Travel Times Of Phases Research Articles

Shallow Focal Depths of the 2022 Ms 6.8 Luding Earthquake and Its M ≥3 Aftershocks

Abstract The accurate determination of earthquake focal depths is crucial, yet notably challenging. The 2022 Ms 6.8 Luding earthquake sequence is a typical example for which focal depths remain controversial. In this study, we conducted a comprehensive regional waveform analysis, including depth-phase waveform modeling and relative location methods, to determine the focal depths of the Ms 6.8 mainshock and its M ≥ 3 aftershocks. Specifically, we first inverted the focal mechanisms of these events using the generalized cut-and-paste method. We then determined their absolute focal depths using array-based stacking and Pn depth-phase modeling. For events without clear depth phases, we calculated their relative depths with respect to the known ones using differential travel times of Pg, Sg, and Pn phases. Our results indicate that the mainshock’s hypocenter lies at a depth of 11 km, whereas its centroid appears at a shallower depth of ∼6.5 km. All M ≥ 3 aftershocks are located within a narrow depth range of 3–7 km, in contrast to the deeper focal depths previously obtained using conventional travel-time-based location methods. This shallow seismogenic depth aligns well with the rheological behavior of the crust along the southern Xianshuihe fault, in which the brittle–ductile transition depth is estimated to be about 10km. Our results reveal that the mainshock nucleated at the base of the seismogenic zone and ruptured toward the shallower portion, consistent with the geodetically constrained mainshock slip distribution. Our study also emphasizes the necessity of caution when interpreting focal depths determined by routine travel-time-based methods, especially in regions with sparse seismic station coverage.

Investigation of Phase Shift and Travel Time of Acoustic Waves in the Lower Solar Atmosphere Using Multiheight Velocities

We report and discuss the phase shift and phase travel time of low-frequency (ν < 5.0 mHz) acoustic waves estimated within the photosphere and photosphere–chromosphere interface regions, utilizing multiheight velocities in the quiet Sun. The bisector method has been employed to estimate seven height velocities in the photosphere within the Fe i 6173 Å line scan, while nine height velocities are estimated from the chromospheric Ca ii 8542 Å line scan observations obtained from the narrowband imager instrument installed on the Multi-Application Solar Telescope operational at the Udaipur Solar Observatory, India. Utilizing a fast Fourier transform at each pixel over the full field of view, phase shift and coherence have been estimated. The frequency and height-dependent phase shift integrated over the regions having an absolute line-of-sight magnetic field of less than 10 G indicates the nonevanescent nature of low-frequency acoustic waves within the photosphere and photosphere–chromosphere interface regions. Phase travel time estimated within the photosphere shows nonzero values, aligning with previous simulations and observations. Further, we report that the nonevanescent nature persists beyond the photosphere, encompassing the photospheric–chromospheric height range. We discuss possible factors contributing to the nonevanescent nature of low-frequency acoustic waves. Additionally, our observations reveal a downward propagation of high-frequency acoustic waves indicating refraction from higher layers in the solar atmosphere. This study contributes valuable insights into the understanding of the complex dynamics of acoustic waves within different lower solar atmospheric layers, shedding light on the nonevanescent nature and downward propagation of the acoustic waves.

Two Mechanisms Generating Intraplate Volcanism in Southeast Asia: Insights From Mantle Transition Zone Discontinuities

