Vertical Travel Time Research Articles

Robust and efficient waveform-based velocity model building by optimal transport in the pseudotime domain: An ocean-bottom cable case study in the North Sea

Full-waveform inversion (FWI) in the North Sea has demonstrated its imaging power starting from low-resolution models obtained by traveltime tomography, enriching them with geologically interpretable fine-scale details. However, building a traveltime-based kinematically accurate starting model for FWI is a time-consuming and rather subjective process requiring phase identification and selection. The two main problems faced by FWI starting from noninformative initial models are the susceptibility to cycle skipping and a lack of sensitivity to low wavenumbers in the deep subsurface not sampled by turning waves. On a North Sea ocean-bottom cable 3D data set, a novel [Formula: see text] building methodology is applied that addresses those issues by jointly inverting reflections and refractions (joint full-waveform inversion [JFWI]) using a robust misfit function in the vertical traveltime domain (pseudotime). Pseudotime addresses reflectivity-velocity coupling and attenuates phase ambiguities at short offsets, whereas a graph-space optimal transport (GSOT) objective function with dedicated data windowing averts cycle skipping at intermediate-to-long offsets. A fast and balanced reflectivity reconstrution is obtained prior to JFWI thanks to an asymptotic-preconditioned impedance waveform inversion ([Formula: see text]WI). Starting from a linearly increasing one-dimensional model, GSOT-pseudotime JFWI is effective at obtaining a meaningful P-wave velocity macromodel down to depths sampled by reflections only, without phase identification and picking. P-wave FWI, starting from the JFWI-based model, injects the high wavenumbers missing in the JFWI solution, attaining apparent improvements in shallow and deep model reconstruction and imaging compared with the previous studies in the literature, and a satisfactory prediction of the ground-truth logs.

Application of ground-penetrating radar method to detect underground pipes in PAIR BATAN utility area

Underground pipeline systems dominate today’s urban area landscape. This buried pipeline system will continuously develop along with the utility change. The planning for underground pipelines should be done to avoid mistakes in the pipeline path. Thus, mapping for the underground pipeline is necessary to obtain a database for any upcoming construction development. This research purpose is to detect underground pipelines around utility areas using the ground-penetrating radar (GPR) method. A frequency of 300 MHz was used to acquire GPR data from 6 lines, with a total length of 22.6m for each line and 0.5m for the line spacing. A sequence of processing stages of the GPR data was conducted using matGPR, a MATLAB-based program. Interpretable GPR profiles from each measurement line are obtained after adjusting signal position, removing DC, Dewow, mean filter, gaining, removing global background, and KL-filter. The results show an obvious amplitude reflection anomaly. Each line has similar detected underground pipes from its vertical axis, travel time, and horizontal distance. Clearly, all lines show an obvious contrast anomaly located at the 2.5 m horizontal distance. This most striking anomaly is interpreted as a water tunnel. In comparison, the other five parabolic-shaped anomalies were identified as underground pipes.

Oriented NMO correction of VTI data in the absence of near-offset traces

Calculating an accurate seismic velocity model serves an important role in many seismic imaging techniques. The process of velocity model building is often time-consuming, specifically for anisotropic areas, where more than a single parameter is involved in the process. In the past few years, more time-efficient approaches have been considered to estimate seismic velocity as well as anellipticity parameter or heterogeneity factor using local event slopes. Nevertheless, some of these techniques are not practical due to curvature-dependency, or due to the lack of near-offset data. To address such limitations, we have used a curvature-independent approach for normal-moveout correction as well as parameter estimation in vertical transverse isotropic media, which is based on local estimation of vertical traveltime using a shifted-hyperbola approximation in the absence of near-offset data. The performance of our approach is tested on synthetic and field common-midpoint gathers. It is also assessed in different signal-to-noise ratios and different missing-near-offset situations. Our findings are consistent with the results achieved by the previous methods that were not developed for sparse data.

