Travel-time Sensitivity Research Articles

Analysis of the Effects of Connected–Automated Vehicle Technologies on Travel Demand

Connected–automated vehicle (CAV) technologies are likely to have significant effects not only on how vehicles operate in the transportation system, but also on how individuals behave and use their vehicles. While many CAV technologies—such as connected adaptive cruise control and ecosignals—have the potential to increase network throughput and efficiency, many of these same technologies have a secondary effect of reducing driver burden, which can drive changes in travel behavior. Such changes in travel behavior—in effect, lowering the cost of driving—have the potential to increase greatly the utilization of the transportation system with concurrent negative externalities, such as congestion, energy use, and emissions, working against the positive effects on the transportation system resulting from increased capacity. To date, few studies have analyzed the potential effects on CAV technologies from a systems perspective; studies often focus on gains and losses to an individual vehicle, at a single intersection, or along a corridor. However, travel demand and traffic flow constitute a complex, adaptive, nonlinear system. Therefore, in this study, an advanced transportation systems simulation model—POLARIS—was used. POLARIS includes cosimulation of travel behavior and traffic flow to study the potential effects of several CAV technologies at the regional level. Various technology penetration levels and changes in travel time sensitivity have been analyzed to determine a potential range of effects on vehicle miles traveled from various CAV technologies.

Research Note: The sensitivity of surface seismic P‐wave data in transversely isotropic media to reflector depth

ABSTRACTThe leading component of the high‐frequency asymptotic description of the wavefield, given by the travel time, is governed by the eikonal equation. In anisotropic media, traveltime measurements from seismic experiments conducted along one surface cannot constrain the long‐wavelength attribute of the medium along the orthogonal‐to‐the‐surface direction, as anisotropy introduces an independent parameter controlling wave propagation in the orthogonal direction. Since travel times measured on the Earth's surface in transversely isotropic media with a vertical symmetry axis are mainly insensitive to the absolute value of the anisotropic parameter responsible for relating these observations to depth δ, the travel time was perturbed laterally to investigate the traveltime sensitivity to lateral variations in δ. This formulation can be used to develop inversion strategies for lateral variations in δ in acoustic transversely isotropic media, as the surface‐recorded data are sensitive to it even if the model is described by the normal moveout velocity and horizontal velocity, or the anellipticity parameter η. Numerical tests demonstrate the enhanced sensitivity of our data when the model is parameterised with a lateral change in δ.

Scanning anisotropy parameters in horizontal transversely isotropic media

ABSTRACTThe horizontal transversely isotropic model, with arbitrary symmetry axis orientation, is the simplest effective representative that explains the azimuthal behaviour of seismic data. Estimating the anisotropy parameters of this model is important in reservoir characterisation, specifically in terms of fracture delineation. We propose a travel‐time‐based approach to estimate the anellipticity parameter η and the symmetry axis azimuth ϕ of a horizontal transversely isotropic medium, given an inhomogeneous elliptic background model (which might be obtained from velocity analysis and well velocities). This is accomplished through a Taylor's series expansion of the travel‐time solution (of the eikonal equation) as a function of parameter η and azimuth angle ϕ. The accuracy of the travel time expansion is enhanced by the use of Shanks transform. This results in an accurate approximation of the solution of the non‐linear eikonal equation and provides a mechanism to scan simultaneously for the best fitting effective parameters η and ϕ, without the need for repetitive modelling of travel times. The analysis of the travel time sensitivity to parameters η and ϕ reveals that travel times are more sensitive to η than to the symmetry axis azimuth ϕ. Thus, η is better constrained from travel times than the azimuth. Moreover, the two‐parameter scan in the homogeneous case shows that errors in the background model affect the estimation of η and ϕ differently. While a gradual increase in errors in the background model leads to increasing errors in η, inaccuracies in ϕ, on the other hand, depend on the background model errors. We also propose a layer‐stripping method valid for a stack of arbitrary oriented symmetry axis horizontal transversely isotropic layers to convert the effective parameters to the interval layer values.

