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.

The Hindu Kush earthquake of March 4, 1949 as recorded in Europe

1964 ◽  
Vol 54 (6A) ◽  
pp. 1915-1925 ◽  
Author(s):  
I. Lehmann
Keyword(s):  
Amplitude Ratio ◽  
Epicentral Distance ◽  
Focal Region ◽  
Travel Times ◽  
Period Range ◽  
Characteristic Appearance ◽  
Hindu Kush ◽  
The Difference ◽  
Deep Focus ◽  
The Many

abstract The European records from distances 36°-50° of the deep Hindu Kush earthquake of March 4, 1949 were studied. The many clearly recorded deep-focus reflections lend to the records a characteristic appearance which is repeated in many other shocks from the same focal region. The ratios of the amplitudes of these phases vary somewhat from one shock to another. In the shock here considered sP and sPP are exceptionally large at most stations; in the Italian stations they are not so large, while pP is a clear phase. pP is not very well defined at most other stations. Most of the 1949 records were from the old type long-period instruments having their highest magnification for periods from about 5 sec to 12 sec. Present day instruments of quite short or of very long proper period while admirable for many purposes do not record waves in this period range very well and therefore do not produce a satisfactory picture of the forerunners of earthquakes. The difference between the records obtained on different instruments is illustrated. It is shown in examples that the amplitude ratio PP:P may differ strongly at the same epicentral distance and also that pP may vary greatly with azimuth. The deficiency of station readings is noted. Travel times and their residuals are tabulated and travel times plotted versus epicentral distances.

scholarly journals Investigation of a sunspot complex by time-distance helioseismology

2010 ◽  
Vol 6 (S273) ◽  
pp. 320-324 ◽  
Author(s):  
A. G. Kosovichev ◽  
T. L. Duvall
Keyword(s):  
Acoustic Waves ◽  
Sound Speed ◽  
Active Regions ◽  
Magnetic Activity ◽  
Depth Range ◽  
Travel Times ◽  
Magnetic Structures ◽  
Flow Maps ◽  
Time Distance ◽  
Deep Focus

AbstractSunspot regions often form complexes of activity that may live for several solar rotations, and represent a major component of the Sun's magnetic activity. It had been suggested that the close appearance of active regions in space and time might be related to common subsurface roots, or “nests” of activity. EUV images show that the active regions are magnetically connected in the corona, but subsurface connections have not been established. We investigate the subsurface structure and dynamics of a large complex of activity, NOAA 10987-10989, observed during the SOHO/MDI Dynamics run in March-April 2008, which was a part of the Whole Heliospheric Interval (WHI) campaign. The active regions in this complex appeared in a narrow latitudinal range, probably representing a subsurface toroidal flux tube. We use the MDI full-disk Dopplergrams to measure perturbations of travel times of acoustic waves traveling to various depths by using time-distance helioseismology, and obtain sound-speed and flow maps by inversion of the travel times. The subsurface flow maps show an interesting dynamics of decaying active regions with persistent shearing flows, which may be important for driving the flaring and CME activity, observed during the WHI campaign. Our analyses, including the seismic sound-speed inversion results and the distribution of deep-focus travel-time anomalies, gave indications of diverging roots of the magnetic structures, as could be expected from Ω-loop structures. However, no clear connection in the depth range of 0-48 Mm among the three active regions in this complex of activity was detected.

The times of origin and depths of focus of intermediate and deep focus earthquakes: Model calculations

1981 ◽  
Vol 71 (5) ◽  
pp. 1539-1552
Author(s):  
A. L. Hales ◽  
K. J. Muirhead ◽  
L. Maki-Lopez
Keyword(s):  
Average Velocity ◽  
Epicentral Distance ◽  
Depth Range ◽  
Depth Of Focus ◽  
P Waves ◽  
Model Calculations ◽  
The Earth ◽  
Deep Focus ◽  
The Times ◽  
Time Of Origin

abstract Two methods for determining the time of origin, depth of focus, and the average velocities from the focus to the surface are described. The first stage in the first method is to determine the time of origin using a modification of the Wadati method. As was pointed out in 1973 by Kisslinger and Engdahl, the relation between (ts − tp and tp is nonlinear and it is necessary to allow for this nonlinearity by including a term in tp2 in the analysis. Thereafter the depth of focus and the average velocity can be found by a modification of the procedure used to determine the depth to a reflector in seismic reflection prospecting. It is necessary to allow for the sphericity of the Earth in this analysis. In the second method, the depth of focus is determined first by analyzing (ts − tp)2 as a function of x2, x being the epicentral distance. The average velocity of separation of S and P waves is also determined at this stage. Thereafter the time of origin and the average P and S velocities are determined. The results of the analysis of the calculated travel times for three models show that systematic errors in the depth of focus using these procedures are less than 2 km over the depth range of 60 to 640 km. Preliminary results of the analysis of a limited set of Japanese earthquakes by these methods give estimates of depth smaller than those given by ISC for depths less than 300 km. For deeper earthquakes, these methods give foci deeper than the ISC, but in these cases the observations close to the epicenter are inadequate for reliable analysis.