Effect of multilayered groundwater mounds on water dynamics beneath a recharge basin: Numerical simulation and assessment of surface injection

AbstractInteractions between groundwater mounds caused by a geologic layer contrast affect the efficiency of managed aquifer recharge in arid areas. However, research has rarely examined the roles of groundwater mounding size variations on soil water dynamics in a stratified vadose zone in response to a sustained infiltration source. Numerical experiments were conducted on a two‐dimensional vertical‐section domain using HYDRUS software to simulate the behaviours of two adjacent (upper and lower) groundwater mounds underlying an infiltration basin subjected to clay loam and sandy alternately‐layered soil profiles. The model successfully predicted the volume and extent of perched water and approximated vertical travel times during events generating downward fluxes from the surface injection. The response time of the mounding width (lateral extension) to the surface injection was delayed as compared to that of the mounding height (vertical extension), especially for the lower water mound. The mounding heights and widths show a strongly positive correlation with the infiltration rates of both high‐ and low‐permeability layers where the injected water mounded, while the water storage amounts in the high‐ and low‐permeability layers were governed by the mounding height and width, respectively. Exploratory simulations were then employed to assess the dependence of groundwater mounding behaviours and recharge performances on surface injection strategies. Results suggest that, by reducing injection rate or shortening injection duration, the near‐term fraction of the surface injection converted to deep recharge is likely to be increased due to the narrowed groundwater mounding size, which would be limited by the water‐retarding effect of layer contrasts. This study has important implications for predicting and understanding multilayered groundwater mounding behaviours and associated water mass balance under the geologic stratification, and is expected to aid in optimizing the infiltration basin operation for aquifer recharge.

Walkaway VSP in ultra-shallow water images deep Paleozoic targets, offshore UAE

In 2019, ADNOC decided to record walkabove and walkaway VSP surveys in a deep deviated well, in ultra-shallow waters offshore Abu Dhabi. The field is part of a major gas and condensate development project in UAE. The primary objectives included vertical travel times and velocities, robust well to seismic tie, and higher-resolution VSP images of the Palaeozoic-age targets. Other objectives included acoustic impedance inversion and anisotropy calibration. This was the first time a walkaway was acquired with only 2 m of water depth and in a deep hostile downhole environment. This study showed the importance of pre-survey modelling to achieve the VSP objectives. The data were acquired in continuous mode with GPS time stamping. Good data quality was recorded, despite high temperature, deep targets, multiple casings and a small volume seismic source deployed at 1 m depth. Wideband 5–90 Hz data were retrieved across 6 km of complex overburden, resulting in images with three-fold resolution improvement compared to the surface seismic data. The VSP also provided acoustic impedance sections of the deeper targets and measurements to optimize surface seismic processing. The results validate the viability of 3DVSP surveys with similar shallow-water source and downhole receiver array for reservoir characterization and well placement.

Sea level anomaly intelligent inversion model based on LSTM-RBF network

Sea level anomaly (SLA) can be decomposed into two contributions: one from changes in mass in the water column (barotropic part) and the other from purely steric changes (baroclinic part) obtained by gravest empirical mode (GEM) lookup table. The establishment of GEM lookup table requires a large amount of data preprocessing (eliminating abnormal data, removing seasonal signals). The relationship between hydrological data (temperature, salinity and depth), vertical acoustic travel time and geopotential height is complex and requires human guidance. In view of the above shortcomings, this paper proposes the neural network-based SLA Intelligent Inversion model to fit the SLA model based on the traditional GEM field. The historical hydrological data is measured by conductivity temperature depth casts in the Eastern Taiwan and the northeastern part of Luzon. During the modeling process, firstly, the long short-term memory (LSTM) network is employed to detect and replace the abnormal data of the hydrological data. Secondly, the radial basis function (RBF) model based on the traditional GEM is constructed. The model can remove the seasonal signals. Besides, it can build the relationship between vertical acoustic travel time and geopotential height. The performance of the model is verified by the data set. It proves that compared with the traditional GEM, the relative error of network based on LSTM-RBF is less than 0.15%. Moreover, it can process abnormal data and remove seasonal signals. This study provides a novel method for preprocessing of hydrological data and SLA inversion based on Pressure-sensor-equipped inverted echo sounders.

Tutorial: unified 1D inversion of the acoustic reflection response.