AbstractDetermining the mechanisms responsible for intraplate volcanism ‐ such as slab devolatilization melting versus active mantle plumes ‐ remains a challenge. The greater South China Sea (SCS) region has experienced extensive intraplate Cenozoic volcanism across areas including Hainan, Southeast Indochina, northern Borneo, the northern SCS, and the post‐spreading SCS basin. The prevalence of volcanism distributed widely across this region prompts fundamental questions about the key geodynamic processes driving such diverse magmatic activities. In this study, we elucidate the mantle transition zone (MTZ) discontinuities in this region using SS precursors, which helps to overcome the sparse seismic coverage due to its predominantly oceanic setting. We collected over 16,000 high‐quality seismograms that sample the upper mantle and MTZ beneath this region from global earthquakes and stations. After correcting for the effects of shallow crustal variations and upper mantle heterogeneity on traveltimes of SS phases and their precursors, we unveil lateral variations in the MTZ boundaries (d410 and d660) and intricate features of the mid‐MTZ reflectors (S520S). Significant MTZ thinning and normal S520S waveforms beneath Hainan provide compelling evidence for mantle upwelling through the MTZ. Conversely, the evident splitting of S520S beneath the northern SCS, Southeast Indochina, and northern Borneo, all characterized by stagnant subducted slabs, indicates that the volcanism in these regions likely originated from a mechanism distinct from the active upwelling beneath Hainan. Dehydration melting attributed to devolatilizing stagnant slabs in the MTZ is a potential cause for Cenozoic volcanism in these regions.

Crustal Velocity Structure of the Sichuan–Yunnan Block Revealed by High-Quality Crustal Phase Travel Time

Abstract The Sichuan–Yunnan block is located at the southeastern margin of the Tibetan Plateau, which is the key area as a transition belt from the active plate extrusion zone to the stable Yangtze Craton. Using a semiautomatic measuring method based on a graphical interface, we pick 81,585 precise travel times from 449 local earthquake records and finally obtain a crustal 3D P-wave velocity model of the Sichuan–Yunnan block. The model reveals an unexpected velocity contrast between the shallower and deeper crusts. It is summarized as weakly perturbed low-velocity belts encircling a high-velocity zone in the upper crust and strongly perturbed low-velocity anomalies in the mid-lower crust, respectively. The weak low-velocity anomalies are revealed along the major strike-slip faults, and their small perturbations may imply a slip-driven mechanism. The strong low-velocity anomalies are distributed extensively in the Sichuan–Yunnan block, and their great perturbations may be related to the partial melting of weak material extruded from Tibet. Besides, our result shows noticeable high-velocity anomalies in the core zone of the Emeishan Large Igneous Province (ELIP), which may be an indication of magma solidification from the ancient mantle plume. The result further exhibits an interesting pattern that the strong low-velocity anomalies are partially separated by the high-velocity anomalies in the ELIP. Such a specific pattern probably reflects that the stable zone in the ELIP leads to the bifurcation of weak Tibetan material.

Topography‐Incorporated Adjoint‐State Surface Wave Traveltime Tomography: Method and a Case Study in Hawaii

AbstractIn this study we recast surface wave traveltime tomography as an inverse problem constrained by an eikonal equation and solve it using the efficient adjoint‐state method. Specifically, recognizing that large topographic variations and high surface wave frequencies can make the topographic effect too significant to ignore, we employ an elliptically anisotropic eikonal equation to describe the traveltime fields of surface waves on undulated topography. The sensitivity kernel of the traveltime objective function with respect to shear wave velocity is derived using the adjoint‐state method. As a result, the newly developed method is inherently applicable to any study regions, whether with or without significant topographic variations. Hawaii is one of the most seismically and magmatically active regions. However, its significant topographic variations have made it less accurate to investigate using conventional surface wave traveltime tomography methods. To tackle this problem, we applied our new method to invert ambient noise Rayleigh wave phase traveltimes and construct a 3D shear wave velocity model. Our results reveal features that are consistent with geological structures and previous tomography results, including high velocities below Mauna Loa Volcano and Kilauea Volcano, and low velocities beneath the Hilina Fault Zone. Additionally, our model reveals a high‐velocity anomaly to the South of Hualalai's summit, which may be related to a buried rift zone. Our findings further demonstrate that including topography can lead to a correction of up to 0.8% in the shear wave velocity model of Hawaii, an island spanning approximately 100 km with volcanoes reaching elevations exceeding 4 km.

