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.

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>

Teleseismic P-wave travel time tomography of the Alpine upper mantle using AlpArray seismic network data

2020 ◽  
Author(s):  
Marcel Paffrath ◽  
Wolfgang Friederich ◽  
Keyword(s):  
Travel Time ◽  
Upper Mantle ◽  
High Velocity ◽  
Eastern Alps ◽  
Alpine Region ◽  
Seismic Network ◽  
P Wave ◽  
Travel Times ◽  
Travel Time Tomography ◽  
Wave Travel

<p>We perform a teleseismic P-wave travel time tomography to examine geometry and slab structure of the upper mantle beneath the Alpine orogen. Vertical component data of the extraordinary dense seismic network AlpArray are used which were recorded at over 600 temporary and permanent broadband stations deployed by 24 different European institutions in the greater Alpine region, reaching from the Massif Central to the Pannonian Basin and from the Po plain to the river Main. Mantle phases of 347 teleseismic events between 2015 and 2019 of magnitude 5.5 and higher are evaluated automatically for direct and core diffracted P arrivals using a combination of higher-order statistics picking algorithms and signal cross correlation. The resulting database contains over 170.000 highly accurate absolute P picks that were manually revised for each event. The travel time residuals exhibit very consistent and reproducible spatial patterns, already pointing at high velocity slabs in the mantle.</p><p>For predicting P-wave travel times, we consider a large computational box encompassing the Alpine region up to a depth of 600 km within which we allow 3D-variations of P-wave velocity. Outside this box we assume a spherically symmetric earth and apply the Tau-P method to calculate travel times and ray paths. These are injected at the boundaries of the regional box and continued using the fast marching method. We invert differences between observed and predicted travel times for P-wave velocities inside the box. Velocity is discretized on a regular grid with an average spacing of about 25 km. The misfit reduction reaches values of up to 75% depending on damping and smoothing parameters.</p><p>The resulting model shows several steeply dipping high velocity anomalies following the Alpine arc. The most prominent structure stretches from the western Alps into the Apennines mountain range reaching depths of over 500 km. Two further anomalies extending down to a depth of 300 km are located below the central and eastern Alps, separated by a clear gap below the western part of the Tauern window. Further to the east the model indicates a possible high-velocity connection between the eastern Alps and the Dinarides. Regarding the lateral position of the central and eastern Alpine slabs, our results confirm previous studies. However, there are differences regarding depth extent, dip angles and dip directions. Both structures dip very steeply with a tendency towards northward dipping. We perform various general, as well as purpose-built resolution tests, to verify the capabilities of our setup to resolve slab gaps as well as different possible slab dipping directions.</p>

Teleseismic P-wave travel time tomography of the Alpine upper mantle using AlpArray seismic network data

2021 ◽  
Author(s):  
Marcel Paffrath ◽  
Wolfgang Friederich ◽  
Keyword(s):  
Travel Time ◽  
Upper Mantle ◽  
High Velocity ◽  
Alpine Region ◽  
Seismic Network ◽  
P Wave ◽  
Travel Times ◽  
Massif Central ◽  
Travel Time Tomography ◽  
Wave Travel

<p>We perform a teleseismic P-wave travel time tomography to examine geometry and slab structure of the upper mantle beneath the Alpine orogen. Vertical component data of the extraordinary dense seismic network AlpArray are used which were recorded at over 600 temporary and permanent broadband stations deployed by 24 different European institutions in the greater Alpine region, reaching from the Massif Central to the Pannonian Basin and from the Po plain to the river Main. Mantle phases of 370 teleseismic events between 2015 and 2019 of magnitude 5.5 and higher are evaluated automatically for direct and core diffracted P arrivals using a combination of higher-order statistics picking algorithms and signal cross correlation. The resulting database contains over 170.000 highly accurate absolute P picks that were manually revised for each event. The travel time residuals exhibit very consistent and reproducible spatial patterns, already pointing at high velocity slabs in the mantle.</p><p>For predicting P-wave travel times we consider a large computational box encompassing the Alpine region up to a depth of 600 km within which we allow 3D-variations of P-wave velocity. To account for influences of the strongly heterogeneous crust that cannot be resolved with teleseismic data, we integrate a complex three-dimensional crustal model directly into our model. Outside the box we assume a spherically symmetric earth and apply the Tau-P method to calculate travel times and ray paths. These are injected at the boundaries of the regional box and continued using the fast marching method (Rawlinson et al. 2005). We invert differences between observed and predicted traveltimes for P-wave velocities inside the box. Velocity is discretized on a regular grid with a spacing of about 25x25x15 km. The misfit reduction reaches values of over 80% depending on damping and smoothing parameters.</p><p>The resulting model shows several steeply dipping high velocity anomalies following the Alpine arc. The most prominent structure stretches from the western Alps into the Apennines mountain range reaching depths of over 500 km. Two further anomalies of high complexity extending down to a depth of 300 km are located below the central and eastern Alps, both being detached from the lithosphere and separated by a clear gap below the western part of the Tauern window. The central anomaly shows mainly southwards dipping, whereas the eastern anomaly is mainly dipping to the northeast. We compare our results to former studies, confirming lateral positions of the anomalies. However, the new results can benefit from the superior resolution capabilities of the dense AlpArray seismic network, providing more accurate insights into depth extent, dip angle and directions. We perform various general, as well as purpose-built resolution tests, to verify the capabilities of our setup to resolve slab gaps as well as different possible slab dipping directions.</p>

scholarly journals Imaging the Mediterranean upper mantle by p- wave travel time tomography

