Angle-Weighted Reverse Time Migration With Wavefield Decomposition Based on the Optical Flow Vector

Reverse time migration (RTM) is based on the two-way wave equation, so its imaging results obtained by conventional zero-lag cross-correlation imaging conditions contain a lot of low-wavenumber noises. So far, the wavefield decomposition method based on the Poynting vector has been developed to suppress these noises; however, this method also has some problems, such as unstable calculation of the Poynting vector, low accuracy of wavefield decomposition, and poor effect of large-angle migration artifacts suppression. This article introduces the optical flow vector method to RTM to realize high-precision wavefield decomposition for both the source and receiver wavefields and obtains four directions of wavefields: up-, down-, left-, and right-going. Then, the cross-correlation imaging sections of one-way propagation components of forward- and back-propagated wavefields are optimized and stacked. On this basis, the reflection angle of each imaging point is calculated based on the optical flow vector, and an attenuation factor related to the reflection angle is introduced as the weight to generate the optimal stack images. The tests of theoretical model and field marine seismic data illustrate that compared with the conventional RTM with wavefield decomposition based on the Poynting vector, the angle-weighted RTM with wavefield decomposition based on the optical flow vector proposed in this article can achieve wavefield decomposition for both the source and receiver wavefields and calculate the reflection angle of each imaging point more accurately and stably. Moreover, the proposed method adopts angle weighting processing, which can further eliminate large-angle migration artifacts and effectively improve the imaging accuracy of RTM.

An Improved Fractional-Order Variational Optical Flow Model Combining Structure Tensor

Dealing with problems of illumination changes in optical flow estimation, an improved variational optical flow model is proposed in this paper. The local structure constancy constraint (LSCC) is applied in the data term of the traditional HS (Horn & Schunck) optical flow model to substitute the brightness constancy constraint. The fractional-order smoothness constraint (FSC) is applied in the smoothness term of the HS model. Then, the detailed calculation processes from the optical flow model to the optical flow value are explained. The structure tensor in LSCC is an image feature that is constant in the illumination changes scene. The fractional differential coefficient in FSC can fuse the local neighborhood optical flow vector into the optical flow vector of the target pixel, which can improve the integrity of the motion region with the same motion speed. Combining LSCC with FSC, our improved optical flow model can obtain an accurate optical flow field with clear outline in the illumination abnormity scene. The experimental results show that, compared with other optical flow models, our model is more suitable for the illumination changes scene and can be employed in outdoor motion detection projects.

Quantitative blood flow estimation in vivo by optical speckle image velocimetry

Speckle based methods are popular non-invasive, label-free full-field optical techniques for imaging blood flow maps at single vessel resolution with a high temporal resolution. However, conventional speckle approach cannot provide an absolute velocity map with magnitude and direction. Here, we report a novel optical speckle image velocimetry (OSIV) technique for measuring the quantitative blood flow vector map by utilizing particle image velocimetry with speckle cross-correlations. We demonstrate that our OSIV instrument has a linearity range up to 7 mm/s, higher than conventional optical methods. Our method can measure the absolute flow vector map at up to 190 Hz without sacrificing the image size, and it eliminates the need for a high-speed camera/detector. We applied OSIV to image the blood flow in a mouse brain, and as a proof of concept, imaged the real-time dynamic changes in the cortical blood flow field during the stroke process in vivo. Our wide-field quantitative flow measurement OSIV method without the need of tracers provides a valuable tool for studying the healthy and diseased brain.

A series of equivalent area circle yield criteria based on unified strength theory

Unified strength theory considering the influence of the intermediate principal stress is widely used in geotechnical engineering, but the singularities bring inconvenience to the numerical calculation. A series of equivalent area circle yield criteria based on unified strength theory are derived. The parameters of the new yield criteria and Drucker-Prager criteria are discussed, and the flow vector coefficients of the new yield criteria are given. The new series of yield criteria are very convenient for numerical calculation and can be served as reference for the evaluation of the effects of strength theory.

Volumes of Flow Polytopes Related to Caracol Graphs

Recently, Benedetti et al. introduced an Ehrhart-like polynomial associated to a graph. This polynomial is defined as the volume of a certain flow polytope related to a graph and has the property that the leading coefficient is the volume of the flow polytope of the original graph with net flow vector $(1,1,\dots,1)$. Benedetti et al. conjectured a formula for the Ehrhart-like polynomial of what they call a caracol graph. In this paper their conjecture is proved using constant term identities, labeled Dyck paths, and a cyclic lemma.