A graphical method for the construction of rays and travel times in spherically layered media

1965 ◽  
Vol 55 (3) ◽  
pp. 641-651 ◽  
Author(s):  
K. Helbig
Keyword(s):  
Travel Time ◽  
Graphical Method ◽  
Layered Media ◽  
Velocity Versus ◽  
Travel Times ◽  
Graphical Construction

Abstract A method is described which allows the graphical construction of rays and travel times. The velocity versus radius curve is graphically converted into a “normalized slowness graph,” in which all variables describing a ray and its travel time can be represented by geometric quantities. It is found that most of the well-known analytic relations between the properties of the velocity versus radius distribution and the form of rays have their geometric counterparts and that these geometric relations can be derived rather simply.

scholarly journals “In cities, it’s not far, but it takes long”: comparing estimated and replicated travel times to reach life-saving obstetric care in Lagos, Nigeria

2021 ◽  
Vol 6 (1) ◽  
pp. e004318
Author(s):  
Aduragbemi Banke-Thomas ◽  
Kerry L M Wong ◽  
Francis Ifeanyi Ayomoh ◽  
Rokibat Olabisi Giwa-Ayedun ◽  
Lenka Benova
Keyword(s):  
Travel Time ◽  
Friction Surface ◽  
Obstetric Care ◽  
Travel Times ◽  
Night Time ◽  
Google Maps ◽  
Surface Approach ◽  
Low Resource ◽  
Life Saving ◽  
The Cost

BackgroundTravel time to comprehensive emergency obstetric care (CEmOC) facilities in low-resource settings is commonly estimated using modelling approaches. Our objective was to derive and compare estimates of travel time to reach CEmOC in an African megacity using models and web-based platforms against actual replication of travel.MethodsWe extracted data from patient files of all 732 pregnant women who presented in emergency in the four publicly owned tertiary CEmOC facilities in Lagos, Nigeria, between August 2018 and August 2019. For a systematically selected subsample of 385, we estimated travel time from their homes to the facility using the cost-friction surface approach, Open Source Routing Machine (OSRM) and Google Maps, and compared them to travel time by two independent drivers replicating women’s journeys. We estimated the percentage of women who reached the facilities within 60 and 120 min.ResultsThe median travel time for 385 women from the cost-friction surface approach, OSRM and Google Maps was 5, 11 and 40 min, respectively. The median actual drive time was 50–52 min. The mean errors were >45 min for the cost-friction surface approach and OSRM, and 14 min for Google Maps. The smallest differences between replicated and estimated travel times were seen for night-time journeys at weekends; largest errors were found for night-time journeys at weekdays and journeys above 120 min. Modelled estimates indicated that all participants were within 60 min of the destination CEmOC facility, yet journey replication showed that only 57% were, and 92% were within 120 min.ConclusionsExisting modelling methods underestimate actual travel time in low-resource megacities. Significant gaps in geographical access to life-saving health services like CEmOC must be urgently addressed, including in urban areas. Leveraging tools that generate ‘closer-to-reality’ estimates will be vital for service planning if universal health coverage targets are to be realised by 2030.

Estimation of Path Travel Time Distributions in Stochastic Time-Varying Networks with Correlations

2021 ◽  
pp. 036119812110184
Author(s):  
Monika Filipovska ◽  
Hani S. Mahmassani ◽  
Archak Mittal
Keyword(s):  
Time Dependence ◽  
Travel Time ◽  
Correlation Structure ◽  
Time Varying ◽  
Travel Times ◽  
Trajectory Data ◽  
Time Varying Networks ◽  
Transportation Research ◽  
Search Approach ◽  
Stochastic Time