1997 ◽  
Vol 40 (4) ◽  
Author(s):  
C. Piromallo ◽  
A. Morelli
Keyword(s):  
Travel Time ◽  
Upper Mantle ◽  
Three Dimensional ◽  
Velocity Model ◽  
Structural Heterogeneity ◽  
Linear Interpolation ◽  
P Wave ◽  
Travel Times ◽  
P Waves ◽  
Tectonic Lineament

Travel times of P-waves in the Euro-Mediterranean region show strong and consistent lateral variations, which can be associated to structural heterogeneity in the underlying crust and mantle. We analyze regional and tele- seismic data from the International Seismological Centre data base to construct a three-dimensional velocity model of the upper mantle. We parameterize the model by a 3D grid of nodes -with approximately 50 km spacing -with a linear interpolation law, which constitutes a three-dimensional continuous representation of P-wave velocity. We construct summary travel time residuals between pairs of cells of the Earth's surface, both inside our study area and -with a broader spacing -on the whole globe. We account for lower mantle heterogeneity outside the modeled region by using empirical corrections to teleseismic travel times. The tomo- graphic images show generai agreement with other seismological studies of this area, with apparently higher detail attained in some locations. The signature of past and present lithospheric subduction, connected to Euro- African convergence, is a prominent feature. Active subduction under the Tyrrhenian and Hellenic arcs is clearly imaged as high-velocity bodies spanning the whole upper mantle. A clear variation of the lithospheric structure beneath the Northem and Southern Apennines is observed, with the boundary running in correspon- dence of the Ortona-Roccamonfina tectonic lineament. The western section of the Alps appears to have better developed roots than the eastern, possibly reflecting à difference in past subduction of the Tethyan lithosphere and subsequent continental collision.

Travel Time Prediction Algorithm Scalable to Freeway Networks with Many Nodes with Arbitrary Travel Routes

2005 ◽  
Vol 1935 (1) ◽  
pp. 147-153 ◽  
Author(s):  
Jaimyoung Kwon ◽  
Karl Petty
Keyword(s):  
Regression Model ◽  
Travel Time ◽  
Traditional Approach ◽  
Computational Cost ◽  
Computation Time ◽  
Prediction Algorithm ◽  
Travel Times ◽  
Travel Time Prediction ◽  
Time Prediction ◽  
Freeway Networks

A travel time prediction algorithm scalable to large freeway networks with many nodes with arbitrary travel routes is proposed. Instead of constructing separate predictors for individual routes, it first predicts the whole future space–time field of travel times and then traverses the required subsection of the predicted travel time field to compute the travel time estimate for the requested route. Compared with the traditional approach that offers the same flexibility, the proposed method substantially reduces storage and computation time requirements at the relatively small computational cost at the time of actual prediction. It is first established that travel times computed by traversing travel time fields are compatible with more direct measurements of travel times from a vehicle reidentification technique based on electronic toll collection tags. This provides a conceptual justification of the proposed approach. When applied to the loop data from an 8.7-mi section of the I-80 freeway, the proposed approach with a time-varying coefficient (TVC) linear regression model as the component predictor not only improves the baseline historical travel time predictor substantially, with a 40% to 60% reduction in the prediction error, but also improves the traditional whole-route predictor based on the same TVC regression model by 6% to 9%. The result suggests that the proposed algorithm not only achieves the scalability but also improves prediction accuracy, both of which are critical for successful deployment of the advanced traveler information system for large freeway networks.

The effects of seismic anisotropy on  S-wave travel time-tomography: the problem of apparent anomalies and possible solutions

2021 ◽  
Author(s):  
Francesco Rappisi ◽  
Brandon Paul Vanderbeek ◽  
Manuele Faccenda
Keyword(s):  
Travel Time ◽  
Upper Mantle ◽  
Shear Velocity ◽  
P Wave ◽  
Travel Times ◽  
S Wave ◽  
Velocity Models ◽  
Travel Time Tomography ◽  
Wave Travel ◽  
Wave Tomography

