Variation In Arrival Time Research Articles

Cancellation of klystron-induced energy and arrival-time variations in linear accelerators with arc-type bunch compressors

We explain how the accelerating field amplitude and phase vary with modulator voltage in pulsed radio frequency high-power amplifiers based on klystron tubes. Changes in modulator voltage give rise to correlated changes of amplitude and phase, affecting the properties of the accelerated beam, in particular energy, arrival time, and bunch duration. We show, both theoretically and experimentally, that there exists a postcrest acceleration phase (the ) where the changes of beam energy due to phase and amplitude shifts caused by modulator-voltage variations cancel out. When accelerating at the magic angle, the klystron modulator voltage jitter no longer contributes to energy and arrival-time jitter in the accelerator. Off-crest operation at the magic angle can be implemented for bunch compression schemes in accelerators with arc-type bunch compressors, which have positive momentum compaction. The experimental results, obtained at the MAX IV laboratory, show the benefit of operating close to the magic angle in arc-type bunch compressors. In a direct measurement of normalized electron-energy jitter, the energy jitter was reduced by a factor of 1.8 down to 8.2×10−5 when operating at the magic angle. Published by the American Physical Society 2024

Oil spill risk analysis for the NEOM shoreline

A risk analysis is conducted considering an array of release sources located around the NEOM shoreline. The sources are selected close to the coast and in neighboring regions of high marine traffic. The evolution of oil spills released by these sources is simulated using the MOHID model, driven by validated, high-resolution met-ocean fields of the Red Sea. For each source, simulations are conducted over a 4-week period, starting from first, tenth and twentieth days of each month, covering five consecutive years. A total of 180 simulations are thus conducted for each source location, adequately reflecting the variability of met-ocean conditions in the region. The risk associated with each source is described in terms of amount of oil beached, and by the time required for the spilled oil to reach the NEOM coast, extending from the Gulf of Aqaba in the North to Duba in the South. To further characterize the impact of individual sources, a finer analysis is performed by segmenting the NEOM shoreline, based on important coastal development and installation sites. For each subregion, source and release event considered, a histogram of the amount of volume beached is generated, also classifying individual events in terms of the corresponding arrival times. In addition, for each subregion considered, an inverse analysis is conducted to identify regions of dependence of the cumulative risk, estimated using the collection of all sources and events considered. The transport of oil around the NEOM shorelines is promoted by chaotic circulations and northwest winds in summer, and a dominant cyclonic eddy in winter. Hence, spills originating from release sources located close to the NEOM shorelines are characterized by large monthly variations in arrival times, ranging from less than a week to more than 2 weeks. Similarly, large variations in the volume fraction of beached oil, ranging from less then 50% to more than 80% are reported. The results of this study provide key information regarding the location of dominant oil spill risk sources, the severity of the potential release events, as well as the time frames within which mitigation actions may need to deployed.

Crustal anisotropy of the South China block and tectonic implications

Exploiting the teleseismic waveform data from permanent seismic stations distributed in the South China block, we obtained the crustal anisotropy parameters at 51 stations by fitting the azimuthal variations of arrival times of the PMs converted wave of radial receiver functions. The results show the dominant direction of fast wave polarity in the South China block is NW–SE, which is basically consistent with the absolute plate motion direction. Combining the shear wave splitting and GPS results, we speculated that the tectonic extension of the Paleo-Pacific plate subduction dominates the crust–mantle anisotropy, which reflects the large-scale tectonic stress setting of the South China block. The fast wave directions of NE–SW and E–W calculated by a few stations might represent a local complex tectonic environment, and the crustal anisotropy of NE–SW is well related to the tectonic deformation in Paleozoic. The delay time of slow waves caused by crustal anisotropy ranges from 0.14 s to 0.71 s, with an average of 0.33 s. The delay time of Jiangnan orogenic belt, which located in the southeast of Yangtze block, is particularly large, which reflects the complex and intense intra-continental tectonic movements since Neoproterozoic. The crustal anisotropy along the southeast coast can be contributed to the local lithosphere underplating caused by the upwelling of asthenosphere in Cretaceous.

Pulse arrival time variation as a non-invasive marker of acute response to cardiac resynchronization therapy.

