scholarly journals The application of an optimal transport to a preconditioned data matching function for robust waveform inversion

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. R923-R945 ◽  
Author(s):  
Bingbing Sun ◽  
Tariq Alkhalifah
Keyword(s):  
High Resolution ◽  
Probability Distribution ◽  
Transport Theory ◽  
Optimal Transport ◽  
Waveform Inversion ◽  
Delta Function ◽  
Dirac Delta Function ◽  
Dirac Delta ◽  
Matching Filter ◽  
Optimal Transport Theory

Full-waveform inversion (FWI) promises a high-resolution model of the earth. It is, however, a highly nonlinear inverse problem; thus, we iteratively update the subsurface model by minimizing a misfit function that measures the difference between the measured and the predicted data. The conventional [Formula: see text]-norm misfit function is widely used because it provides a simple, high-resolution misfit function with a sample-by-sample comparison. However, it is susceptible to local minima if the low-wavenumber components of the initial model are not accurate. Deconvolution of the predicted and measured data offers an extended space comparison, which is more global. The matching filter calculated from the deconvolution has energy focused at zero lag, like an approximated Dirac delta function, when the predicted data matches the measured one. We have introduced a framework for designing misfit functions by measuring the distance between the matching filter and a representation of the Dirac delta function using optimal transport theory. We have used the Wasserstein [Formula: see text] distance, which provides us with the optimal transport between two probability distribution functions. Unlike data, the matching filter can be easily transformed to a probability distribution satisfying the requirement of the optimal transport theory. Though in one form, it admits the conventional normalized penalty applied to the nonzero-lag energy in the matching filter, the proposed misfit function is metric and extracts its form from solid mathematical foundations based on optimal transport theory. Explicitly, we can derive the adaptive waveform inversion (AWI) misfit function based on our framework, and the critical “normalization” for AWI occurs naturally per the requirement of a probability distribution. We use a modified Marmousi model and the BP salt model to verify the features of the proposed method in avoiding cycle skipping. We use the Chevron 2014 FWI benchmark data set to further highlight the effectiveness of the proposed approach.

Research on the Dark Fiber Causes and Variety of the Acidic Fiber Imaging Bundle

2015 ◽  
Vol 1096 ◽  
pp. 275-279
Author(s):  
De Chun Zhou ◽  
Zhong Liang Qiao ◽  
Xue Mei Bai
Keyword(s):  
Electron Microscope ◽  
High Resolution ◽  
Probability Distribution ◽  
Scanning Electron Microscope ◽  
Delta Function ◽  
Dirac Delta Function ◽  
Experimental Results ◽  
Genetic Mechanism ◽  
Dirac Delta ◽  
Scanning Electron

The paper carried out a research on the dark fiber shape and genetic mechanism of the acidic fiber imaging bundle. The Dirac delta function is firstly used to analyze the probability distribution variety of the dark silk. The experimental results for the detection of the scanning electron microscope (SEM) and resolution show that the genetic ratio of the dark fiber is proportionate to length of the bundle and inversely proportional to the monofilament diameter. However, the monofilament diameter should be decreased to increase the resolution. The technique and the structure should be improved to meet the requirements of both high resolution and low dark silk rate. Therefore, solutions and effective measurements for reducing even if avoiding the dark silk are proposed in the paper. The research will guide the preparation and application of the high-resolution fiber imaging bundle.

scholarly journals Robust full-waveform inversion with Radon-domain matching filter

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. R707-R724 ◽  
Author(s):  
Bingbing Sun ◽  
Tariq Alkhalifah
Keyword(s):  
Radon Transform ◽  
Waveform Inversion ◽  
Delta Function ◽  
Measured Data ◽  
Dirac Delta Function ◽  
Full Waveform Inversion ◽  
Dirac Delta ◽  
Full Waveform ◽  
Matching Filter ◽  
Filter Approach

Cycle skipping is a severe issue in full-waveform inversion. One option to overcome it is to extend the search space to allow for data comparisons beyond the “point-to-point” subtraction. A matching filter can be computed by deconvolving the measured data from the predicted ones. If the model is correct, the resulting matching filter would be a Dirac delta function in which the energy is focused at zero lag. An optimization problem can be formulated by penalizing this matching filter departure from a Dirac delta function. Because the matching filter replaces the local sample-by-sample comparison with a global one using deconvolution, it can reduce the cycle-skipping problem. Because the matching filter is computed using the whole trace of the measured and predicted data, it is prone to unwanted crosstalk of different events. We perform the deconvolution in the Radon domain to reduce crosstalk and improve the inversion. We first transform the measured and the predicted data into the [Formula: see text] domain using the local Radon transform. We then perform deconvolution for the trace indexed by the same slope value. The main objective of the proposal is to use the slope information embedded in the Radon-transform representation to separate the events and reduce the crosstalk in the deconvolution step. As a result, the objective function tends to be more convex and stabilizes the inversion process. The result obtained for the modified Marmousi model demonstrates the proposed Radon-domain matching-filter approach can converge to a meaningful model given data without the low frequencies of less than 3 Hz and a [Formula: see text] initial model. Compared to the conventional time-space matching-filter approach, the Radon-domain approach indicates fewer artifacts in the model and better fitting of the measured data. The result corresponding to the Chevron 2014 benchmark data set also indicates the good performance of the proposed approach.