ABSTRACTAcoustic inversion in one‐dimension gives impedance as a function of travel time. Inverting the reflection response is a linear problem. Recursive methods, from top to bottom or vice versa, are known and use a fundamental wave field that is computed from the reflection response. An integral over the solution to the Marchenko equation, on the other hand, retrieves the impedance at any vertical travel time instant. It is a non‐recursive method, but requires the zero‐frequency value of the reflection response. These methods use the same fundamental wave field in different ways. Combining the two methods leads to a non‐recursive scheme that works with finite‐frequency bandwidth. This can be used for target‐oriented inversion. When a reflection response is available along a line over a horizontally layered medium, the thickness and wave velocity of any layer can be obtained together with the velocity of an adjacent layer and the density ratio of the two layers. Statistical analysis over 1000 noise realizations shows that the forward recursive method and the Marchenko‐type method perform well on computed noisy data.

3D diffraction imaging with Kirchhoff time migration using vertical traveltime difference gathers

We have built a vertical traveltime difference (VTD) gather to image diffractions in the 3D time domain. This significantly improves detection of small-scale faults and heterogeneities in 3D seismic data. The VTD gather is obtained using 3D Kirchhoff prestack time migration based on the traveltime-related inline and crossline dip angles, which is closely related to the 2D dip-angle gather. In VTD gathers, diffraction events exhibit flattening, whereas reflection events have convex upward-sloping shapes. Different from the 2D dip-angle gather, Fresnel zone-related specular reflections are precisely focused on the given regions over all offsets and azimuths, thus leaving more diffraction energy after muting. To image linear diffractors, such as faults in three dimensions, the VTD gather can be extended into two dimensions by adding a dip-azimuth dimension. This makes it possible to correct phases of edge diffractions and detect the orientations of the linear diffractors. The memory requirement of the VTD or VTD plus azimuth gathers is much less than that of the 2D dip-angle gathers. We can store the gathers at each lateral position and then correct the phase and enhance the weak diffractions in 3D cases. Synthetic and field data tests demonstrate the effectiveness of our 3D diffraction imaging method.

Optimization of flexible lift processes on high-rise building construction sites

Abstract Timely delivery of materials and laborers to workface is critical to the smooth progression of a task on the construction site. This subject is of particular importance in high-rise building projects where the vertical transportation may turn into a bottleneck in the delivery process, if not precisely planned. In such contexts, lift cars represent a contested resource for movement of people and materials and any delayed lifting leads to disrupted tasks on the building floors. The available literature predominantly relies on predefined or rule-based scenarios in addressing the lifting problem which may result in suboptimal solutions to the operation of the lifts. Therefore, this research aims to develop a holistic mathematical model which identifies the optimum operational plan for the entire lift systems in high rise construction. The model has a mixed integer nature incorporating characteristics and constraints of lift cars, construction resources and activities, and site conditions. The optimality is targeted through minimum travel time both at the whole scale and for a single lift car. To improve generalizability, the model has been adapted to variant lift optimization problems under different construction scenarios. It is then integrated with the zoning problem in order to determine optimal zoning configuration for a given lift system. The model is tested on a hypothetical case replicating complexities and constraints of real-world situations. The results indicate that the model can efficiently find an optimal solution for the lift systems which imposes minimum vertical travel time to the project.

A plane-wave formulation and numerical analysis of elastic multicomponent inverse scattering series internal multiple prediction

Internal multiple prediction and removal is a critical component of seismic data processing prior to imaging, inversion, and quantitative interpretation. Inverse scattering series methods predict multiples without identification of generators, and without requiring a velocity model. Land environments present several challenges to the inverse scattering series prediction process. This is particularly true for algorithm versions that explicitly account for elastic conversions and incorporate multicomponent data. The theory for elastic reference medium inverse scattering series internal multiple prediction was introduced several decades ago, but no numerical analysis or practical discussion of how to prepare data for it currently exists. We have focused our efforts on addressing this gap. We extend the theory from 2D to 3D, analyze the properties of the input data required by the existing algorithm, and, motivated by earlier research results, reformulate the algorithm in the plane-wave domain. The success of the prediction process relies on the ordering of events in either pseudodepth or vertical traveltime being the same as the ordering of reflecting interfaces in true depth. In elastic-multicomponent cases, it is difficult to ensure that this holds true because the events to be combined may have undergone multiple conversions as they were created. Several variants of the elastic-multicomponent prediction algorithm are introduced and examined for their tendency to violate ordering requirements (and create artifacts). A plane-wave domain prediction, based on elastic data that have been prepared (1) using variable, “best-fit” velocities as reference velocities, and (2) with an analytically determined vertical traveltime stretching formula, is identified as being optimal in the sense of generating artifact-free predictions with relatively small values of the search parameter [Formula: see text], while remaining fully data driven. These analyses are confirmed with simulated data from a layered model; these are the first numerical examples of elastic-multicomponent inverse scattering series internal multiple prediction.

