Traveltime Computation Research Articles

Efficient approach to computing travel time with the parabolic equation model

An efficient method for computing the travel time of an acoustic wave using the parabolic equation model is presented. The frequency derivative of the acoustic phase is the differential travel time associated with a propagation in range. By taking this difference across closely spaced frequencies this method computes the acoustic travel time. This method requires the computation of the field at two frequencies rather than over the full band. The method compares well with other travel time methods for four different cases, including deep water, upslope and shallow water, and a three-dimensional propagation environment.

APLIKASI DOUBLE DIFFERENCE UNTUK IDENTIFIKASI ZONA PATAHAN MIKRO WILAYAH SULAWESI BARAT

West Sulawesi is an area in South Sulawesi province that is experiencing a sudden increase in seismic activity. There have been 264 earthquake events recorded during the 2021-2022 period. The increase in seismic activity occurred around the west Sulawesi segment and the Mamuju segment, which are local faults located in west Sulawesi. Sulawesi Island itself is the result of fragments due to larger complex reactions and has quite high seismic activity. Therefore, it is necessary to calculate the earthquake hypocenter relocation to obtain more accurate hypocenter parameters for fault zone identification and micro fault orientation. This study aims to relocate the earthquake hypocenter based on mathematical measurement data using the Double-Difference method for identification of fault zones and micro-fault orientation. The data used is BMKG earthquake catalog data for the western Sulawesi region with a range of 118.49 East - 119.59 East and 3.67 LS -2.45 LS in the 2021-2022 period. The Double-Difference method is a method based on the Geiger method using residual travel time data from each pair of hypocenters to the earthquake recording station. The principle is to compare two earthquake hypocenters that are close to the earthquake recording station with the assumption that the distance between the two hypocenters must be closer than the distance between the hypocenter and the earthquake recording station. This is done so that the raypath of the two hypocenters can be considered close to the same value. From the calculation of the earthquake hypocenter relocation, it was found that the hypocenter after relocation experienced changes in distribution that accumulated in the Mamasa fault segment area. From the residual histogram, it is found that the RMS residual is close to 0, indicating an improvement in data quality as evidenced by the observation travel time and the calculated travel time are almost close to the same value. In the cross-section results, it is obtained that the depth changes vary in the subsurface depth from the initial depth of 10 km before being relocated, indicating that the earthquake that occurred in West Sulawesi was included in the shallow crustal earthquake type.

Using the Exact Equivalent π-Circuit Model for Representing Three-Phase Transmission Lines Directly in the Time Domain

This paper presents a novel three-phase transmission line model for electromagnetic transient simulations that are executed directly within the time domain. This model relies on distributed and frequency-dependent parameters, as well as employs modal transformation for its implementation. The single-phase model of the exact equivalent π-circuit is utilized for each propagation mode. This model combines discrete components, such as resistors, inductors, and capacitors, to accurately emulate the transmission line behavior via linear circuit elements. This model can be seamlessly integrated into various electrical circuit simulation software, thus allowing easy utilization and incorporating time-varying elements to analyze transmission lines. The JMarti model, which comes by default in the Alternative Transient Program, and the numerical Laplace transform method implemented in MATLAB were utilized to validate the proposed solution across various scenarios. An advantage of this model is its independence from the prior calculation of travel time and its exemption from convolutions, inverse Laplace transforms, and Fourier transforms, thus streamlining the simulation process.

Toward assimilation of acoustic travel times into an ocean state estimate

Direct ocean observing systems are a scarce set of data that build the backbone for understanding the current state of the ocean. These systems are limited in areas of high variability in temperature and salinity. Pioneering work of Wunsch (1977) proposed efforts to extract detailed hydrographic information using sound propagation through the ocean, providing the scaffolding to improve our understanding of the ocean's interior. The integrated nature of such measurements makes acoustic thermometry a powerful application for monitoring regional to basin-averaged hydrographic changes in the ocean, a measurement that is difficult to achieve by individual “point” measurements (moorings, ship-borne CTD casts, or autonomous floats) alone. This work models acoustic travel times corresponding to eigenrays between a fixed source and receiver from an evolving ocean state. Inclusive computation of acoustic travel times within a dynamically evolving modeled ocean state provide a novel approach to model data comparison within a general ocean circulation model. An adjoint assimilation framework combines observations with numerical models to estimate and update oceanic state variables Forget et al. (2015). This process provides the necessary operators for model data comparison of ocean acoustic observable quantities within a consistent state estimation framework allowing for data assimilation from acoustic tomography measurements.