Successful cardiac resynchronization therapy (CRT) shortens the pre-ejection period (PEP) which is prolonged in the left bundle branch block (LBBB). In a combined animal and patient study, we investigated if changes in the pulse arrival time (PAT) could be used to measure acute changes in PEP during CRT implantation and hence be used to evaluate acute CRT response non-invasively and in real time. In six canines, a pulse transducer was attached to a lower limb and PAT was measured together with left ventricular (LV) pressure by micromanometer at baseline, after induction of LBBB and during biventricular pacing. Time-to-peak LV dP/dt (Td) was used as a surrogate for PEP. In twelve LBBB patients during implantation of CRT, LV and femoral pressures were measured at baseline and during five different pacing configurations. PAT increased from baseline (277 ± 9 ms) to LBBB (313 ± 16 ms, P < 0.05) and shortened with biventricular pacing (290 ± 16 ms, P < 0.05) in animals. There was a strong relationship between changes in PAT and Td in patients (r2 = 0.91). Two patients were classified as non-responders at 6 months follow-up. CRT decreased PAT from 320 ± 41 to 298 ± 39 ms (P < 0.05) in the responders, while PAT increased by 5 and 8 ms in the two non-responders. This proof-of-concept study indicates that PAT can be used as a simple, non-invasive method to assess the acute effects of CRT in real time with the potential to identify long-term response in patients.

Constraints on complex crustal structures from gravity data and harmonic analysis of receiver functions

SUMMARY The traditional H–κ stacking technique is often used to determine the crustal thickness (H) and Vp/Vs (κ) using multiple Moho converted P-to-S phases, but weak crustal multiples and variation of arrival time of crustal multiples in receiver function resulting from complex crustal structure, such as dipping interface and/or crustal anisotropy, can cause bias estimates leading to erroneous interpretations. In this study, we overcome these problems by combining the Ps arrival times in receiver functions and independent constraint from gravity data, providing a complementary to the H–κ method for estimating H and H with the advantage of not relying on the crustal multiples which are commonly hardly identified. Harmonic corrections are only made to arrival time variations of Ps phase before H–κ stacking. Independent gravity data can help constrain the trade-off between the H and κ when using Ps times only. Stacking these two complementary data sets allows us to yield a more accurate estimation of H and κ. The reliability and validity of our method to constrain the crustal properties are confirmed using synthetic data from multiple types of models and real data recorded by two permanent seismic stations belonging to different geological regions.

Optimal scheduling model based on unmanned collector truck arrival time variation field bridge under balanced strategy

Abstract The scheduling of container yard bridges has an important impact on the operational efficiency of the terminal. For the future automated terminal, to reasonably schedule the field bridges, under a given batch of tasks, considering the change of the arrival time of unmanned trucks and the balance of the workload of each field bridge, a balanced strategy is established based on the change of the arrival time of unmanned trucks. The optimal scheduling model of field bridges is given, and an example of field bridge scheduling is given through experiments. Provides a scientific solution for the future automated dock, yard, and bridge scheduling

Crustal Structure and Anisotropy in the Lower Yangtze Region and its Metallogenic Implications

In this study, we performed receiver function profiling and fitted harmonic functions to the arrival time variations of Pms phases to calculate the crustal seismic anisotropy with delay time and fast polarization direction, using broadband seismic data obtained from 55 temporary stations in two linear profiles and 39 stations in the Lower Yangtze and adjacent region. Moreover, we determined the crustal thickness and Poisson’s ratio using a novel H-κ-c stacking method. Our results revealed that the Middle-Lower Yangtze Metallogenic Belt and the north east section of the Qinzhou-Hangzhou Metallogenic Belt are characterized by Moho upliftment (&amp;lt;32 km), a relatively high Poisson’s ratio (&amp;gt;0.26), local lithospheric thinning (&amp;lt;70 km), and a pattern of deep faults that connect the crust and asthenosphere and serve as conduits for magma upwelling. The NE-SW fast polarization direction was consistent with the SKS splitting results, and the average delay time was 0.45 s. Moreover, underplating of deep magma and upwelling along the weak zone caused local Moho uplift and ductile shear of the lower crust, resulting in the directional arrangement of amphibole and other minerals, which may be the controlling mechanism for the crustal anisotropy in the study area. The variations in crustal structure and anisotropy characteristics indicated that in the context of the northeastern Paleo-Pacific plate subduction, the existence of weak lithospheric zones and the northeastern asthenospheric flow are important conditions for metal supernormal enrichment in the Lower Yangtze region.