Ambient‐Noise Wave‐Equation Tomography of the Alps and Ligurian‐Provence Basin

AbstractTaking benefit of the AlpArray temporary network and permanent networks in W‐Europe, we construct a 3‐D onshore‐offshore velocity model of the crust and upper mantle using ambient‐noise wave‐equation tomography. We use a frequency‐dependent phase traveltime misfit function in an iterative procedure to refine a recent 3‐D Vs model computed from a Bayesian two‐step ambient noise tomography. Observed waveforms consist of vertical‐component noise correlations from 600 broadband stations in the Alps and surroundings, including ocean‐bottom seismometers in the Ligurian sea. We perform 3‐D inversion in the 5–85 s period range. In the long‐period band (20–85 s), an elastic approximation is considered, while in the 5–20 s band, we account for the effect of water layer in the Ligurian sea by applying a fluid‐solid coupling for acoustic‐elastic waveform simulations. The resulting Vs model enhances the shape and contrast of velocity structures, accounting for 3‐D and finite‐frequency effects. It emphasizes the deep sediments of the Ligurian‐Provence basin and focuses on the low‐velocity anomalies of the crust in the W‐Alps. We obtain a high‐resolution Moho depth map covering the Alps and Ligurian sea. In the W‐Alps, this map confirms the deepening of the European crust following the subduction beneath Adria and the existence of major structures such as the Moho jump beneath the external crystalline massifs and shallow depths associated with the Ivrea Body. It provides further constraints on the deep structure beneath the Ligurian‐Provence basin, regarding the lateral and along‐strike crustal‐thickness variations from the oceanic domain to the conjugate margins.

Exploring the Connection between Helioseismic Travel Time Anomalies and the Emergence of Large Active Regions during Solar Cycle 24

We investigate deviations in the mean phase travel time of acoustic waves preceding the emergence of 46 large active regions observed by the Helioseismic and Magnetic Imager. In our investigation, we consider two different procedures for obtaining the mean phase travel time, by minimizing the difference between cross-correlations and a reference, as well as the Gabor wavelet fitting procedure. We cross-correlate the time series of mean phase travel time deviations with the surface magnetic field and determine the peak correlation time lag. We also compute the perturbation index—the area integrated mean phase travel time deviations exceeding quiet Sun thresholds—and compare the time of peak perturbation index with the correlation time lag. We find that the lag times derived from the difference minimization procedure precede the flux emergence for 36 of the 46 active regions, and that this lag time has a noticeable correlation with the maximum flux rate. However, only 28 of the active regions have peak perturbation index times in the range of 24–48 hr prior to the flux emergence. Additionally, we examine the relationship between the properties of the emerged active regions and the strength of helioseismic signals prior to their emergence.

Mars Seismology

For the first time, from early 2019 to the end of 2022, Mars’ shallow and deep interiors have been explored by seismology with the InSight mission. Thanks to the performances of its seismometers and the quality of their robotic installation on the ground, 1,319 seismic events have been detected, including about 90 marsquakes at teleseismic distances, with Mw from 2.5 to 4.7 and at least 6 impacts, the largest ones with craters larger than 130 m. A large fraction of these marsquakes occur in Cerberus Fossae, demonstrating active regional tectonics. Records of pressure-induced seismic noise and signals from the penetration of a heat flow probe have provided subsurface models below the lander. Deeper direct and secondary body wave phase travel time, receiver function, and surface wave analysis have provided the first interior models of Mars, including crustal thickness and crustal layering, mantle structure, thermal lithospheric thickness, and core radius and state. ▪ With InSight's SEIS (Seismic Experiment for Interior Structure of Mars) experiment and for the first time in planetary exploration, Mars’ internal structure and seismicity are constrained. ▪ More than 1,300 seismic events and seismic noise records enable the first comparative seismology studies together with Earth and lunar seismic data. ▪ Inversion of seismic travel times and waveforms provided the first interior model of another terrestrial planet, down to the core. ▪ Several impacts were also seismically recorded with their craters imaged from orbit, providing the first data on impact dynamic on Mars.