scholarly journals Probing sunspots with two-skip time–distance helioseismology

2018 ◽  
Vol 613 ◽  
pp. A73 ◽  
Author(s):  
Thomas L. Duvall ◽  
Paul S. Cally ◽  
Damien Przybylski ◽  
Kaori Nagashima ◽  
Laurent Gizon
Keyword(s):  
Magnetic Field ◽  
Travel Time ◽  
Large Distance ◽  
Ray Theory ◽  
Travel Times ◽  
Sunspot Model ◽  
Modeling Effort ◽  
Time Distance ◽  
The Waves ◽  
The Magnetic Field

Context. Previous helioseismology of sunspots has been sensitive to both the structural and magnetic aspects of sunspot structure. Aims. We aim to develop a technique that is insensitive to the magnetic component so the two aspects can be more readily separated. Methods. We study waves reflected almost vertically from the underside of a sunspot. Time–distance helioseismology was used to measure travel times for the waves. Ray theory and a detailed sunspot model were used to calculate travel times for comparison. Results. It is shown that these large distance waves are insensitive to the magnetic field in the sunspot. The largest travel time differences for any solar phenomena are observed. Conclusions. With sufficient modeling effort, these should lead to better understanding of sunspot structure.

Seismic inversion for the shape of a boundary between two layer stacks

1978 ◽  
Vol 68 (3) ◽  
pp. 599-608 ◽  
Author(s):  
George A. McMechan
Keyword(s):  
Travel Time ◽  
Epicentral Distance ◽  
Seismic Inversion ◽  
Time Constraint ◽  
Travel Times ◽  
Entire Process

abstract A completely geometrical inversion can be performed to determine the shape and position of a boundary between two layer stacks. The constraints are observed epicentral distances, ray parameters, and travel times. The solution is iterative and involves finding all combinations of ray segments that give an observed epicentral distance, and then choosing the correct combination by imposing the travel-time constraint. The entire process can be performed by manipulation of areas in the p-Δ plane.

scholarly journals Teleseismic P waves at the AlpArray seismic network: wave fronts, absolute travel times and travel-time residuals

Solid Earth ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 1635-1660
Author(s):  
Marcel Paffrath ◽  
Wolfgang Friederich ◽  
Keyword(s):  
Travel Time ◽  
Cross Correlation ◽  
Field Experiments ◽  
Epicentral Distance ◽  
Seismic Network ◽  
Corner Frequency ◽  
Travel Times ◽  
Wave Fronts ◽  
P Waves ◽  
Waveform Cross Correlation

Abstract. We present an extensive dataset of highly accurate absolute travel times and travel-time residuals of teleseismic P waves recorded by the AlpArray Seismic Network and complementary field experiments in the years from 2015 to 2019. The dataset is intended to serve as the basis for teleseismic travel-time tomography of the upper mantle below the greater Alpine region. In addition, the data may be used as constraints in full-waveform inversion of AlpArray recordings. The dataset comprises about 170 000 onsets derived from records filtered to an upper-corner frequency of 0.5 Hz and 214 000 onsets from records filtered to an upper-corner frequency of 0.1 Hz. The high accuracy of absolute and residual travel times was obtained by applying a specially designed combination of automatic picking, waveform cross-correlation and beamforming. Taking travel-time data for individual events, we are able to visualise in detail the wave fronts of teleseismic P waves as they propagate across AlpArray. Variations of distances between isochrons indicate structural perturbations in the mantle below. Travel-time residuals for individual events exhibit spatially coherent patterns that prove to be stable if events of similar epicentral distance and azimuth are considered. When residuals for all available events are stacked, conspicuous areas of negative residuals emerge that indicate the lateral location of subducting slabs beneath the Apennines and the western, central and eastern Alps. Stacking residuals for events from 90∘ wide azimuthal sectors results in lateral distributions of negative and positive residuals that are generally consistent but differ in detail due to the differing direction of illumination of mantle structures by the incident P waves. Uncertainties of travel-time residuals are estimated from the peak width of the cross-correlation function and its maximum value. The median uncertainty is 0.15 s at 0.5 Hz and 0.18 s at 0.1 Hz, which is more than 10 times lower than the typical travel-time residuals of up to ±2 s. Uncertainties display a regional dependence caused by quality differences between temporary and permanent stations as well as site-specific noise conditions.

scholarly journals Longitudinal waves through the Earth's Core*

1952 ◽  
Vol 42 (2) ◽  
pp. 119-134
Author(s):  
M. E. Denson
Keyword(s):  
Velocity Distribution ◽  
Travel Time ◽  
Focal Point ◽  
Epicentral Distance ◽  
Outer Core ◽  
Travel Times ◽  
Time Curve ◽  
Longitudinal Waves ◽  
The Core ◽  
The Waves

Abstract Amplitudes, periods, and travel times of the longitudinal P′ or PKP core waves have been investigated. Results indicate that the epicentral distance of the main focal point and the travel time of P′ phases vary with the periods of the waves. This variation would seem reasonably explained in terms of dispersion. The point of reversal in the travel-time curve of the waves through the outer core is believed to lie near 157°. Data suggest a discontinuity between 120° and 125° rather than 110°. Anomalies existing in energy, period, and travel-time relationships of the P′ phases indicate that current concepts of velocity distribution and of propagation paths within the core are in need of modification.

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.

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