Full-scale experimental study on fire under natural ventilation in the T-shaped and curved tunnel groups

To assess the fire risk during the construction of the pumped storage power station, full-scale fire experiments in the ventilation and safety tunnel were conducted to research temperature distribution and smoke diffusion under ventilation. The temperature profile and airflow velocity of air flow under different conditions were recorded and analyzed. The results show that the airflow velocity was mainly influenced by the large space like powerhouse and transformer chamber under natural ventilation. By analyzing smoke propagation characteristic parameters including the maximum ceiling temperature rise, smoke front arrival time and temperature variation with time, the fire-induced smoke hazard under different fire locations was assessed. The research results can provide reference data for smoke exhaust design and help developing the emergency evacuation plan for the large underground space building with similar structure.

Data-driven approaches for ray-based ocean acoustic tomography

Ray-based acoustical tomography typically provides estimates of local ocean sound speed fluctuations from precise measurements of acoustic travel times fluctuations (with respect to a reference environment) between multiple sources and receiver arrays along with a model of the ray propagation in the reference (i.e., fluctuation-free) environment. Traditionally, this is achieved using a sensitivity kernel, a Born–Frechet linearization of the non-linear relationship between ray arrival-times and sound speeds fluctuations. However, computing the full sensitivity kernel can be computationally intensive and is restricted to only small sound-speed fluctuations (due to the linearization procedure) and does not inherently leverage any available history of the arrival time or sound speed fluctuations which may have been collected prior to performing the inversion procedure. As an alternative solution for ray-based acoustical tomography, we investigated the use of data-driven methods, such as linear regression, nearest neighbors, neural networks, and kernel (ridge) regression, to directly learn the non-linear relationship between sound speed fluctuations and ray arrival time variations using previously collected measurements. Additionally, the experimental training data set is augmented by generating synthetic SSPs based on empirical orthogonal function analysis of the historical SSP data. This approach is demonstrated for short vertical bottom-mounted arrays deployed in littoral environments.

Three-dimensional passive-source anisotropic reverse time migration for imaging lithospheric discontinuities

SUMMARY The scattered teleseismic body waves have been used intensively to characterize the receiver-side lithospheric structures. The routinely used ray-theory-based methods have limitations to image complex structures and tackle strong heterogeneities. The newly developed wave-equation based, passive-source reverse time migration (RTM) approach can overcome such limitations. To date, passive-source RTM has been developed only for isotropic media. However, at least to the first-order, most lithospheric structures possess effective transverse isotropy with spatially variable symmetry directions. It is important to know the magnitudes of imaging errors that may be introduced by passive-source RTM when seismic anisotropy is treated in an incorrect way. In this paper, we investigate the influence of elastic anisotropy on teleseismic P-to-S conversions at the lithospheric discontinuities and explain why an isotropic RTM may fail to focus the converted wavefields from the perspective of relative arrival time variations with backazimuth and shear wave splitting. Accordingly, we extend the passive-source RTM approach for imaging 3-D lithospheric targets possessing transverse isotropy from the following two aspects: First, the teleseismic recordings with direct P and converted S phases are reverse-time extrapolated using rotated staggered grid (RSG) pseudospectral method, which can tackle strong heterogeneity and transverse isotropies with symmetry axes in arbitrary direction; Secondly, the backward elastic wavefields are efficiently decomposed into vector anisotropic P and S modes to support accurate imaging.

Baseline monitoring for time-lapse pressure tomography: Initial results from Otway Stage 3

As part of the CO2CRC Otway stage 3 project, time-lapse cross-well pressure tomography methods are being developed to demonstrate unobtrusive, continuous and low-cost monitoring of an injected CO2 plume. Active pressure tomography relies on a robust baseline set of water injections and environmental monitoring to characterise the aquifer in its base state, before CO2 has been injected. Here, we report the initial results from such baseline testing. In late 2019, 4 new monitoring wells were drilled (CRC-4 to 7), in addition to the existing CRC-2 well (where CO2 injection occurred during the stage 2C project) and the CRC-3 well which is the primary CO2 injection well for stage 3. These wells were completed in the Paaratte aquifer formation at depth ≈1500m TVD. Two sets of baseline test sequences were performed, with water injection occurring sequentially at CRC-4, 5, 6 and 7, with all wells (including CRC-2 and 3) continuously monitoring the subsurface pressure. High-quality downhole, surface and weather data were acquired for each sequence, with monitored downhole pressures generally repeatable to within the base environmental noise level. An adjoint Bayesian inversion method was developed to invert for the depth-averaged aquifer petrophysical properties, based on the monitored pressure signals. The Bayesian framework utilised prior aquifer information - interpreted faults and an independently developed geological static model - to inform and constrain the inversion. The resulting baseline model is able to capture the complex time-series pressure propagation across the aquifer subject to the various water injections. Heterogeneous regions of permeability, porosity and aquifer thickness account for the subtle variations in pressure peak arrival time and magnitude observed at the various wells, with spatial variations at a resolution that is a small fraction of the well spacing. The baseline injections and aquifer model provide a robust base for repeat water injections once CO2 has been injected in the next stages of the project.