Imaging the Earth Using Time‐Domain Surface‐Wave Measurements: Evaluation and Correction of the Finite‐Frequency Phase Shift

AbstractSurface waves propagating from earthquakes, active sources or within the ambient noise wavefield are widely used to image Earth structure at various scales, from centimeters to hundreds of kilometers. The accuracy of surface‐wave, phase‐velocity measurements is essential for the accuracy of the Earth models they constrain. Here, we identify a finite‐frequency phase shift in the phase travel time that causes systematic errors in time‐domain, phase‐velocity measurements. The phase shift arises from the approximation of monochromatic surface waves with narrow‐band filtered surface waves. We derive an explicit formula of the finite‐frequency phase shift and present a numerical method for its evaluation and for the correction of the measurements. Applications to high‐frequency and long‐period examples show that the phase shift is typically around π/60‐π/16 for the common settings of ambient‐noise imaging studies, which translates to 0.2%–0.8% phase‐velocity measurement errors. The finite‐frequency phase shift depends on the (a) second derivative of the wavenumber with respect to frequency; (b) width of the narrow‐band filter; (c) epicentral or interstation distance; and (d) center frequency of the filter. In conversion to phase velocity, the last two factors cancel out. Frequency‐domain methods for phase‐velocity measurements have the advantage of not producing the finite‐frequency phase shift. Both time‐ and frequency‐domain measurements, however, can be impacted by a break‐down of the far‐field approximation (near‐field phase shift), which our calculations also show. Our method offers an effective means of improving the accuracy of the widely used time‐domain, phase‐velocity measurements via the evaluation of and corrections for the finite‐frequency phase shift.

Detection of Travel Time Anisotropy from Subsurface Horizontal Magnetic Fields

A time–distance measurement technique is derived to isolate phase travel time anisotropy caused by subsurface horizontal magnetic fields; a method that uses the measured anisotropy to estimate the field’s orientation is also derived. A simulation of acoustic waves propagating in a uniform, inclined magnetic field with solar background structure is used to verify the derived technique. Then the procedure is applied to a numerical simulation of a sunspot for which the subsurface state is known to provide context for the results obtained from the study of several sunspots observed by the Helioseismic and Magnetic Imager. Significant anisotropies are detected, on the order of 1 minute, and the subsurface field’s azimuth is estimated and compared with the azimuth of the surface magnetic field. In all cases, the subsurface azimuth is found to be well aligned with that of the surface, and the results from the numerical simulation are used to interpret features in the detected travel time anisotropy.

Determination of near-surface shear-velocity structure based on the joint inversion of Rayleigh-wave dispersion and ellipticity from multistation active-seismic records

The dispersive characteristics of high-frequency (≥2 Hz) Rayleigh waves have been widely applied to determine subsurface shear velocity ([Formula: see text]). However, the [Formula: see text] of the high-velocity surface layers (e.g., rigid roads in urban areas) and underlying layers is poorly constrained in the Rayleigh-wave dispersion inversion. Compared to the phase velocity, the Rayleigh-wave horizontal-to-vertical (H/V) ratios of particle motion (i.e., ellipticity) are particularly sensitive to shallow [Formula: see text] structures. Therefore, we have proposed a robust method for obtaining near-surface [Formula: see text] structures by inverting Rayleigh-wave dispersion and H/V data. Initially, we separate the fundamental-mode Rayleigh waves from the active-seismic records using a high-resolution linear Radon transformation method. Then, we extract the high-frequency H/V and interstation phase traveltimes from the separated fundamental mode using deconvolution interferometry and the frequency-time analysis method. Based on the phase traveltimes, we calculate the phase velocity dispersion using ray-based tomography. Finally, we perform the joint inversion of dispersion and H/V data to obtain the [Formula: see text] structure. According to the inversion results of synthetic and field data, the accuracy of the [Formula: see text] in the rigid surface layer and underlying layers is considerably improved. We find that the joint inversion of Rayleigh-wave phase velocity dispersion and H/V data from surface-wave surveys is a useful tool for accurately determining the complex shallow [Formula: see text] structures.