Towards consideration of epistemic uncertainty in shear-wave velocity measurements obtained via seismic cone penetration testing (SCPT)

Seismic cone penetration testing (SCPT) is a powerful geotechnical site characterization tool, allowing for simultaneous collection of routine cone penetration testing data and rapid downhole-type measurements of shear-wave velocity (VS). However, the uncertainties associated with developing VS profiles from SCPT measurements are rarely considered or communicated to the end-user. One important source of VS uncertainty is related to how the shear wave travel times are interpreted from the recorded waveforms, while another critical source of uncertainty is related to the analysis method used to transform the travel times to velocities. In this study, four common ways of obtaining travel times were considered: (i) first arrival picks, (ii) peaks and troughs picks, (iii) crossover picks, and (iv) the peak response of the cross-correlation function. Using these different travel times, a number of VS profiles were developed using four different velocity analysis methods: (i) pseudo-interval, (ii) true-interval, (iii) corrected vertical travel time slope-based, and (iv) raytracing. Through consideration of multiple wave arrival time and velocity analysis methods, a robust and meaningful quantification of the intramethod, depth-dependent epistemic uncertainty in VS obtained from several example SCPT datasets has been developed. VS uncertainty is further examined through consideration of the intermethod variability and bias between SCPT and direct-push crosshole testing.

Internal tides in the northwestern South China Sea observed by pressure-recording inverted echo sounders

This study presents IT observations in the northwestern SCS from five pressure-recording inverted echo sounders (PIESs). The vertical round-trip acoustic travel times that PIESs measures are proportional to the vertical thermocline displacements; therefore, PIESs can be used to monitor the 1st mode internal tides. PIESs were deployed along a section between the continental shelf break in the north and Xisha Islands in the south. Measurements show that both diurnal and semidiurnal ITs were stronger on the northern and southern sides of the section than those in the middle. Their temporal variations were coherent with local surface tides, which implies locally generated ITs may be important. Complex empirical orthogonal function analysis reveals a small phase difference (the south leads the north by 70°) across the section for diurnal ITs, but a significant phase difference (the north leads the south by 360°) for semidiurnal ITs. These observations indicate that the dominant diurnal ITs propagate across the section (from east to west), while the semidiurnal ITs propagate along the section (from north to south). A ray-tracing model was utilized to demonstrate the impact of mesoscale circulation patterns on the propagation of diurnal ITs from the Luzon Strait to the PIES sites. The model explains the temporal IT variations, which were incoherent with local surface tides. The result indicates that diurnal ITs in the northwestern SCS can be affected by ITs propagating from the Luzon Strait, while semidiurnal ITs are primarily generated locally from the continental shelf break in the north.

In-well time-of-travel approach to evaluate optimal purge duration during low-flow sampling of monitoring wells

A common assumption with groundwater sampling is that low (<0.5 L/min) pumping rates during well purging and sampling captures primarily lateral flow from the formation through the well-screened interval at a depth coincident with the pump intake. However, if the intake is adjacent to a low hydraulic conductivity part of the screened formation, this scenario will induce vertical groundwater flow to the pump intake from parts of the screened interval with high hydraulic conductivity. Because less formation water will initially be captured during pumping, a substantial volume of water already in the well (preexisting screen water or screen storage) will be captured during this initial time until inflow from the high hydraulic conductivity part of the screened formation can travel vertically in the well to the pump intake. Therefore, the length of the time needed for adequate purging prior to sample collection (called optimal purge duration) is controlled by the in-well, vertical travel times. A preliminary, simple analytical model was used to provide information on the relation between purge duration and capture of formation water for different gross levels of heterogeneity (contrast between low and high hydraulic conductivity layers). The model was then used to compare these time–volume relations to purge data (pumping rates and drawdown) collected at several representative monitoring wells from multiple sites. Results showed that computation of time-dependent capture of formation water (as opposed to capture of preexisting screen water), which were based on vertical travel times in the well, compares favorably with the time required to achieve field parameter stabilization. If field parameter stabilization is an indicator of arrival time of formation water, which has been postulated, then in-well, vertical flow may be an important factor at wells where low-flow sampling is the sample method of choice.