Efficient parabolic equation based travel time computation

In this paper an efficient method for computing the travel time of an acoustic wave as a function of range using the parabolic equation model. The frequency derivative of the acoustic phase is the differential travel time associated with a propagation in range. By taking this difference across closely spaced frequencies (0.02 f0) and integrating in range, this method computes the travel time of the dominant acoustic arrival. The method compares well with other travel time methods for four different cases, including deep water (shallow source, axial source), upslope and shallow water, and a global 3D propagation environment.

Travel times and ray paths for acoustic and elastic waves in generally anisotropic media

Wavefield travel time tomography is used for a variety of purposes in acoustics, geophysics and non-destructive testing. Since the problem is non-linear, assessing uncertainty in the results requires many forward evaluations. It is therefore important that the forward evaluation of travel times and ray paths is efficient, which is challenging in generally anisotropic media. Given a computed travel time field, ray tracing can be performed to obtain the fastest ray path from any point in the medium to the source of the travel time field. These rays can then be used to speed up gradient based inversion methods. We present a forward modeller for calculating travel time fields by localised estimation of wavefronts, and a novel approach to ray tracing through those travel time fields. These methods have been tested in a complex anisotropic weld and give travel times comparable to those obtained using finite element modelling while being computationally cheaper.

An adaptive finite-difference method for seismic traveltime modeling based on 3D eikonal equation

3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing, source localization, reflection migration, seismic monitoring and tomographic imaging. In recent years, many advanced methods have been developed to solve the 3D eikonal equation in heterogeneous media. However, there are still challenges for the stable and accurate calculation of first-arrival traveltimes in 3D strongly inhomogeneous media. In this paper, we propose an adaptive finite-difference (AFD) method to numerically solve the 3D eikonal equation. The novel method makes full use of the advantages of different local operators characterizing different seismic wave types to calculate factors and traveltimes, and then the most accurate factor and traveltime are adaptively selected for the convergent updating based on the Fermat principle. Combined with global fast sweeping describing seismic waves propagating along eight directions in 3D media, our novel method can achieve the robust calculation of first-arrival traveltimes with high precision at grid points either near source point or far away from source point even in a velocity model with large and sharp contrasts. Several numerical examples show the good performance of the AFD method, which will be beneficial to many scientific applications.

Estimating pedestrian traffic with Bluetooth sensor technology

ABSTRACT The increasing availability of ubiquitous sensor data on the built environment holds great potential for a new generation of travel and mobility research. Bluetooth technology, for example, is already vastly used in vehicular transportation management solutions and services. Current studies discuss the potential of this emerging technology for pedestrian mobility research, but it has yet to be examined in a large urban setting. One of the main problems is detecting pedestrians from Bluetooth records since their behavior and movement patterns share similarities with other urban transportation modes. This study aims to accurately detect pedestrians using a network of 65 Bluetooth detectors located in Tel-Aviv, Israel, which record on average over 60,000 unique daily Bluetooth Media-Access-Control addresses. We propose a detection methodology that includes system calibration, effective travel time calculation, and classification by velocity that takes into consideration the probability of vehicular traffic jams. An evaluation of the proposed methodology presents a promising pedestrian detection accuracy rate of 89%. We showcase the results of pedestrian traffic analysis, together with a discussion on the data analysis challenges and limitations. To the best of our knowledge, this work is the first to analyze pedestrian records detection from a Bluetooth network employed in a dynamic urban environment setting.