Azimuthal anisotropy from eikonal tomography: example from ambient-noise measurements in the AlpArray network

SUMMARY Ambient-noise records from the AlpArray network are used to measure Rayleigh wave phase velocities between more than 150 000 station pairs. From these, azimuthally anisotropic phase-velocity maps are obtained by applying the eikonal tomography method. Several synthetic tests are shown to study the bias in the Ψ2 anisotropy. There are two main groups of bias, the first one caused by interference between refracted/reflected waves and the appearance of secondary wave fronts that affect the phase traveltime measurements. This bias can be reduced if the amplitude field can be estimated correctly. Another source of error is related to the incomplete reconstruction of the traveltime field that is only sparsely sampled due to the receiver locations. Both types of bias scale with the magnitude of the velocity heterogeneities. Most affected by the spurious Ψ2 anisotropy are areas inside and at the border of low-velocity zones. In the isotropic velocity distribution, most of the bias cancels out if the azimuthal coverage is good. Despite the lack of resolution in many parts of the surveyed area, we identify a number of anisotropic structures that are robust: in the central Alps, we find a layered anisotropic structure, arc-parallel at mid-crustal depths and arc-perpendicular in the lower crust. In contrast, in the eastern Alps, the pattern is more consistently E–W oriented which we relate to the eastward extrusion. The northern Alpine forleand exhibits a preferential anisotropic orientation that is similar to SKS observations in the lowermost crust and uppermost mantle.

Denoising Surface Waves Extracted From Ambient Noise Recorded by 1‐D Linear Array Using Three‐Station Interferometry of Direct Waves

AbstractWe develop an automatic workflow for enhancing surface wave signals in ambient noise cross correlations (ANCs) calculated for a one‐dimensional (1‐D) linear array. The proposed array‐based method is applied to a 1.6 km‐long dense linear nodal array crossing surface traces of the San Jacinto fault near Anza, California. Fundamental and higher modes of surface waves are observed in ANCs of the nodal array. After attenuating the surface wave overtones by applying a frequency‐dependent tapering window to the ANCs, signals dominated by the fundamental mode surface wave are then enhanced through a denoising process based on three‐station interferometry of direct waves. The signal‐to‐noise ratio is significantly increased at high frequencies (&gt;2 Hz) after denoising. Phase travel times are extracted reliably in the frequency domain for the period ranges of 0.3–1.2 s and 0.3–1.6 s for Rayleigh and Love waves, respectively. The corresponding period‐dependent phase velocity profiles derived from the eikonal equation reveal high‐resolution details of fault zone internal structures beneath the array. A broad (500–1,000 m) low‐velocity zone that narrows with increasing period is observed, illuminating a flower‐shaped structure of the San Jacinto fault damage zone.

Analysis of Time–Distance Helioseismology for Detection of Emerging Active Regions

Abstract A time–distance helioseismic technique, similar to the one used by Ilonidis et al., is applied to two independent numerical models of subsurface sound-speed perturbations to determine the spatial resolution and accuracy of phase travel time shift measurements. The technique is also used to examine pre-emergence signatures of several active regions observed by the Michelson Doppler Imager and the Helioseismic Magnetic Imager. In the context of similar measurements of quiet-Sun regions, three of the five studied active regions show strong phase travel time shifts several hours prior to emergence. These results form the basis of a discussion of noise in the derived phase travel time maps and possible criteria to distinguish between true and false-positive detection of emerging flux.