Analysis of the traveltime sensitivity kernels for an acoustic transversely isotropic medium with a vertical axis of symmetry

ABSTRACTIn anisotropic media, several parameters govern the propagation of the compressional waves. To correctly invert surface recorded seismic data in anisotropic media, a multi‐parameter inversion is required. However, a tradeoff between parameters exists because several models can explain the same dataset. To understand these tradeoffs, diffraction/reflection and transmission‐type sensitivity‐kernels analyses are carried out. Such analyses can help us to choose the appropriate parameterization for inversion. In tomography, the sensitivity kernels represent the effect of a parameter along the wave path between a source and a receiver. At a given illumination angle, similarities between sensitivity kernels highlight the tradeoff between the parameters. To discuss the parameterization choice in the context of finite‐frequency tomography, we compute the sensitivity kernels of the instantaneous traveltimes derived from the seismic data traces. We consider the transmission case with no encounter of an interface between a source and a receiver; with surface seismic data, this corresponds to a diving wave path. We also consider the diffraction/reflection case when the wave path is formed by two parts: one from the source to a sub‐surface point and the other from the sub‐surface point to the receiver. We illustrate the different parameter sensitivities for an acoustic transversely isotropic medium with a vertical axis of symmetry. The sensitivity kernels depend on the parameterization choice. By comparing different parameterizations, we explain why the parameterization with the normal moveout velocity, the anellipitic parameter η, and the δ parameter is attractive when we invert diving and reflected events recorded in an active surface seismic experiment.

Interpretation of Helioseismic Travel Times

Time-distance helioseismology uses cross-covariances of wave motions on the solar surface to determine the travel times of wave packets moving from one surface location to another. We review the methodology to interpret travel-time measurements in terms of small, localized perturbations to a horizontally homogeneous reference solar model. Using the first Born approximation, we derive and compute 3D travel-time sensitivity (Fr\'echet) kernels for perturbations in sound-speed, density, pressure, and vector flows. While kernels for sound speed and flows had been computed previously, here we extend the calculation to kernels for density and pressure, hence providing a complete description of the effects of solar dynamics and structure on travel times. We treat three thermodynamic quantities as independent and do not assume hydrostatic equilibrium. We present a convenient approach to computing damped Green's functions using a normal-mode summation. The Green's function must be computed on a wavenumber grid that has sufficient resolution to resolve the longest lived modes. The typical kernel calculations used in this paper are computer intensive and require on the order of 600 CPU hours per kernel. Kernels are validated by computing the travel-time perturbation that results from horizontally-invariant perturbations using two independent approaches. At fixed sound-speed, the density and pressure kernels are approximately related through a negative multiplicative factor, therefore implying that perturbations in density and pressure are difficult to disentangle. Mean travel-times are not only sensitive to sound-speed, density and pressure perturbations, but also to flows, especially vertical flows. Accurate sensitivity kernels are needed to interpret complex flow patterns such as convection.

Wave-equation-based travel-time seismic tomography – Part 1: Method

Abstract. In this paper, we propose a wave-equation-based travel-time seismic tomography method with a detailed description of its step-by-step process. First, a linear relationship between the travel-time residual Δt = Tobs–Tsyn and the relative velocity perturbation δ c(x)/c(x) connected by a finite-frequency travel-time sensitivity kernel K(x) is theoretically derived using the adjoint method. To accurately calculate the travel-time residual Δt, two automatic arrival-time picking techniques including the envelop energy ratio method and the combined ray and cross-correlation method are then developed to compute the arrival times Tsyn for synthetic seismograms. The arrival times Tobs of observed seismograms are usually determined by manual hand picking in real applications. Travel-time sensitivity kernel K(x) is constructed by convolving a~forward wavefield u(t,x) with an adjoint wavefield q(t,x). The calculations of synthetic seismograms and sensitivity kernels rely on forward modeling. To make it computationally feasible for tomographic problems involving a large number of seismic records, the forward problem is solved in the two-dimensional (2-D) vertical plane passing through the source and the receiver by a high-order central difference method. The final model is parameterized on 3-D regular grid (inversion) nodes with variable spacings, while model values on each 2-D forward modeling node are linearly interpolated by the values at its eight surrounding 3-D inversion grid nodes. Finally, the tomographic inverse problem is formulated as a regularized optimization problem, which can be iteratively solved by either the LSQR solver or a~nonlinear conjugate-gradient method. To provide some insights into future 3-D tomographic inversions, Fréchet kernels for different seismic phases are also demonstrated in this study.

