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

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.

Children with Cerebral Palsy Have Similar Walking and Running Quality Assessed by an Overall Kinematic Index

Running ability is critical to maintaining activity participation with peers. Children and adolescents with cerebral palsy (CP) are often stated to run better than they walk, but running is not often quantitatively measured. The purpose of this study was to utilize overall gait deviation indices to determine if children with diplegic CP run closer to typically developing children than they walk. This retrospective comparative study utilized 3D running kinematics that were collected after walking data at two clinical motion analysis centers for children with diplegic cerebral palsy. Separate walking and running Gait Deviation Indices (GDI Walk and GDI* Run), overall indices of multiple plane/joint motions, were calculated and scaled for each participant so that a typically developing mean was 100 with standard deviation of 10. An analysis of variance was used to compare the variables Activity (walking vs running) and Center (data collected at two different motion analysis laboratories). Fifty participants were included in the study. The main effect of Activity was not significant, mean GDI Walk = 76.4 while mean GDI* Run = 77.1, p = 0.84. Mean GDI scores for walking and running were equivalent, suggesting children with diplegic cerebral palsy as a group have similar walking and running quality. However, individual differences varied between activities, emphasizing the need for individual assessment considering specific goals related to running.

The hybrid Cramér-Rao lower bound for simultaneous self-localization and room geometry estimation

This paper addresses the problem of tracking a moving source, e.g., a robot, equipped with both receivers and a source, that is tracking its own location and simultaneously estimating the locations of multiple plane reflectors. We assume a noisy knowledge of the robot’s movement. We formulate this problem, which is also known as simultaneous localization and mapping (SLAM), as a hybrid estimation problem. We derive the extended Kalman filter (EKF) for both tracking the robot’s own location and estimating the room geometry. Since the EKF employs linearization at every step, we incorporate a regulated kinematic model, which facilitates a successful tracking. In addition, we consider the echo-labeling problem as solved and beyond the scope of this paper. We then develop the hybrid Cramér-Rao lower bound on the estimation accuracy of both the localization and mapping parameters. The algorithm is evaluated with respect to the bound via simulations, which shows that the EKF approaches the hybrid Cramér-Rao bound (CRB) (HCRB) as the number of observation increases. This result implies that for the examples tested in simulation, the HCRB is an asymptotically tight bound and that the EKF is an optimal estimator. Whether this property is true in general remains an open question.

Multiple Plane Fitting Algorithm to Evaluate the Accuracy of 3D Point Cloud Using Structured Light Measurement

3D shape measurement by structured light is a high-speed method and capable of profiling complex surfaces. In particular, the processing of measuring data also greatly affects the accuracy of obtained point clouds. In this paper, an algorithm to detect multiple planes on point cloud data was developed based on RANSAC algorithm to evaluate the accuracy of point cloud measured by structural light. To evaluate the accuracy of the point cloud obtained, two-step height parts are used. The planes are detected and the distance between them needs to be measured with high accuracy. Therefore, the distance measurement data between the planes found in the point cloud is compared with the data measured by CMM measurement. The experimental results have shown that the proposed algorithm can identify multiple planes at the same time with a maximum standard deviation of 0.068 (mm) and the maximum relative error is 1.46%.