Transportation research has increasingly focused on the modeling of travel time uncertainty in transportation networks. From a user’s perspective, the performance of the network is experienced at the level of a path, and, as such, knowledge of variability of travel times along paths contemplated by the user is necessary. This paper focuses on developing approaches for the estimation of path travel time distributions in stochastic time-varying networks so as to capture generalized correlations between link travel times. Specifically, the goal is to develop methods to estimate path travel time distributions for any path in the networks by synthesizing available trajectory data from various portions of the path, and this paper addresses that problem in a two-fold manner. Firstly, a Monte Carlo simulation (MCS)-based approach is presented for the convolution of time-varying random variables with general correlation structures and distribution shapes. Secondly, a combinatorial data-mining approach is developed, which aims to utilize sparse trajectory data for the estimation of path travel time distributions by implicitly capturing the complex correlation structure in the network travel times. Numerical results indicate that the MCS approach allowing for time-dependence and a time-varying correlation structure outperforms other approaches, and that its performance is robust with respect to different path travel time distributions. Additionally, using the path segmentations from the segment search approach with a MCS approach with time-dependence also produces accurate and robust estimates of the path travel time distributions with the added benefit of shorter computation times.

scholarly journals Dynamic Bus Travel Time Prediction Models on Road with Multiple Bus Routes

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Cong Bai ◽  
Zhong-Ren Peng ◽  
Qing-Chang Lu ◽  
Jian Sun
Keyword(s):  
Travel Time ◽  
Dynamic Model ◽  
Kalman Filtering ◽  
Prediction Models ◽  
Support Vector ◽  
Travel Times ◽  
Travel Time Prediction ◽  
Real World Data ◽  
Time Prediction ◽  
Bus Travel Time

Accurate and real-time travel time information for buses can help passengers better plan their trips and minimize waiting times. A dynamic travel time prediction model for buses addressing the cases on road with multiple bus routes is proposed in this paper, based on support vector machines (SVMs) and Kalman filtering-based algorithm. In the proposed model, the well-trained SVM model predicts the baseline bus travel times from the historical bus trip data; the Kalman filtering-based dynamic algorithm can adjust bus travel times with the latest bus operation information and the estimated baseline travel times. The performance of the proposed dynamic model is validated with the real-world data on road with multiple bus routes in Shenzhen, China. The results show that the proposed dynamic model is feasible and applicable for bus travel time prediction and has the best prediction performance among all the five models proposed in the study in terms of prediction accuracy on road with multiple bus routes.

Intensities and travel times of seismic rays in a sphere with a linear velocity function

1977 ◽  
Vol 67 (1) ◽  
pp. 33-42
Author(s):  
Mark E. Odegard ◽  
Gerard J. Fryer
Keyword(s):  
Velocity Profile ◽  
Travel Time ◽  
Upper Mantle ◽  
Intensity Ratio ◽  
Computation Time ◽  
Spherical Body ◽  
Travel Times ◽  
Velocity Function ◽  
Intensity Ratios ◽  
Distance Travel

Abstract Equations are presented which permit the calculation of distances, travel times and intensity ratios of seismic rays propagating through a spherical body with concentric layers having velocities which vary linearly with radius. In addition, a method is described which removes the infinite singularities in amplitude generated by second-order discontinuities in the velocity profile. Numerical calculations involving a reasonable upper mantle model show that the standard deviations of the errors for distance, travel time and intensity ratio are 0.0046°, 0.057 sec, and 0.04 dB, respectively. Computation time is short.

A method of obtaining P and S travel-time curves within a “Stripped Earth”*

1952 ◽  
Vol 42 (4) ◽  
pp. 313-314
Author(s):  
V. C. Stechschulte
Keyword(s):  
Travel Time ◽  
Depth Distribution ◽  
Epicentral Distance ◽  
Travel Times ◽  
Depth Of Focus ◽  
Distance Curve ◽  
Simple Method ◽  
Time Distance ◽  
Deep Focus

Abstract A simple method is outlined for obtaining from a time-distance curve of a deep-focus earthquake a table of travel times within an earth “stripped” to the depth h, the depth of focus. The method depends on the fact that such a curve for a deep-focus earthquake has a point of inflection and therefore has the same slope at two different values of epicentral distance. The Herglotz-Wiechert method may then be applied to these travel times to obtain a velocity-depth distribution.