Identification of factors influencing bicycling in small sized cities: A case study of Kharagpur, India

With increasing concern about global warming, greenhouse gas emissions and rising fuel prices, non-motorized modes, such as bicycle are gaining importance as viable mode in urban transportation worldwide. In small sized Indian cities non-motorized transportation accounts for over two thirds of all trips, but with increase in purchasing power and affordability, Indian commuters are leaning towards motorized private modes leading to a rapid growth in motorized vehicle population and thus increasingly congested roadways and urban air pollution. At this juncture it is very important to investigate that what influences people's mode choice in general and bicycle mode choice in particular.This study has identified specific attitudinal attributes related to Physical factors, Psychological factors, Travel Time sensitivity, Economic aspects, Congestion, Parking, Route or Link level facilities, Route topography, Safety related factors, Security related factor, Environmental awareness and Weather related factors. A travel behavior survey with questionnaire designed to address these attributes was conducted to understand user's attitude toward bicycling in a small Indian city. The survey outcomes were then used in exploratory factor analysis (EFA), which revealed Perceived Benefits, Physical Barriers, Safety Hazards, Social Barriers, and Road Condition to be the major factor classes influencing bicycle mode choice.In order to compare user perception with expert perception, a pair-wise comparison using analytical hierarchy process (AHP) has also been performed on factors related to user-specific, route-related and journey-related components. The results reveal physical factors, safety related concerns and route topography to be the key and common set of parameters influencing bicycle choice both from the user's and as well as expert's point of view.

Using a numerical model to understand the connection between the ocean and acoustic travel-time measurements

Measurements of acoustic ray travel-times in the ocean provide synoptic integrals of the ocean state between source and receiver. It is known that the ray travel-time is sensitive to variations in the ocean at the transmission time, but the sensitivity of the travel-time to spatial variations in the ocean prior to the acoustic transmission have not been quantified. This study examines the sensitivity of ray travel-time to the temporally and spatially evolving ocean state in the Philippine Sea using the adjoint of a numerical model. A one year series of five day backward integrations of the adjoint model quantify the sensitivity of travel-times to varying dynamics that can alter the travel-time of a 611 km ray by 200 ms. The early evolution of the sensitivities reveals high-mode internal waves that dissipate quickly, leaving the lowest three modes, providing a connection to variations in the internal tide generation prior to the sample time. They are also strongly sensitive to advective effects that alter density along the ray path. These sensitivities reveal how travel-time measurements are affected by both nearby and distant waters. Temporal nonlinearity of the sensitivities suggests that prior knowledge of the ocean state is necessary to exploit the travel-time observations.

Long-range asymptotic behavior of vertical travel-time sensitivity kernels

Vertical travel-time sensitivity kernels (VTSKs) describe the effect of horizontally uniform sound-speed changes on travel times in range-independent ocean environments. Wave-theoretic VTSKs can be obtained either analytically, through perturbation of the normal-mode representation, or numerically, as horizontal marginals of the corresponding two-dimensional and three-dimensional travel-time sensitivity kernels. In previous works, it has been observed that wave-theoretic finite-frequency VTSKs approach the corresponding ray-theoretic sensitivity kernels as the propagation range increases. The present work is an attempt to explain this behavior. A stationary-phase approach is used to obtain a long-range asymptotic expression for the wave-theoretic VTSKs. The resulting asymptotic VTSKs are very close to the corresponding ray-theoretic ones. The smoothness condition, required for the stationary-phase approximation to hold, is used to obtain an estimate for the range beyond which the asymptotic behavior sets in.