<p>Teleseismic travel-time tomography remains one of the most popular methods for obtaining images of Earth's upper mantle. While teleseismic shear phases, most notably SKS, are commonly used to infer the anisotropic properties of the upper mantle, anisotropic structure is often ignored in the construction of body wave shear velocity models. Numerous researchers have demonstrated that neglecting anisotropy in P-wave tomography can introduce significant imaging artefacts that could lead to spurious interpretations. Less attention has been given to the effect of anisotropy on S-wave tomography partly because, unlike P-waves, there is not a ray-based methodology for modelling S-wave travel-times through anisotropic media. Here we evaluate the effect that the isotropic approximation has on tomographic images of the subsurface when shear waves are affected by realistic mantle anisotropy patterns. We use SPECFEM to model the teleseismic shear wavefield through a geodynamic model of subduction that includes elastic anisotropy predicted from micromechanical models of polymineralic aggregates advected through the simulated flow field. We explore how the chosen coordinates system in which S-wave arrival times are measured (e.g., radial versus transverse) affects the imaging results. In all cases, the isotropic imaging assumption leads to numerous artefacts in the recovered velocity models that could result in misguided inferences regarding mantle dynamics. We find that when S-wave travel-times are measured in the direction of polarisation, the apparent anisotropic shear velocity can be approximated using sinusoidal functions of period pi and two-pi. This observation allows us to use ray-based methods to predict S-wave travel-times through anisotropic models. We show that this parameterisation can be used to invert S-wave travel-times for the orientation and strength of anisotropy in a manner similar to anisotropic P-wave travel-time tomography. In doing so, the magnitude of imaging artefacts in the shear velocity models is greatly reduced.</p>

scholarly journals Exploring Travel Time Distribution and Variability Patterns Using Probe Vehicle Data: Case Study in Beijing

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Peng Chen ◽  
Rui Tong ◽  
Guangquan Lu ◽  
Yunpeng Wang
Keyword(s):  
Travel Time ◽  
Time Distribution ◽  
Goodness Of Fit ◽  
Travel Times ◽  
Unit Distance ◽  
Probe Vehicle ◽  
Vehicle Data ◽  
Travel Time Distribution ◽  
Road Type ◽  
Distance Travel

Exploring travel time distribution and variability patterns is essential for reliable route choices and sophisticated traffic management and control. State-of-the-art studies tend to treat different types of roads equally, which fails to provide more detailed analysis of travel time characteristics for each specific road type. In this study, based on a vast amount of probe vehicle data, 200 links inside the Third Ring Road of Beijing, China, were investigated. Four types of roads were covered including urban expressways, auxiliary roads of urban expressways, major roads, and secondary roads. The day-of-week distributions of unit distance travel time were first analyzed. Kolmogorov-Smirnov test, Anderson-Darling test, and chi-squared test were employed to test the goodness-of-fit of different distributions and the results showed lognormal distribution was best-fitted for different time periods and road types compared with normal, gamma, and Weibull distribution. In addition, four reliability measures, that is, unit distance travel time, coefficient of variation, buffer time index, and punctuality rate, were used to explore the day-of-week travel time variability patterns. The results indicated that urban expressways, auxiliary roads of urban expressways, and major roads have regular and distinct morning and afternoon peaks on weekdays. It is noteworthy that in daytime the travel times on auxiliary roads of urban expressways and major roads share similar variability patterns and appear relatively stable and reliable, while urban expressways have most reliable travel times at night. The results of analysis help enable a better understanding of the volatile travel time characteristics of each road type in urban network.

Characterization of global seismograms using an automatic-picking algorithm

1994 ◽  
Vol 84 (2) ◽  
pp. 366-376
Author(s):  
Paul S. Earle ◽  
Peter M. Shearer
Keyword(s):  
Travel Time ◽  
Upper Mantle ◽  
Low Frequency ◽  
Travel Times ◽  
Comparable Amount ◽  
Arrival Times ◽  
Long Period ◽  
Automatic Phase ◽  
Short Period ◽  
Sample Rate

Abstract An automatic phase picker is useful for quickly identifying and timing phase arrivals in large seismic data bases. We have developed an automatic phase picker that is sensitive to small changes in amplitude and applied it to over 7 yr of global data distributed by the National Earthquake Information Center (NEIC). Our phase-picking algorithm is based on a short-term-average to long-term-average ratio (STA/LTA) taken along an envelope function generated from the seismogram. The algorithm returns arrival times and corresponding pick qualities. The procedure requires few input parameters and is easily adapted to various types of data. We produce global travel-time plots from both high-frequency (20- or 40-Hz sample rate) and low-frequency (1-Hz sample rate) data. These plots clearly image the predominant high- and low-frequency phases in the NEIC data base. Picks made from the long-period seismograms are less precise, but they reveal far more phase arrivals than the short-period picks. A number of phases resulting from reflections and phase conversions at upper mantle discontinuities can be identified in the low-frequency picks; however, a search of the short-period picks for upper mantle discontinuity phases, between P and PP and prior to P′P′, has so far been unsuccessful. In the long-period S and SS picks, we observe a discrepancy in SV and SH travel times, a possible result of upper mantle anisotropy. To check the accuracy and consistency of our algorithm, we present comparisons between hand-picked times and automatic-picked times for identical seismograms. Travel-time residuals from the short-period automatic picks and data reported to the International Seismological Centre (ISC) picks exhibit a comparable amount of scatter. Histograms of the ISC residuals and automatic-pick residuals are similar in shape and width for P and PcP. These observations suggest that human picking errors are not a major contributor to the scatter observed in ISC travel times, although direct comparisons between ISC reported picks and automatic picks on particular seismograms occasionally identify operator mispicks.

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.

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