Analytical approach unifying the two-regime scaling for bedload particle motions

2021 ◽  
Author(s):  
Zi Wu ◽  
Arvind Singh ◽  
Efi Foufoula-Georgiou ◽  
Michele Guala ◽  
Xudong Fu ◽  
...  
Keyword(s):  
Travel Time ◽  
Velocity Variation ◽  
Travel Times ◽  
Scaling Exponents ◽  
Time Scaling ◽  
Dispersion Regime ◽  
The Mean ◽  
Bedload Sediment ◽  
Distance Travel ◽  
First Time

<p>Bedload particle hops are defined as successive motions of a particle from start to stop, characterizing one of the most fundamental processes describing bedload sediment transport in rivers. Although two transport regimes have been recently identified for short- and long-hops, respectively <strong>(Wu et al., <em>Water Resour Res</em>, 2020)</strong>, there still lacks a theory explaining how the mean hop distance-travel time scaling may extend to cover the phenomenology of bedload particle motions. Here we propose a velocity-variation based formulation, and for the first time, we obtain analytical solution for the mean hop distance-travel time relation valid for the entire range of travel times, which agrees well with the measured data <strong>(Wu et al., <em>J Fluid Mech</em>, 2021)</strong>. Regarding travel times, we identify three distinct regimes in terms of different scaling exponents: respectively as ~1.5 for an initial regime and ~5/3 for a transition regime, which define the short-hops; and 1 for the so-called Taylor dispersion regime defining long-hops. The corresponding probability density function of the hop distance is also analytically obtained and experimentally verified. </p>

Willingness to Travel for Cellular Therapy: The Influence of Follow-Up Care Location, Oncologist Continuity, and Race

2021 ◽  
pp. OP.21.00312
Author(s):  
Zachary A. K. Frosch ◽  
Esin C. Namoglu ◽  
Nandita Mitra ◽  
Daniel J. Landsburg ◽  
Sunita D. Nasta ◽  
...  
Keyword(s):  
Travel Time ◽  
Cellular Therapy ◽  
Treatment Plan ◽  
Admission Rate ◽  
B Cell Lymphoma ◽  
Travel Times ◽  
Importance Weights ◽  
Follow Up Care ◽  
Treatment Plans

PURPOSE Patients weigh competing priorities when deciding whether to travel to a cellular therapy center for treatment. We conducted a choice-based conjoint analysis to determine the relative value they place on clinical factors, oncologist continuity, and travel time under different post-treatment follow-up arrangements. We also evaluated for differences in preferences by sociodemographic factors. METHODS We administered a survey in which patients with diffuse large B-cell lymphoma selected treatment plans between pairs of hypothetical options that varied in travel time, follow-up arrangement, oncologist continuity, 2-year overall survival, and intensive care unit admission rate. We determined importance weights (which represent attributes' value to participants) using generalized estimating equations. RESULTS Three hundred and two patients (62%) responded. When all follow-up care was at the center providing treatment, plans requiring longer travel times were less attractive ( v 30 minutes, importance weights [95% CI] of –0.54 [–0.80 to –0.27], –0.57 [–0.84 to –0.29], and –0.17 [–0.49 to 0.14] for 60, 90, and 120 minutes). However, the negative impact of travel on treatment plan choice was mitigated by offering shared follow-up (importance weights [95% CI] of 0.63 [0.33 to 0.93], 0.32 [0.08 to 0.57], and 0.26 [0.04 to 0.47] at 60, 90, and 120 minutes). Black participants were less likely to choose plans requiring longer travel, regardless of follow-up arrangement, as indicated by lower value importance weights for longer travel times. CONCLUSION Reducing travel burden through shared follow-up may increase patients' willingness to travel to receive cellular therapies, but additional measures are required to facilitate equitable access.