A COMPARATIVE STUDY OF METHODS FOR DRIVE TIME ESTIMATION ON GEOSPATIAL BIG DATA: A CASE STUDY IN USA

Abstract. Travel time estimation is crucial for several geospatial research studies, particularly healthcare accessibility studies. This paper presents a comparative study of six methods for drive time estimation on geospatial big data in the USA. The comparison is done with respect to the cost, accuracy, and scalability of these methods. The six methods examined are Google Maps API, Bing Maps API, Esri Routing Web Service, ArcGIS Pro Desktop, OpenStreetMap NetworkX (OSMnx), and Open Source Routing Machine (OSRM). Our case study involves calculating driving times of 10,000 origin-destination (OD) pairs between ZIP code population centroids and pediatric hospitals in the USA. We found that OSRM provides a low-cost, accurate, and efficient solution for calculating travel time on geospatial big data. Our study provides valuable insight into selecting the most appropriate drive time estimation method and is a benchmark for comparing the six different methods. Our open-source scripts are published on GitHub (https://github.com/wybert/Comparative-Study-of-Methods-for-Drive-Time-Estimation) to facilitate further usage and research by the wider academic community.

Inland Vessel Travel Time Prediction via a Context-Aware Deep Learning Model

Accurate vessel travel time estimation is crucial for optimizing port operations and ensuring port safety. Existing vessel travel time prediction models primarily rely on path-finding algorithms and corresponding distance/speed relationships to calculate travel time. However, these models overlook the complex nature of vessel travel time, which is influenced by multiple traffic-related factors such as collision avoidance, shortest path selection, and vessel personnel performance. The lack of consideration for these specific aspects limits the accuracy and applicability of current models. We propose a novel context-aware deep learning approach for inland vessel travel time prediction. Firstly, we introduce a complex network that captures vessel–vessel interaction contexts, providing valuable traffic environment information as an input for the deep learning model. Additionally, we employ a convolutional neural network to extract spatial trajectory information, which is then integrated with interaction contexts and indirect context information. In the vessel travel time prediction procedure, we utilize a long short-term memory network to capture the temporal dependence within consecutive channel sections’ fused multiple context feature sets. Extensive experiments incorporating historical data from the Wuhan section of the Yangtze River in China demonstrate the superiority of our proposed model over classical models in predicting vessel travel time. Importantly, our model accounts for the specific traffic contexts that had previously been overlooked, leading to improved accuracy and applicability in inland vessel travel time prediction.

Pyekfmm: A Python Package for 3D Fast-Marching-Based Travel-Time Calculation and its Applications in Seismology

Abstract We present a multifunctional open-source package—pyekfmm for eikonal-based travel-time calculation in 2D and 3D heterogeneous anisotropic media based on the well-documented fast marching method. Different from existing travel-time calculation packages, the pyekfmm package offers a seamless compilation of the backbone C programs in the Python environment through a state-of-the-art pip installation. As a result, the users can use the pyekfmm package for different scientific purposes with the convenience enabled by Python interfaces and with the efficiency offered by C programs. The pyekfmm package offers the option of travel-time calculation to second-order accuracy. More importantly, the pyekfmm provides the option for travel-time calculation in anisotropic media, which enables its exclusive applications in special cases in which strong anisotropy exists. We introduce the mathematical principles and the structure of the package in detail. To demonstrate its potential, we apply it to a wide spectrum of applications, including travel-time calculation in different situations with increasing complexities, ray tracing, earthquake source location, relocation, and surface-wave tomography.