3D Seismic Velocity Models for Alaska from Joint Tomographic Inversion of Body-Wave and Surface-Wave Data

AbstractWe present two new seismic velocity models for Alaska from joint inversions of body-wave and ambient-noise-derived surface-wave data, using two different methods. Our work takes advantage of data from many recent temporary seismic networks, including the Incorporated Research Institutions for Seismology Alaska Transportable Array, Southern Alaska Lithosphere and Mantle Observation Network, and onshore stations of the Alaska Amphibious Community Seismic Experiment. The first model primarily covers south-central Alaska and uses body-wave arrival times with Rayleigh-wave group-velocity maps accounting for their period-dependent lateral sensitivity. The second model results from direct inversion of body-wave arrival times and surface-wave phase travel times, and covers the entire state of Alaska. The two models provide 3D compressional- (VP) and shear-wave velocity (VS) information at depths ∼0–100 km. There are many similarities as well as differences between the two models. The first model provides a clear image of the high-velocity subducting plate and the low-velocity mantle wedge, in terms of the seismic velocities and the VP/VS ratio. The statewide model provides clearer images of many features such as sedimentary basins, a high-velocity anomaly in the mantle wedge under the Denali volcanic gap, low VP in the lower crust under Brooks Range, and low velocities at the eastern edge of Yakutat terrane under the Wrangell volcanic field. From simultaneously relocated earthquakes, we also find that the depth to the subducting Pacific plate beneath southern Alaska appears to be deeper than previous models.

Imaging Alpine crust using ambient noise wave-equation tomography

SUMMARYWe present an improved crustal Vs model and Moho depth map using ambient noise wave-equation tomography. The so-called ‘ambient noise wave-equation tomography’ is a method to invert seismic ambient noise phase dispersion data based on elastic waveform simulation, which accounts for 3-D and finite-frequency effects. We use cross-correlations of up to 4 yr of continuous vertical-component ambient seismic noise recordings from 304 high-quality broad-band stations in the Alpine region. We use model LSP_Eucrust1.0 obtained from traditional ambient noise tomography as initial model, and we iteratively improve the initial model by minimizing frequency-dependent phase traveltime differences between the observed and synthetic waveforms of Rayleigh waves in the period range 10–50 s. We obtain the final model after 15 iterations with ∼65 per cent total misfit reduction compared to the initial model. At crustal depth, the final model significantly enhances the amplitudes and adjusts the shapes of velocity anomalies. At Moho and upper-mantle depth, the final model corrects an obvious systematic velocity shift of the initial model. The resulting isovelocity Moho map confirms a Moho step along the external side of the external crystalline massifs of the northwestern Alps and reveals underplated gabbroic plutons in the lower most crust of the central and eastern Alps. Ambient noise wave-equation tomography turns out to be a useful tool to refine shear wave velocity models obtained by traditional ambient noise tomography based on ray theory.

Magmatic and Sedimentary Structure beneath the Klyuchevskoy Volcanic Group, Kamchatka, From Ambient Noise Tomography

AbstractThe Klyuchevskoy Volcanic Group is a cluster of the world's most active subduction volcanoes, situated on the Kamchatka Peninsula, Russia. The volcanoes lie in an unusual off‐arc position within the Central Kamchatka Depression (CKD), a large sedimentary basin whose origin is not fully understood. Many gaps also remain in the knowledge of the crustal magmatic plumbing system of these volcanoes. We conducted an ambient noise surface wave tomography, to image the 3‐D shear wave velocity structure of the Klyuchevskoy Volcanic Group and CKD within the surrounding region. Vertical component cross correlations of the continuous seismic noise are used to measure interstation Rayleigh wave group and phase traveltimes. We perform a two‐step surface wave tomography to model the 3‐D Vsv velocity structure. For each inversion stage we use a transdimensional Bayesian Monte Carlo approach, with coupled uncertainty propagation. This ensures that our model provides a reliable 3‐D velocity image of the upper 15 km of the crust, as well as a robust assessment of the uncertainty in the observed structure. Beneath the active volcanoes, we image small slow velocity anomalies at depths of 2–5 km but find no evidence for magma storage regions deeper than 5 km—noting the 15 km depth limit of the model. We also map two clearly defined sedimentary layers within the CKD, revealing an extensive 8 km deep sedimentary accumulation. This volume of sediments is consistent with the possibility that the CKD was formed as an Eocene‐Pliocene fore‐arc regime, rather than by recent (&lt;2 Ma) back‐arc extension.