Day-to-Day Travel-Time Trends and Travel-Time Prediction from Loop-Detector Data

2000 ◽  
Vol 1717 (1) ◽  
pp. 120-129 ◽  
Author(s):  
Jaimyoung Kwon ◽  
Benjamin Coifman ◽  
Peter Bickel
Keyword(s):  
Linear Regression ◽  
Travel Time ◽  
Prediction Errors ◽  
Travel Times ◽  
Travel Time Prediction ◽  
Time Prediction ◽  
Loop Detectors ◽  
Stepwise Variable Selection ◽  
Planning Models ◽  
Current Implementation

An approach is presented for estimating future travel times on a freeway using flow and occupancy data from single-loop detectors and historical travel-time information. Linear regression, with the stepwise-variable-selection method and more advanced tree-based methods, is used. The analysis considers forecasts ranging from a few minutes into the future up to an hour ahead. Leave-a-day-out cross-validation was used to evaluate the prediction errors without underestimation. The current traffic state proved to be a good predictor for the near future, up to 20 min, whereas historical data are more informative for longer-range predictions. Tree-based methods and linear regression both performed satisfactorily, showing slightly different qualitative behaviors for each condition examined in this analysis. Unlike preceding works that rely on simulation, real traffic data were used. Although the current implementation uses measured travel times from probe vehicles, the ultimate goal is an autonomous system that relies strictly on detector data. In the course of presenting the prediction system, the manner in which travel times change from day to day was examined, and several metrics to quantify these changes were developed. The metrics can be used as input for travel-time prediction, but they also should be beneficial for other applications, such as calibrating traffic models and planning models.

scholarly journals The Effect of Route-choice Strategy on Transit Travel Time Estimates

2019 ◽  
Author(s):  
Nate Wessel ◽  
Steven Farber
Keyword(s):  
Travel Time ◽  
Shortest Path ◽  
Imperfect Information ◽  
Optimal Path ◽  
Shortest Paths ◽  
Route Choice ◽  
Travel Times ◽  
Selection Strategies ◽  
Time Estimates ◽  
Average Travel Time

Estimates of travel time by public transit often rely on the calculation of a shortest-path between two points for a given departure time. Such shortest-paths are time-dependent and not always stable from one moment to the next. Given that actual transit passengers necessarily have imperfect information about the system, their route selection strategies are heuristic and cannot be expected to achieve optimal travel times for all possible departures. Thus an algorithm that returns optimal travel times at all moments will tend to underestimate real travel times all else being equal. While several researchers have noted this issue none have yet measured the extent of the problem. This study observes and measures this effect by contrasting two alternative heuristic routing strategies to a standard shortest-path calculation. The Toronto Transit Commission is used as a case study and we model actual transit operations for the agency over the course of a normal week with archived AVL data transformed into a retrospective GTFS dataset. Travel times are estimated using two alternative route-choice assumptions: 1) habitual selection of the itinerary with the best average travel time and 2) dynamic choice of the next-departing route in a predefined choice set. It is shown that most trips present passengers with a complex choice among competing itineraries and that the choice of itinerary at any given moment of departure may entail substantial travel time risk relative to the optimal outcome. In the context of accessibility modelling, where travel times are typically considered as a distribution, the optimal path method is observed in aggregate to underestimate travel time by about 3-4 minutes at the median and 6-7 minutes at the \nth{90} percentile for a typical trip.

scholarly journals Wave velocities in the earth's core

1958 ◽  
Vol 48 (4) ◽  
pp. 301-314
Author(s):  
B. Gutenberg
Keyword(s):  
Travel Time ◽  
Transition Zone ◽  
Southern California ◽  
Inner Core ◽  
Travel Times ◽  
Earth’S Core ◽  
Earth's Core ◽  
The Core ◽  
Wave Velocities

Abstract More than 700 seismograms of 39 shocks recorded mainly in southern California at epicentral distances between 105 and 140 degrees are used to investigate records of phases which have penetrated the earth's core. Properties of PKIKP, SKP, SKIKP, PKS, and PKIKS are discussed. Portions of travel-time curves of these phases are revised. Travel times of waves starting and ending at the surface of the core, and wave velocities in the core, are recalculated. Between about 1,500 and 1,200 km. from the earth's center in the transition zone from the liquid outer to the probably solid inner core, waves having lengths of the order of 10 km. travel faster than longer waves. This is probably caused by a rather rapid increase in viscosity toward the earth's center in this transition zone.

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