Structure and stability of wave-theoretic kernels in the ocean

Wave-theoretic modeling can be applied to obtain travel-time sensitivity kernels (TSKs) representing the amount ray travel times are affected by sound-speed variations anywhere in the medium. This work explores the spatial frequency content of the TSK compared to expected ocean variability. It also examines the stability of the TSK in environments that produce strong sensitivity of ray paths to initial conditions. The conclusion is that the linear TSK model is an effective predictor of travel-time changes and that the rays perform nearly as well as the full-wave kernel. The TSK is examined in physical space and in wavenumber space, and it is found that this is the key to understanding how the travel time reacts to ocean perturbations. There are minimum vertical and horizontal length scales of ocean perturbations that are required for the travel time to be affected. The result is that the correspondence between true travel times and those calculated from the kernel is high for large-scale perturbations and somewhat less for the small scales. This demonstrates the validity of ray-based inversion of travel time observations for the cases under study.

Wave equation tomographic velocity inversion method based on the Born/Rytov approximation

This paper discusses Born/Rytov approximation tomographic velocity inversion methods constrained by the Fresnel zone. Calculations of the sensitivity kernel function and traveltime residuals are critical in tomographic velocity inversion. Based on the Born/Rytov approximation of the frequency-domain wave equation, we derive the traveltime sensitivity kernels of the wave equation on the band-limited wave field and simultaneously obtain the traveltime residuals based on the Rytov approximation. In contrast to single-ray tomography, the modified velocity inversion method improves the inversion stability. Tests of the near-surface velocity model and field data prove that the proposed method has higher accuracy and Computational efficiency than ray theory tomography and full waveform inversion methods.

Toward quantitative CO2 storage estimates from time-lapse 3D seismic travel times: An example from the IEA GHG Weyburn–Midale CO2 monitoring and storage project

Time-lapse seismic interval travel time differences are determined during 7years of CO2 injection within the Weyburn oil field, Saskatchewan, Canada. Travel time difference maps are used in conjunction with geophysical and geological logs, and depth dependant fluid properties to provide upper bounds on the amount of CO2 that may reside within various geological intervals. Calculated travel time sensitivity values increase from 0.01ms/m to ∼0.25ms/m moving upward from the reservoir depth (1450m) to the shallowest aquifer considered (600m). The seismic-based apportionment of CO2 shows the fraction of CO2 within or below the reservoir increasing from at least 62–70% after 1year of injection to at least 92–94% after 7years of injection, whereas the proportion of the total injected CO2 in the zone immediately overlying the reservoir decreases from a maximum of 30–36% to ∼5–6% over the same time period. The estimates of CO2 quantities residing within this zone are significantly overestimated due to clearly identified pressure effects in this zone. The maximum estimated proportion of CO2 residing in either interval above the regional sealing formation is ≤1%. The maximum amount of CO2 potentially residing above the regional seal by 2007 is <56, 000tonnes, with a maximum of 0.31Mtonnes just above the reservoir, and 4.6–4.7Mtonnes in the reservoir-containing interval.

On the sensitivity of infrasonic traveltimes in the equatorial region to the atmospheric tides

In comparison to the lower atmosphere where comprehensive global atmospheric specifications are commonplace, the ability to perform routine global measurements of the properties of the atmosphere above the stratopause continues to be an active area of scientific research. In this paper, we revisit the use of infrasound as a remote sensing technique for horizontal winds in the upper atmosphere. To use infrasound to monitor the winds in the upper atmosphere, a sufficiently strong and persistent infrasound source is required. In addition, because of the highly attenuating nature of the thermosphere, the signals used must have low enough frequency content to survive. In this paper, impulsive signals from the Tungurahua volcano in Ecuador are used. This volcano has gone through periods of intense activity during which impulsive signals of dominant periods between 3 and 5 s are emitted. Depending on the atmospheric conditions, stratospheric, mesospheric, and thermospheric arrivals are observed. It is found that the traveltimes of the thermospheric arrivals exhibit a coherent variability with periods equal to those of the tidal harmonics. As such, these observations suggest a means of passive atmospheric remote sensing that can be utilized in conjunction with other techniques to routinely measure the state of the upper atmosphere.