A neural network based global traveltime function (GlobeNN)

Global traveltime modeling is an essential component of modern seismological studies with a whole gamut of applications ranging from earthquake source localization to seismic velocity inversion. Emerging acquisition technologies like distributed acoustic sensing (DAS) promise a new era of seismological discovery by allowing a high-density of seismic observations. Conventional traveltime computation algorithms are unable to handle virtually millions of receivers made available by DAS arrays. Therefore, we develop GlobeNN—a neural network based traveltime function that can provide seismic traveltimes obtained from the cached realistic 3-D Earth model. We train a neural network to estimate the traveltime between any two points in the global mantle Earth model by imposing the validity of the eikonal equation through the loss function. The traveltime gradients in the loss function are computed efficiently using automatic differentiation, while the P-wave velocity is obtained from the vertically polarized P-wave velocity of the GLAD-M25 model. The network is trained using a random selection of source and receiver pairs from within the computational domain. Once trained, the neural network produces traveltimes rapidly at the global scale through a single evaluation of the network. As a byproduct of the training process, we obtain a neural network that learns the underlying velocity model and, therefore, can be used as an efficient storage mechanism for the huge 3-D Earth velocity model. These exciting features make our proposed neural network based global traveltime computation method an indispensable tool for the next generation of seismological advances.

T* Revise Attenuation Tomography for Q Estimation

Seismic attenuation is often calculated by attenuated travel time tomography. The accuracy of this method is controlled by the precision of attenuated travel time. In this paper, a novel T* revise in attenuated travel time tomography method for Q inversion was developed. The attenuated travel time was calculated from seismic data by using a logarithmic spectral ratio inversion strategy. In the inversion process, multiple offset traces were used for multiple attenuated travel time calculations. The proposed method produced more accurate results compared to those of the conventional approach without the requirement of choosing an optimistic frequency band. The accuracy of the proposed method was improved by avoiding the effect of overburden. Both synthetic and real data examples prove the viability and effectiveness of the proposed method.

A Three-Stage model for Clustering, Storage, and joint online order batching and picker routing Problems: Heuristic algorithms

The online shopping center is an electronic commerce where customer orders arrive over time. The joint online order batching and picker routing is essential for managing online shopping, as it allows for the retrieval of products from storage locations as order arrival timings become known. Meanwhile, the picker routing performance is substantially affected by the product allocation to storage locations, whereas the success of the storage assignment depends on the product grouping. In order to handle such a system, this study offers a novel three-stage model, the first stage of which aims to classify products according to various available capacity levels to maximize similarity measures among products. The second stage determines the assignments of the obtained classes to carriers and storage locations in a multi-block 3D warehouse to minimize the total transportation costs and the energy costs of carriers. The third stage provides a joint online order batching and picker routing model in a picker-to-parts system to minimize completion time in the 3D warehouse. Since learning effects affect the search and pick times, and pickers’ horizontal and vertical velocities are dissimilar, these crucial factors are considered for calculating travel time of pickers. In addition, two efficient heuristic algorithms are proposed to solve the developed models in the first two stages, and an effective online 2-competitive heuristic algorithm is developed to solve the proposed model in the third stage. Moreover, a broad range of numerical experiments illustrates the validity and applicability of the proposed models and solution approaches. What is more, a competitive analysis evaluates the effectiveness of the proposed online heuristic algorithm. The results reveal that the developed hierarchical framework can provide high-quality solutions in a reasonable time and reduce the total cost and makespan by 35.65% and 12.48% on average, respectively.

A Framework to Elaborate on the Requirements for Electrified Commuter and Regional Aircraft

With increasing capabilities of electric motors and energy storage, aircraft designs for electrified commuter and regional aircraft become more relevant than ever. Design concepts are often derived and optimised according to existing, conventional reference aircraft; however, their characteristics differ and the underlying trade-offs are divergent. This work aims to derive and describe major external requirements for the design of proposed commuter and regional aircraft system. Therefore, a travel time benefit analysis was conducted that considered the European NUTS-3 regions, as well as the concentration of population. Total travel times for individual road, high-speed rail, commuter air services, and traditional airline services were compared. Travel time calculations were based mostly on third-party road and railway APIs, whereas airline services were based on air traffic management data. The data show a concentration of potential commuter connections on distances between 200 and 950 km. The majority of these connections are currently operated on airline flights, which involve extraordinarily long first/last mile transportation. The majority of regions are already well covered with airfields offering sufficient runway length; however, air traffic capacities and apron space could become major bottlenecks when considering a possible shift from airline to decentral commuter air services.