Preferential flow, diffuse flow, and perching in an interbedded fractured-rock unsaturated zone

Layers of strong geologic contrast within the unsaturated zone can control recharge and contaminant transport to underlying aquifers. Slow diffuse flow in certain geologic layers, and rapid preferential flow in others, complicates the prediction of vertical and lateral fluxes. A simple model is presented, designed to use limited geological site information to predict these critical subsurface processes in response to a sustained infiltration source. The model is developed and tested using site-specific information from the Idaho National Laboratory in the Eastern Snake River Plain (ESRP), USA, where there are natural and anthropogenic sources of high-volume infiltration from floods, spills, leaks, wastewater disposal, retention ponds, and hydrologic field experiments. The thick unsaturated zone overlying the ESRP aquifer is a good example of a sharply stratified unsaturated zone. Sedimentary interbeds are interspersed between massive and fractured basalt units. The combination of surficial sediments, basalts, and interbeds determines the water fluxes through the variably saturated subsurface. Interbeds are generally less conductive, sometimes causing perched water to collect above them. The model successfully predicts the volume and extent of perching and approximates vertical travel times during events that generate high fluxes from the land surface. These developments are applicable to sites having a thick, geologically complex unsaturated zone of substantial thickness in which preferential and diffuse flow, and perching of percolated water, are important to contaminant transport or aquifer recharge.

Joint inversion of receiver functions and dispersion data for crustal study at VLC seismographic station (Italy)

Joint inversion of body wave receiver functions and dispersion data was used to model the shear wave velocity distribution of the crust and upper mantle below VLC (44.16°N, 10.39°E), a broadband seismographic station in Italy. Receiver functions are primarily sensitive to the shear wave velocity contrasts and vertical travel times, whereas the surface wave dispersion measurements are sensitive to absolute vertical shear wave velocity averages, thus, both data sets are sensitive to the same medium parameter. Each data set has inherent lapses but by jointly inverting both we are able to draw on the capabilities of one to compensate the imperfections of the other and this provides better S-wave velocity constraints than we would obtain by inverting either data set individually. The receiver functions were computed from the teleseismic earthquakes recorded by VLC station between 2005 and 2012, while the dispersion curves at regional scale were determined by the frequency time analysis and have been used to obtain tomography maps, using the two-dimensional tomography algorithm developed by Ditmar and Yanovskaya in 1987. The inversion results include a crust with a sharp gradient near the surface (shear velocity changing from 2.15 to 3.4 km s−1 in 5 km) underlain by a 13-km-thick layer with a shear velocity of and 3.4 km s−1 another 15-km-thick layer with a shear velocity of 3.72 km s−1, and an upper mantle with an average shear velocity of 4.4 km s−1. The crust–mantle transition has a significant gradient, with velocity values varying from 3.72 to 4.4 km s−1 at about 32 km depth. This result is also in agreement with shear wave velocity cross-section of the area obtained from ITA-LSO data sets.

Piecewise‐continuous velocity inversion

ABSTRACTWe suggest a new method to determine the piecewise‐continuous vertical distribution of instantaneous velocities within sediment layers, using different order time‐domain effective velocities on their top and bottom points. We demonstrate our method using a synthetic model that consists of different compacted sediment layers characterized by monotonously increasing velocity, combined with hard rock layers, such as salt or basalt, characterized by constant fast velocities, and low velocity layers, such as gas pockets. We first show that, by using only the root‐mean‐square velocities and the corresponding vertical travel times (computed from the original instantaneous velocity in depth) as input for a Dix‐type inversion, many different vertical distributions of the instantaneous velocities can be obtained (inverted). Some geological constraints, such as limiting the values of the inverted vertical velocity gradients, should be applied in order to obtain more geologically plausible velocity profiles. In order to limit the non‐uniqueness of the inverted velocities, additional information should be added. We have derived three different inversion solutions that yield the correct instantaneous velocity, avoiding any a priori geological constraints. The additional data at the interface points contain either the average velocities (or depths) or the fourth‐order average velocities, or both. Practically, average velocities can be obtained from nearby wells, whereas the fourth‐order average velocity can be estimated from the quartic moveout term during velocity analysis. Along with the three different types of input, we consider two types of vertical velocity models within each interval: distribution with a constant velocity gradient and an exponential asymptotically bounded velocity model, which is in particular important for modelling thick layers. It has been shown that, in the case of thin intervals, both models lead to similar results. The method allows us to establish the instantaneous velocities at the top and bottom interfaces, where the velocity profile inside the intervals is given by either the linear or the exponential asymptotically bounded velocity models. Since the velocity parameters of each interval are independently inverted, discontinuities of the instantaneous velocity at the interfaces occur naturally. The improved accuracy of the inverted instantaneous velocities is particularly important for accurate time‐to‐depth conversion.