Asymptotic behavior of vertical travel-time sensitivity kernels with increasing propagation range

Vertical travel-time sensitivity kernels (VTSKs) describe the effect of horizontally uniform sound-speed changes on travel-times in range-independent environments. Wave-theoretic VTSKs can be obtained either analytically, through perturbation of the normal-mode representation, or numerically, as horizontal marginals of the corresponding 2D and 3D travel-time sensitivity kernels. In previous works it has been observed that, as the propagation range increases, wave-theoretic VTSKs approach the corresponding ray-theoretic sensitivity kernels even for low frequencies. In the present work an asymptotic expression of the wave-theoretic finite-frequency VTSKs is obtained, using a stationary-phase approach. Numerical results show that wave-theoretic VTSKs converge with increasing range toward the asymptotic form, which in turn lies very close to the ray-theoretic VTSK. [Work supported by ONR.]

Second-Order Sensitivity of Acoustic Travel Times to Sound Speed Perturbations

The second-order sensitivity of finite-frequency acoustic travel times to sound speed perturbations in range-independent environments is studied. Using the notion of peak arrivals and the normal-mode representation of the Green's function first- and second-order perturbation expressions are derived for the travel times in terms of the underlying perturbations in the Green's function and finally in the sound speed profile. The resulting theoretical expressions are numerically validated. Assuming small and local perturbations the non-linear effects appear to be strongest for sound speed perturbations taking place close to the lower turning depths of the corresponding eigenrays. At the upper turning depths ― in the case of temperate propagation conditions ― the effects are much weaker due to the larger sound speed gradients. The magnitude of the second-order sensitivity of travel times relative to the first-order sensitivity can be used to obtain an estimate for the limits of linearity.

Validated helioseismic inversions for 3D vector flows

According to time-distance helioseismology, information about internal fluid motions is encoded in the travel times of solar waves. The inverse problem consists of inferring 3-D vector flows from a set of travel-time measurements. Here we investigate the potential of time-distance helioseismology to infer 3-D convective velocities in the near-surface layers of the Sun. We developed a new Subtractive Optimally Localised Averaging (SOLA) code suitable for pipeline pseudo-automatic processing. Compared to its predecessor, the code was improved by accounting for additional constraints in order to get the right answer within a given noise level. The main aim of this study is to validate results obtained by our inversion code. We simulate travel-time maps using a snapshot from a numerical simulation of solar convective flows, realistic Born travel-time sensitivity kernels, and a realistic model of travel-time noise. These synthetic travel times are inverted for flows and the results compared with the known input flow field. Additional constraints are implemented in the inversion: cross-talk minimization between flow components and spatial localization of inversion coefficients. Using modes f, p1 through p4, we show that horizontal convective flow velocities can be inferred without bias, at a signal-to-noise ratio greater than one in the top 3.5 Mm, provided that observations span at least four days. The vertical component of velocity (v_z), if it were to be weak, is more difficult to infer and is seriously affected by cross-talk from horizontal velocity components. We emphasise that this cross-talk must be explicitly minimised in order to retrieve v_z in the top 1 Mm. We also show that statistical averaging over many different areas of the Sun allows for reliably measuring of average properties of all three flow components in the top 5.5 Mm of the convection zone.

Travel-time sensitivity kernels in long-range propagation

Wave-theoretic travel-time sensitivity kernels (TSKs) are calculated in two-dimensional (2D) and three-dimensional (3D) environments and their behavior with increasing propagation range is studied and compared to that of ray-theoretic TSKs and corresponding Fresnel-volumes. The differences between the 2D and 3D TSKs average out when horizontal or cross-range marginals are considered, which indicates that they are not important in the case of range-independent sound-speed perturbations or perturbations of large scale compared to the lateral TSK extent. With increasing range, the wave-theoretic TSKs expand in the horizontal cross-range direction, their cross-range extent being comparable to that of the corresponding free-space Fresnel zone, whereas they remain bounded in the vertical. Vertical travel-time sensitivity kernels (VTSKs)-one-dimensional kernels describing the effect of horizontally uniform sound-speed changes on travel-times-are calculated analytically using a perturbation approach, and also numerically, as horizontal marginals of the corresponding TSKs. Good agreement between analytical and numerical VTSKs, as well as between 2D and 3D VTSKs, is found. As an alternative method to obtain wave-theoretic sensitivity kernels, the parabolic approximation is used; the resulting TSKs and VTSKs are in good agreement with normal-mode results. With increasing range, the wave-theoretic VTSKs approach the corresponding ray-theoretic sensitivity kernels.