Berlin Pankow: a 15-min city for everyone? A case study combining accessibility, traffic noise, air pollution, and socio-structural data

Cars are dominating urban traffic in cities around the world, even though daily trips in many cities are often realized with active modes of transportation or public transport. Urban transport planning processes need to adapt to this reality and the necessity of climate change mitigation. Against this background, the research project “Mobility Reporting”, a joint undertaking of the district Pankow in Berlin and researchers from TU Berlin and TU Dresden, established a new, goal-driven, and participative planning process. The process identified local mobility as one of the central planning goals. The 15-min city (FMC) was thus adduced as a benchmark to analyze the district’s current mobility system and development potential. We conducted extensive accessibility analyses to examine the status quo concerning the FMC. We calculated travel times to essential destinations in daily life by foot, public transport, and car. This analysis was accompanied by a mixed online and paper–pencil survey conducted to evaluate the perceived accessibility of people in Pankow. The survey results shed light on the question of which walking time thresholds constitute a “very good” or “good” accessibility. Further analyses included environmental and social variables, allowing us to check whether areas with different accessibility levels also differ regarding the socio-economic characteristics of their inhabitants. For example, do socially advantaged neighborhoods have better local accessibility? Is there a trade-off between exposure to environmental pollution and good accessibility? With this contribution, we shed light on what an FMC is and ought to be. Results from the survey support the normative and political vision of the FMC. Pankow generally offers the merits of a walkable city, showing the expected travel time differences between the dense inner city and the outskirts. Socially disadvantaged neighborhoods are not consistently less accessible. However, there seems to be a trade-off between good accessibility (especially PT accessibility) and correlated externalities of transport, namely air pollution and noise.

A topography-dependent eikonal solver for accurate and efficient computation of traveltimes and their derivatives in 3D heterogeneous media

Accurate and efficient computation of traveltimes and their spatial derivatives for 3D heterogeneous media is essential in many areas of seismology, such as traveltime/slope tomography and quantitative migration. A popular method of obtaining this information is to solve the eikonal equation using a finite-difference (FD) scheme. However, the complex surface of the earth causes numerical complications when applying FD methods based on rectangular grids. To overcome the challenge of taking into account topographic effects, we make use of the 3D topography-dependent eikonal equation (TDEE) which is a 3D surface-flattening scheme that uses curvilinear grids to transform irregular surfaces in the physical domain into regular surfaces in the computational domain. Unfortunately, solving the TDEE in three dimensions starting from the initial point-source condition needs to get around the point-source singularity. Therefore, we formulate the 3D factored TDEE (FTDEE) according to a factorization principle. Furthermore, to numerically solve the 3D original TDEE, as well as the FTDEE, we apply a lock sweeping method, which avoids the problem of repetitive computation when using the fast sweeping method. Several numerical examples demonstrate the efficiency of the new lock scheme in terms of computation time and accuracy of the 3D FTDEE solver for the calculation of traveltimes and their derivatives. This scheme provides a good choice for the calculation of traveltimes and their spatial derivatives using models with irregular surfaces, which means greater potential for seismic data processing under conditions of complex topography.

Abstract P135: Travel Time to Specialty Care and Risk of Death for Children With CHD

Introduction: Children with congenital heart disease (CHD) typically require care from a multi-disciplinary team of providers and treatment at specialized care centers. Although access to specialty care is known to influence patient outcomes, little is known regarding geographic access to care for children with congenital heart disease. This study calculated travel time to specialized care centers and the relationship with mortality for children residing in Colorado. Methods: We analyzed all payer claims data (APCD) from Colorado (CO) from 2012-2019. Travel times were calculated using a network analysis of the road distance weighted by travel speeds from the geographic centroid of every ZIP code in CO to that of the actual specialized care center. Specialty care centers were uniquely identified by their National Provider ID (NPI) and defined by categorizations from the American Medical Association (AMA). Mortality was defined by discharge status. Results: There were 27,344 children with CHD who received specialized care in the study period, accounting for 437,071 total encounters. Of the children with CHD, there were 355 deaths. Children that died had an average of 98 visits per year, while children that survived had an average of 70 visits (p=<0.001). Among the children who lived, 62.8% of their total specialty care visits were <30 minutes away, compared to 59.7% among those who died. CHD who died had a consistently higher proportion of visits that required greater travel to care. Conclusion: Specialized care centers are often located in urban areas and treat patients from diverse geographic areas. There is significant travel burden for children with CHD.