Eikonal Tomography of the Southern California Plate Boundary Region

AbstractWe use Eikonal tomography to derive phase and group velocities of surface waves for the plate boundary region in Southern California. Seismic noise data in the period range 2 and 20 s recorded in year 2014 by 346 stations with ~1‐ to 30‐km station spacing are analyzed. Rayleigh and Love wave phase travel times are measured using vertical‐vertical and transverse‐transverse noise cross correlations, and group travel times are derived from the phase measurements. Using the Eikonal equation for each location and period, isotropic phase and group velocities and 2‐psi azimuthal anisotropy are determined statistically with measurements from different virtual sources. Starting with the SCEC Community Velocity Model, the observed 2.5‐ to 16‐s isotropic phase and group dispersion curves are jointly inverted on a 0.05° × 0.05° grid to obtain local 1‐D piecewise shear wave velocity (Vs) models. Compared to the starting model, the final results have generally lower Vs in the shallow crust (top 3–10 km), particularly in areas such as basins and fault zones. The results also show clear velocity contrasts across the San Andreas, San Jacinto, Elsinore, and Garlock Faults and suggest that the San Andreas Fault southeast of San Gorgonio Pass is dipping to the northeast. Investigation of the nonuniqueness of the 1‐D Vs inversion suggests that imaging the top 3‐km Vs structure requires either shorter period (≤2 s) surface wave dispersion measurements or other types of data set such as Rayleigh wave ellipticity.

Magnetic Fields and the Supply of Low-frequency Acoustic Wave Energy to the Solar Chromosphere

Abstract The problem of solar chromospheric heating remains a challenging one with wider implications for stellar physics. Several studies in the recent past have shown that small-scale inclined magnetic field elements channel copious energetic low-frequency acoustic waves, which are normally trapped below the photosphere. These magnetoacoustic waves are expected to shock at chromospheric heights, contributing to chromospheric heating. In this work, exploiting simultaneous observations of photospheric vector magnetic field, Doppler, continuum, and line-core intensity (of Fe i 6173 Å) from the Helioseismic and Magnetic Imager and lower-atmospheric UV emission maps in the 1700 and 1600 Å channels of the Atmospheric Imaging Assembly, both on board the Solar Dynamics Observatory of NASA, we revisit the relationships between magnetic field properties (inclination and strength) and the propagation of acoustic waves (phase travel time). We find that the flux of acoustic energy, in the 2–5 mHz frequency range, between the upper photosphere and lower chromosphere is in the range of 2.25–2.6 kW m−2, which is about twice the previous estimates. We identify that the relatively less inclined magnetic field elements in the quiet Sun channel a significant amount of waves of frequency lower than the theoretical minimum acoustic cutoff frequency due to magnetic inclination. We also derive indications that these waves steepen and start to dissipate within the height ranges probed, while those let out due to inclined magnetic fields pass through. We explore connections with existing theoretical and numerical results that could explain the origin of these waves.

Evaluation of traveltime tomography in estimating near‐surface velocity inversion

ABSTRACTNear‐surface velocity structures are generally inverted by ray‐based traveltime tomography in which the objective function is usually constructed using raypath traveltime residuals. However, inversion accuracy in these situations remains low due to the asymptotic assumption. On the contrary, phase and instantaneous traveltime tomographies invert frequency‐dependent traveltime rather than the asymptotic raypath version that is contained in the first‐arrival waveform for near‐surface velocities. They also take the finite‐frequency effect of the seismic wave propagation into account by using wavepaths instead of raypaths as sensitivity kernels. In this context, we firstly compare synthetic results between raypath traveltime, phase traveltime and instantaneous traveltime in this study before comparing their corresponding sensitivity kernels. We then analyse three sets of inversion results to prove that it is still an acceptable way to construct the objective function using raypath traveltime for tomography within the seismic exploration frequency band. In this way, time‐domain wave‐equation forward simulation can be avoided and therefore the computational cost can be dramatically reduced. We also demonstrate that a sensitivity kernel that takes the finite‐frequency effect into account is more important for inversion accuracy than traveltime used in tomography.