A case study of consistent vehicle routing problem with time windows

AbstractWe develop a heuristic for the consistent vehicle routing problem with time windows (ConVRPTW), which is motivated by a real‐world application at a food company's distribution center. Besides standard VRPTW restrictions, ConVRPTW assigns each customer just one driver to fulfill his or her orders during the whole multiperiod planning horizon. For each driver and period, a route is sought to serve all their customers with positive demand. For each customer, the number of periods between consecutive orders and the ordered quantities is highly irregular. This causes difficulties in the daily routing, negatively impacting the service level of the company. Similar problems have been studied as ConVRP, where the number of drivers is fixed a priori, and only the total travel time is minimized. Moreover, the clients present no time window constraints, but the visits should be scheduled with a small arrival time variation. In our model, the objective is to minimize the number of drivers. We impose hard time windows but do not consider time consistency in more detail. We compare solutions given by the heuristic with solutions of a mixed‐integer linear programming model on a set of small artificial instances and solutions used by the food company on real‐world instances. The results show the effectiveness of the heuristic. For the company, we obtain significant improvements in the routing plans, with a lower number of vehicles and a higher rate of orders delivered within the prescribed time window.

Multi-objective periodic cash transportation problem with path dissimilarity and arrival time variation

This paper introduces a multi-objective periodic routing problem in the context of cash transportation, which attempts to increase security by generating unpredictable alternative paths and spreading arrival times at each demand node. The current study covers the shortcomings of previous models on dissimilar routing and cash transportation problems from several aspects. The studied problem has three objectives, including completion times, risk of robbery, and customers’ satisfaction level considering the effects of traffic congestion as a daily phenomenon. On top of these, we extend the studied routing problem in multigraph setting, which can keep a set of efficient paths with multiple attributes (e.g., risk, time). Such representation enables us to evoke dissimilar route plans not only by reordering the sequence of nodes but also by employing alternative links even in a fix sequence of nodes. To handle the computational challenges arising from these properties, we propose a new evolutionary algorithm based on NSGA-II. The proposed method is embedded with a fuzzy logic technique to guide the applied operators and benefits from caching memory to accelerate and diversify the searching process. The results of implementing the proposed algorithm on test instances confirm the effectiveness of our method in compression to standard NSGA-II. In addition, our performed sensitivity analyses show that the multigraph setting can substantially improve the quality of solutions with respect to all studied objectives.

Self-similar stochastic slip distributions on a non-planar fault for tsunami scenarios for megathrust earthquakes

Megathrust earthquakes that occur repeatedly along the plate interface of subduction zones can cause severe damage due to strong ground motion and the destructive tsunamis they can generate. We developed a set of scenario earthquakes to evaluate tsunami hazards and tsunami early warning systems for such devastating earthquakes. Although it is known that the slip distribution on a fault strongly affects the tsunami height distribution in near-field coastal areas, the slip distribution of future earthquakes cannot be exactly predicted. One way to resolve this difficulty is to create a set of scenario earthquakes in which a set of heterogeneous slip distributions on the source fault is stochastically generated based on a given slip probability density function (SPDF). The slip distributions generated in this manner differ from event to event, but their average over a large ensemble of models converges to a predefined SPDF resembling the long-term average of ruptures on the target fault zone. We created a set of SPDF-based scenario earthquakes for an expected future Mw 8.2 Tonankai earthquake in the eastern half of the Nankai trough, off southwest Japan, and computed the ensuing tsunamis. We found that the estimated peak coastal amplitudes among the ensemble of tsunamis along the near-field coast differed by factors of 3 to 9, and the earliest and latest arrivals at each observation site differed by 400 to 700 s. The variations in both peak tsunami amplitude and arrival time at each site were well approximated by a Gaussian distribution. For cases in which the slip distribution is unknown, the average and standard deviation of these scenario datasets can provide first approximations of forecast tsunami height and arrival time and their uncertainties, respectively. At most coastal observation sites, tsunamis modeled similarly but using a uniform slip distribution underpredicted tsunami amplitudes but gave earlier arrival times than those modeled with a heterogeneous slip distribution. Use of these earlier arrival times may be useful for providing conservative early warnings of tsunami arrivals. Therefore, tsunami computations for both heterogeneous and uniform slip distributions are important for tsunami disaster mitigation.Graphical abstract