Sensitivity kernels for seismic Fresnel volume tomography

Fresnel volume tomography (FVT) offers higher resolution and better accuracy than conventional seismic raypath tomography. A key problem in FVT is the sensitivity kernel. We propose amplitude and traveltime sensitivity kernels expressed directly with Green’s functions for transmitted waves for 2D/3D homogeneous/heterogeneous media. The Green’s functions are calculated with a finite-difference operator of the full wave equation in the frequency-space domain. In the special case of homogeneous media, we analyze the properties of the sensitivity kernels extensively and gain new insight into these properties. According to the constructive interference of waves, the spatial distribution ranges of the monochromatic sensitivity kernels in FVT differ from each other greatly and are [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] periods of seismic waves, respectively, for 2D amplitude, 3D amplitude, 2D traveltime, and 3D traveltime conditions. We also have a new understanding of the relationship between raypath tomography and FVT. Within the first Fresnel volume of the dominant frequency, the band-limited sensitivity kernels of FVT in homogeneous media or smoothly heterogeneous media are very close to those of the dominant frequency. Thus, it is practical to replace the band-limited sensitivity kernel with a few selected frequencies or even the single dominant frequency to save computation when performing band-limited FVT. The numerical experiment proves that FVT using our sensitivity kernels can achieve more accurate results than traditional raypath tomography.

Travel-time sensitivity kernels versus diffraction patterns obtained through double beam-forming in shallow water

In recent years, the use of sensitivity kernels for tomographic purposes has been frequently discussed in the literature. Sensitivity kernels of different observables (e.g., amplitude, travel-time, and polarization for seismic waves) have been proposed, and relationships between adjoint formulation, time-reversal theory, and sensitivity kernels have been developed. In the present study, travel-time sensitivity kernels (TSKs) are derived for two source-receiver arrays in an acoustic waveguide. More precisely, the TSKs are combined with a double time-delay beam-forming algorithm performed on two source-receiver arrays to isolate and identify each eigenray of the multipath propagation between a source-receiver pair in the acoustic waveguide. A relationship is then obtained between TSKs and diffraction theory. It appears that the spatial shapes of TSKs are equivalent to the gradients of the combined direction patterns of the source and receiver arrays. In the finite-frequency regimes, the combination of TSKs and double beam-forming both simplifies the calculation of TSK and increases the domain of validity for ray theory in shallow-water ocean acoustic tomography.

Shallow water tomography: Ray theory vs travel-time sensitivity kernels.

In underwater acoustics, ray tomography is the classical method used to estimate velocity variations, but recently. Travel-Time Sensitivity Kernels (TSK) approaches have been developed. In this paper, we deal with TSK for two source-receive arrays in an acoustic waveguide for shallow water tomography. As a first step, we show that separation of the different raypaths is improved by using a recently proposed new array processing [time-delay double beamforming (DBF) algorithm]. DBF consists of changing the 3-D data space from source depth, receiver depth and time into a new 3-D space related to ray propagation expressed by the beamformed variables, source angle, receive angle and time. As a consequence, each eigenray of the multipath propagation for a source-receiver couple can be identified and separated through DBF. In this context of DBF, the TSK is no longer point-to-point as usual, but relies on all source-receiver time series. Kernels are computed using the fact that the processed signal is a linear combination of time-delayed signals between all sources and receivers. Results in simulated data and in real datasets recorded in an ultrasonic tank prove that combination of TSK and DBF increases the resolution and robustness performance of shallow-water acoustic tomography.