scholarly journals Electromagnetic Waves Through Disordered Systems: Comparison of Intensity, Transmission and Conductance

2001 ◽  
Vol 694 ◽  
Author(s):  
Fredy R Zypman ◽  
Gabriel Cwilich
Keyword(s):  
Probability Distribution ◽  
Disordered Systems ◽  
Electromagnetic Waves ◽  
Delta Function ◽  
Rayleigh Distribution ◽  
Dirac Delta Function ◽  
Universal Form ◽  
Dirac Delta ◽  
Diffusive Regime ◽  
Analytical Expressions

AbstractWe obtain the statistics of the intensity, transmission and conductance for scalar electromagnetic waves propagating through a disordered collection of scatterers. Our results show that the probability distribution for these quantities x, follow a universal form, YU(x) = xne−xμ. This family of functions includes the Rayleigh distribution (when α=0, μ=1) and the Dirac delta function (α →+ ∞), which are the expressions for intensity and transmission in the diffusive regime neglecting correlations. Finally, we find simple analytical expressions for the nth moment of the distributions and for to the ratio of the moments of the intensity and transmission, which generalizes the n! result valid in the previous case.

scholarly journals A robust waveform inversion using a global comparison of modeled and observed data

2019 ◽  
Vol 38 (3) ◽  
pp. 185-192 ◽  
Author(s):  
Bingbing Sun ◽  
Tariq Alkhalifah
Keyword(s):  
Optimal Transport ◽  
Waveform Inversion ◽  
Alternative Formulation ◽  
Initial Model ◽  
Data Set ◽  
Dirac Delta ◽  
Global Comparison ◽  
L2 Norm ◽  
Highly Nonlinear ◽  
Matching Filter

A high-resolution model of the subsurface is the product of a successful full-waveform inversion (FWI) application. However, this optimization problem is highly nonlinear, and thus, we iteratively update the subsurface model by minimizing a misfit function that measures the difference between observed and modeled data. The L2-norm misfit function provides a simple, sample-by-sample comparison between the observed and modeled data. However, it is susceptible to local minima in the objective function if the low-wavenumber components of the initial model are not accurate enough. We review an alternative formulation of FWI based on a more global comparison. A combination of Radon transform and utilizing a matching filter allows for comparisons beyond sample to sample. We combine two recent developments to suggest the following algorithm for optimal inversion: (1) we compute the matching filter between the observed and modeled data in the Radon domain, which helps reduce the crosstalk introduced in the deconvolution step of computing the matching filter, and (2) we use Wasserstein distance to measure the distance between the resulting matching filter in the Radon domain and a representation of the Dirac delta function, which provides us with the optimal transport between the two distribution functions. We use a modified Marmousi model to show how this Radon-domain optimal-transport-based matching-filter approach can mitigate cycle skipping. Starting from a rather simplified v(z) media as the initial model, the proposed method can invert for the Marmousi model with considerable accuracy, while standard L2-norm formulation is trapped in a local minimum. Application of the proposed method to an offshore data set further demonstrates its robustness and effectiveness.

Dirac delta regularization

2020 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Delta Function ◽  
Dirac Delta Function ◽  
Dirac Delta ◽  
Finite Result

I present a finite result for the Dirac delta "function."

scholarly journals Wildlife Monitoring Using a Multi-UAV System with Optimal Transport Theory

2021 ◽  
Vol 11 (9) ◽  
pp. 4070
Author(s):  
Rabiul Hasan Kabir ◽  
Kooktae Lee
Keyword(s):  
Detection Rate ◽  
Transport Theory ◽  
Optimal Transport ◽  
Position Estimation ◽  
Wildlife Monitoring ◽  
High Detection Rate ◽  
Monitoring Strategies ◽  
Spatio Temporal ◽  
Optimal Transport Theory ◽  
Multi Uav

This paper addresses a wildlife monitoring problem using a team of unmanned aerial vehicles (UAVs) with the optimal transport theory. The state-of-the-art technology using UAVs has been an increasingly popular tool to monitor wildlife compared to the traditional methods such as satellite imagery-based sensing or GPS trackers. However, there still exist unsolved problems as to how the UAVs need to cover a spacious domain to detect animals as many as possible. In this paper, we propose the optimal transport-based wildlife monitoring strategy for a multi-UAV system, to prioritize monitoring areas while incorporating complementary information such as GPS trackers and satellite-based sensing. Through the proposed scheme, the UAVs can explore the large-size domain effectively and collaboratively with a given priority. The time-varying nature of wildlife due to their movements is modeled as a stochastic process, which is included in the proposed work to reflect the spatio-temporal evolution of their position estimation. In this way, the proposed monitoring plan can lead to wildlife monitoring with a high detection rate. Various simulation results including statistical data are provided to validate the proposed work. In all different simulations, it is shown that the proposed scheme significantly outperforms other UAV-based wildlife monitoring strategies in terms of the target detection rate up to 3.6 times.

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