Stochastic terminal flight arrival and departure scheduling problem under performance-based navigation environment

Flight arrival and departure scheduling (FAADS) problem, one of the critical tasks in terminal air traffic operation, faces new challenges as the terminal air traffic management has transformed to adapt to the performance-based navigation (PBN) environment; beside of that, the terminal system uncertainties which are usually due to the time-varying interference of the convective weather and flight arrival time will also exacerbate the difficulty to realize an efficient terminal air traffic operation. In order to effectively address the above issues, we propose the formulation and solution approach for a stochastic terminal FAADS problem under PBN environment. The proposed FAADS problem formulation combines the flexible 4-dimensional trajectory requirement under PBN environment and the stochastic quantifications both from the convective weather and flight arrival time uncertainties, which can finally make the FAADS results realize the avoidance of the convective weather and immunity of the flight arrival time variations within tolerable risk probabilities. We provide an efficient solution approach to tackle this problem with complex mixed integer and nonlinear programming basics and illustrate the capabilities of the solution approach by a test case on real terminal system in Shanghai Metroplex. Numerical results demonstrate the effectiveness of proposed problem formulation and solution approach.

The dimensions of scatterers in the lower mantle using USArray recordings of S-wave to P-wave conversions

Seismic recordings from the USArray of the October 1, 2013 Sea of Okhotsk earthquake and the May 24, 2010 Western Brazil earthquake include high-amplitude SxP signals due to S-wave to P-wave scattering about 150 to 200 km below the 660-km discontinuity below these events. The scattering structures have been mapped previously and interpreted as fragments of folded crust that subducted into the uppermost lower mantle. The USArray recordings are unique because SxP is visible at all stations of the USArray over a distance of 2000 km. The arrival times of SxP with respect to the P arrival times vary by 2–3 s across the USArray.The 2–3 s arrival time variations of SxP suggest the finite dimensions of the scattering structures. We estimate the dimensions by beamforming waveforms for subsets of USArray stations and the uncertainty ranges by bootstrapping. In our analysis we assume that the high-frequency wave traveltimes can be modeled using ray theory and that wave-speed heterogeneity between the scattering point and the array does not affect SxP-P differential traveltimes. The results indicate that the scattering structures beneath the Sea of Okhotsk and western Brazil have dimensions of 20–160 km but the uncertainties are large. The variation of the SxP amplitude by a factor of two to three is likely due to the complex geometry of the folded crust. We attribute the down-and-up SxP waveform to the interference of S-wave to P-wave conversions at the top and bottom of a 10–20 km thick portion of the folded crust. Our results suggest that the subducted crust can retain thicknesses of 10–20 km even after being folded by subduction into the viscous lower mantle.

Hydrodynamics of Palu Bay during the Event of 2018 Palu Earthquake and Tsunami

The devastation of coastal area in Palu Bay few minutes after the September 28th, 2018 Sulawesi earthquake showed high variation of tsunami arrival time as well as the tsunami run-up and inundation. Recent findings showed that both local submarine landslides and the normal-slip components inside the Palu Bay may contribute to the generation of tsunami. However, the fact that the event occurred during high tide, the hydrodynamic characteristics of this narrow bay and their role in the dynamics of the generated of tsunami were unknown. Hydrodynamics simulation (Mike21-flow model) using the latest available bathymetry field data (the 2018 deep water of the Indonesian navy data and 2015 shallow water of the BIG data) was conducted to investigate the variation of sea levels and tidal currents within the bay during the event of earthquake and tsunami or within the first 8 minutes timeframe. Results showed that significant increase of water elevation up to 6 cm and current velocity up to 1 cm/s directed towards the city of Palu were observed that may contribute to the dynamics of the tsunami e.g. the speed of tsunami arrival time and the transformation of tsunami. Therefore, considering that multiple tsunami arrivals were in few minutes after the earthquakes, the hydrodynamics of Palu Bay during the event should also be considered in future tsunami simulation scenarios.