Consequences of varied soil hydraulic and meteorological complexity on unsaturated zone time lag estimates

The true efficacy of a programme of agricultural mitigation measures within a catchment to improve water quality can be determined only after a certain hydrologic time lag period (subsequent to implementation) has elapsed. As the biophysical response to policy is not synchronous, accurate estimates of total time lag (unsaturated and saturated) become critical to manage the expectations of policy makers. The estimation of the vertical unsaturated zone component of time lag is vital as it indicates early trends (initial breakthrough), bulk (centre of mass) and total (Exit) travel times. Typically, estimation of time lag through the unsaturated zone is poor, due to the lack of site specific soil physical data, or by assuming saturated conditions. Numerical models (e.g. Hydrus 1D) enable estimates of time lag with varied levels of input data. The current study examines the consequences of varied soil hydraulic and meteorological complexity on unsaturated zone time lag estimates using simulated and actual soil profiles. Results indicated that: greater temporal resolution (from daily to hourly) of meteorological data was more critical as the saturated hydraulic conductivity of the soil decreased; high clay content soils failed to converge reflecting prevalence of lateral component as a contaminant pathway; elucidation of soil hydraulic properties was influenced by the complexity of soil physical data employed (textural menu, ROSETTA, full and partial soil water characteristic curves), which consequently affected time lag ranges; as the importance of the unsaturated zone increases with respect to total travel times the requirements for high complexity/resolution input data become greater. The methodology presented herein demonstrates that decisions made regarding input data and landscape position will have consequences for the estimated range of vertical travel times. Insufficiencies or inaccuracies regarding such input data can therefore mislead policy makers regarding the achievability of water quality targets.

Low‐frequency normal wave propagation in a periodically layered medium with weak contrast in elastic properties

ABSTRACTWe derive the phase velocity dispersion and the scattering for wave vertically propagating in a periodically weak‐contrast horizontally layered medium with arbitrary number of layers in a period. Phase velocity dispersion is defined as the frequency dependence of vertical travel time, and scattering is defined as a reflection coefficient at the interface between the multilayered system and the corresponding Backus medium. Low‐frequency approximation is used to define a dynamic effective medium with frequency‐dependent phase velocity. The results are compared with those obtained earlier for a gradient medium. We show that the low‐frequency weak‐contrast approximation is valid for models with realistic contrasts in elastic properties.

Prestack time imaging algorithm with simultaneous velocity estimation in hard rock environments

Reflection seismic imaging faces several difficulties in hard rock environments. One of them is the estimation of the propagation velocity of seismic waves. Therefore, imaging algorithms that do not require prior construction of a velocity model seem promising for such environments. In this paper we illustrate an application of prestack time migration, which does not require an input velocity model, to hard rock conditions, and we demonstrate its effectiveness on synthetic data. This approach is based on an estimation of local event slopes (horizontal slownesses) in common-shot and common-receiver gathers and a subsequent calculation of the migration attributes (migration velocity, vertical traveltime and horizontal coordinates of the migrated reflection point). These attributes allow us to derive all the information needed to construct a time-migrated image. We also use the obtained migration velocities as an input velocity model for Kirchhoff prestack time migration (PSTM) and compare the results of the proposed approach with a conventional Kirchhoff migration using as an input the picked NMO velocity model. This application to a hard rock synthetic model illustrates the potential of the presented migration algorithm for imaging in hard rock seismic exploration. We believe that this approach can be used in hard rock seismic processing workflows as an automatic tool to obtain an input velocity model for the Kirchhoff PSTM.

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.