic Functions ◽  
Full Waveform Inversion ◽  
Full Waveform

Full-waveform inversion (FWI) is a nonlinear optimization problem, and a typical optimization algorithm such as the nonlinear conjugate gradient or limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) would iteratively update the model mainly along the gradient-descent direction of the misfit function or a slight modification of it. Based on the concept of meta-learning, rather than using a hand-designed optimization algorithm, we have trained the machine (represented by a neural network) to learn an optimization algorithm, entitled the “ML-descent,” and apply it in FWI. Using a recurrent neural network (RNN), we use the gradient of the misfit function as the input, and the hidden states in the RNN incorporate the history information of the gradient similar to an LBFGS algorithm. However, unlike the fixed form of the LBFGS algorithm, the machine-learning (ML) version evolves in response to the gradient. The loss function for training is formulated as a weighted summation of the L2 norm of the data residuals in the original inverse problem. As with any well-defined nonlinear inverse problem, the optimization can be locally approximated by a linear convex problem; thus, to accelerate the training, we train the neural network by minimizing randomly generated quadratic functions instead of performing time-consuming FWIs. To further improve the accuracy and robustness, we use a variational autoencoder that projects and represents the model in latent space. We use the Marmousi and the overthrust examples to demonstrate that the ML-descent method shows faster convergence and outperforms conventional optimization algorithms. The energy in the deeper part of the models can be recovered by the ML-descent even when the pseudoinverse of the Hessian is not incorporated in the FWI update.

scholarly journals Source‐independent full‐waveform inversion of seismic data

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 2010-2015 ◽  
Author(s):  
Ki Ha Lee ◽  
Hee Joon Kim
Keyword(s):  
Frequency Domain ◽  
Seismic Data ◽  
Waveform Inversion ◽  
Source Spectrum ◽  
Full Waveform Inversion ◽  
Source Inversion ◽  
Inversion Algorithm ◽  
Source Information ◽  
Full Waveform ◽  
Precise Knowledge

A rigorous full‐waveform inversion of seismic data has been a challenging subject, partly because of the lack of precise knowledge of the source. Since currently available approaches involve some form of approximations to the source, inversion results are subject to the quality and choice of the source information used. We propose a new full‐waveform inversion methodology that does not involve source spectrum information. Thus, potential inversion errors from source estimation can be eliminated. A gather of seismic traces is first Fourier transformed into the frequency domain, and a normalized wavefield is obtained for each trace in the frequency domain. Normalization is done with respect to the frequency response of a reference trace selected from the gather, so the complex‐valued normalized wavefield is dimensionless. The source spectrum is eliminated during the normalization procedure. With its source spectrum eliminated, the normalized wavefield lets us construct an inversion algorithm without the source information. The inversion algorithm minimizes misfits between a measured normalized wavefield and a numerically computed normalized wavefield. The proposed approach has been demonstrated successfully using a simple 2D scalar problem.

Full-Waveform Inversion of High-Frequency Teleseismic Body Waves Based on Multiple Plane-Wave Incidence: Methods and Practical Applications

2021 ◽  
Author(s):  
Kai Wang ◽  
Yi Wang ◽  
Xin Song ◽  
Ping Tong ◽  
Qinya Liu ◽  
...  
Keyword(s):  
Plane Wave ◽  
Hybrid Method ◽  
Waveform Inversion ◽  
Body Waves ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Multiple Plane ◽  
Spherical Curvature ◽  
Wave Incidence ◽  
Plane Wave Incidence

ABSTRACT Teleseismic full-waveform inversion has recently been applied to image subwavelength-scale lithospheric structures (typically a few tens of kilometers) by utilizing hybrid methods in which an efficient solver for the 1D background model is coupled with a full numerical solver for a small 3D target region. Among these hybrid methods, the coupling of the frequency–wavenumber technique with the spectral element method is one of the most computationally efficient ones. However, it is normally based on a single plane-wave incidence, and thus cannot synthesize secondary global phases generated at interfaces outside the target area. To remedy the situation, we propose to use a multiple plane-wave injection method to include secondary global phases in the hybrid modeling. We investigate the performance of the teleseismic full-waveform inversion based on single and multiple plane-wave incidence through an application in the western Pyrenees and compare it with previously published images and the inversion based on a global hybrid method. In addition, we also test the influence of Earth’s spherical curvature on the tomographic results. Our results demonstrate that the teleseismic full-waveform inversion based on a single plane-wave incidence can reveal complex lithospheric structures similar to those imaged using a global hybrid method and is reliable for practical tomography for small regions with an aperture of a few hundred kilometers. However, neglecting the Earth’s spherical curvature and secondary phases leads to errors on the recovered amplitudes of velocity anomalies (e.g., about 2.8% difference for density and VS, and 4.2% for VP on average). These errors can be reduced by adopting a spherical mesh and injecting multiple plane waves in the frequency–wavenumber-based hybrid method. The proposed plane-wave teleseismic full-waveform inversion is promising for mapping subwavelength-scale seismic structures using high-frequency teleseismic body waves (>1  Hz) including coda waves recorded at large N seismic arrays.

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