Acesulfame allows the tracing of multiple sources of wastewater and riverbank filtration

Aquifers providing drinking water are increasingly threatened by emerging contaminants due to wastewater inputs from multiple sources. These inputs have to be identified, differentiated, and characterized to allow an accurate risk assessment and thus ensure the safety of drinking water through appropriate management. We hypothesize, that in climates with seasonal temperature variations, the sweetener acesulfame potassium (ACE) provides new pathways to study wastewater inputs to aquifers. Specifically, this study investigates the temperature-driven seasonal oscillation of ACE to assess multiple sources of wastewater inputs at a riverbank filtration site. ACE concentrations in the river water varied from 0.2 to 1 μg L−1 in the cold season (T < 10 °C) to 0–0.1 μg L−1 in the warm season (T > 10 °C), due to temperature-dependent biodegradation during wastewater treatment. This oscillating signal could be traced throughout the aquifer over distances up to 3250 m from two different infiltration sources. A transient numerical model of groundwater flow and ACE transport was calibrated over hydraulic heads and ACE concentrations, allowing the accurate calculation of mixing ratios, travel times, and flow-path directions for each of the two infiltration sources. The calculated travel time from the distant infiltration source was of 67 days, while that from the near source was of 20 days. The difference in travel times leads to different potential degradation of contaminants flowing into the aquifer from the river, thus demonstrating the importance of individually assessing the locations of riverbank infiltration. The calibrated ACE transport model allowed calculating transient mixing ratios, which confirmed the impact of river stage and groundwater levels on the mixing ratio of the original groundwater and the bank filtrate. Therefore, continuous monitoring of ACE concentrations can help to optimize the management of the water works with the aim to avoid collection of water with very short travel times, which has important regulative aspects. Our findings demonstrate the suitability of ACE as a transient tracer for identifying multiple sources of wastewater, including riverbank filtration sites affected by wastewater treatment plant effluents. ACE seasonal oscillation tracking thus provides a new tool to be used in climates with pronounced seasonal temperature variations to assess the origins of contamination in aquifers, with time and cost advantages over multi-tracer approaches.

Timely Access to Essential Surgery, Surgical Workforce, and Surgical Volume: Global Surgery Indicators in Mexico.

The Lancet Commission on Global Surgery seeks to improve surgical care outcomes and equity for the world population through 6 indicators outlined in its 2030 Global Surgery Report. Our study aimed to estimate the percentage of the Mexican population with access to surgical care within the 2-hour distance range (indicator 1), the surgical workforce density (indicator 2), and the number of surgical procedures performed per 100,000 inhabitants (indicator 3) during the year 2020. Knowing these indicators can help to design and implement policies to increase surgical care access coverage and equity in our country. Data related to population distribution, local referral hospitals, and surgical volume were obtained from the 2020 Mexican National Census. Information relating to hospital characteristics and surgical specialists was collected from the Secretariat of Health's public records. We calculated travel time between health care facilities and municipalities using the TrueWay Matrix API and R Studio. Taking into consideration the health care system affiliation, the proportion of the Mexican population with timely access to essential surgery was 81.7%, with 29.3 specialists per 100,000 inhabitants and 726.9 annual procedures performed per 100,000 inhabitants. We identified clusters of municipalities where a low proportion of the population has timely access to essential surgery. These findings illustrate that changes in Mexican policy are required to facilitate more equitable and timely access to essential surgical care among the population.