Simplifying CPS Application Development through Fine-grained, Automatic Timeout Predictions

Application development for Cyber Physical Systems (CPS) is challenging, because the wireless network and the devices introduce latencies that vary continuously along with the load, status, or environmental conditions of the infrastructure. Reactive programming is well suited for the development of event-driven applications, yet current reactive programming frameworks require developers to predict event arrival time-boundaries at compile time, which is impractical, if not impossible, for CPS. Thus, there is a tradeoff between timeliness and completeness of complex event computations, e.g., operational efficiency in a manufacturing plant: Waiting too long until all individual events arrive can fail to produce a useful result, while not waiting long enough may lead to faults due to incomplete status information. In this article, we propose (a) a set of extensions to state-of-the-art reactive programming frameworks, which remove the burden of specifying timeouts at compile time by utilizing (b) Khronos, a middleware that automatically determines timeouts by taking into account variations in event arrival times due to the underlying infrastructure. Evaluation on a physical testbed shows that the extensions significantly decrease developer effort and that Khronos considerably improves timeliness under varying network configurations and conditions, while still satisfying the application’s tolerance to missed events.

Heterospecific information supports a foraging mutualism between corvids and raptors

Although animal social information is most commonly utilized by conspecifics, some conditions may favour heterospecific transmission. Generalists living in social groups are thought to produce information that is conspicuous and broadly useful to other species. Information may be signalled intentionally to other species when the sender benefits. We examined these predictions in a scavenger guild comprising two generalist social corvids (ravens, Corvus corax; magpies, Pica hudsonia), four raptor species and coyotes, Canis latrans. We used game cameras to monitor scavenging at 89 mule deer, Odocoileus hemionus, carcasses in Oregon and Washington, U.S.A. Corvid appearance times explained variation in golden eagle, Aquila chrysaetos, bald eagle, Haliaeetus leucocephalus, hawk (Buteo jamaicensis and Buteo lagopus) and coyote arrivals, indicating that raptors and canids use corvids to locate food. Larger numbers of magpies, but not ravens, were associated with shorter raptor appearance times, providing partial support for the importance of group size in broadcasting information to heterospecifics. We also directly observed simulated carcasses composed of a deer hide and antler. Seventy one corvids and 13 raptors appeared among 16 treatments accompanied by raven decoys and playbacks, whereas only one corvid and no raptors appeared at paired controls. The time that ravens first flew in circles above a simulated carcass explained 98% of the variation in subsequent raptor arrival time, indicating that a specific raven behaviour provides a cue of carrion. After hide-cutting raptors opened a carcass, corvids benefited by switching from feeding at the eyes and the anus to feeding on flesh. However, raptors did not arrive sooner after corvids at closed carcasses than experimentally pre-opened carcasses, suggesting that corvids do not intentionally transmit more information to raptors when a carcass requires opening, at least under these conditions. A scavenging mutualism with corvids built on carrion discovery and access, but not intentional recruitment, may facilitate winter survival of raptors.

A Generalized H‐κ Method With Harmonic Corrections on Ps and Its Crustal Multiples in Receiver Functions

AbstractThe H‐κ method (Zhu &amp; Kanamori, 2000, https://doi.org/10.1029/1999JB900322) has been widely used to estimate the crustal thickness (H) and the ratio of P to S velocities (VP/VS ratio, κ) with receiver functions. However, in regions where the crustal structure is complicated, the method may produce biased results, arising particularly from dipping Moho and/or crustal anisotropy. H‐κ stacking in case of azimuthal or radial anisotropy with flat Moho has been proposed but not for cases with plunging anisotropy and dipping Moho. Here we propose a generalized H‐κ method called H‐κ‐c, which corrects for these effects first before stacking. We consider rather general cases, including plunging anisotropy and dipping interfaces of multiple layers, and use harmonic functions to correct for arrival time variations of Ps and its crustal multiples with back azimuth (θ). Systematic synthetic tests show that the arrival time variations can be well fitted by cosθ and cos2θ functions even for very complex crustal structures. Correcting for the back azimuthal variations significantly enhances H‐κ stacking. We verify the feasibility of the H‐κ‐c method by applying it to 40 permanent stations in various geological setting across the Mainland China. The results show clear improvement after the harmonic corrections, with clearer multiples and stronger stacking energy, as well as more reliable H‐κ values. Large differences in H (up to 5.0 km) and κ (up to 0.09) between the new and traditional methods occur mostly in mountainous regions, where the crustal structure tends to be more complex. We caution in particular about systematic bias when the traditional method is used in the presence of dipping interfaces. The modified method is simple and applicable anywhere in the world.