Eikonal Tomography Research Articles

Continent‐Side Uplifted Mantle and Geological Imprints Along a Paleo Rift in the Western East Sea (Sea of Japan)

AbstractWe investigate the continent‐size lithospheric structures of paleo rift around the central Korean Peninsula using ambient noise tomography and earthquake‐based Eikonal tomography based on dense seismic networks. We determine Rayleigh‐wave group velocities at periods of 1–15 s from ambient noise tomography and Rayleigh‐wave phase velocities at periods of 20–80 s from earthquake‐based Eikonal tomography. We determine a 3‐D shear‐wave velocity model in the lithosphere from the Rayleigh wave velocities. The model exhibits high lateral variations ranging from ‒9% to 8%, depending on depth. The shear‐wave velocities at shallow depths (2 km) are relatively high in mountain regions and low in coastal and basin regions. Strong velocity contrasts are observed around major earthquake hypocenters at depths of 3–20 km, which may be due to the presence of seismogenic faults. Shear‐wave velocities at depths of 30–40 km are high along the east coast, suggesting uplifted mantle that is responsible for the opening of the East Sea (Sea of Japan). High velocity structures beneath Moho around the coast may suggest solidified underplated magma caused by the paleo rifting. The root of coast‐parallel high‐mountain range (Taebaek Mountain Range) is bounded by the uplifted mantle, presenting mountain range development in rift flank along paleo‐rift axis. Low shear‐wave velocities along the coast at depths km may imply elevated temperature beneath the solidified underplated magma. The continent‐side paleo rift affects the geological, thermal, and seismological properties around the continental margin at present.

Bayesian eikonal tomography using Gaussian processes


 Eikonal tomography has become a popular methodology for deriving phase velocity maps from surface wave phase delay measurements. Its high efficiency makes it popular for handling datasets deriving from large-N arrays, in particular in the ambient-noise tomography setting. However, the results of eikonal tomography are crucially dependent on the way in which phase delay measurements are predicted from data, a point which has not been thoroughly investigated. In this work, I provide a rigorous formulation for eikonal tomography using Gaussian processes (GPs) to smooth observed phase delay measurements, including uncertainties. GPs allow the posterior phase delay gradient to be analytically derived. From the phase delay gradient, an excellent approximate solution for phase velocities can be obtained using the saddlepoint method. The result is a fully Bayesian result for phase velocities of surface waves, incorporating the nonlinear wavefront bending inherent in eikonal tomography, with no sampling required. The results of this analysis imply that the uncertainties reported for eikonal tomography are often underestimated.

Physics‐Informed Neural Networks for Elliptical‐Anisotropy Eikonal Tomography: Application to Data From the Northeastern Tibetan Plateau

AbstractWe develop a novel approach for multi‐frequency, elliptical‐anisotropic eikonal tomography based on physics‐informed neural networks (pinnEAET). This approach simultaneously estimates the medium properties controlling anisotropic Rayleigh waves and reconstructs the traveltimes. The physics constraints built into pinnEAET's neural network enable high‐resolution results with limited inputs by inferring physically plausible models between data points. Even with a single source, pinnEAET can achieve stable convergence on key features where traditional methods lack resolution. We apply pinnEAET to ambient noise data from a dense seismic array (ChinArray‐Himalaya II) in the northeastern Tibetan Plateau with only 20 quasi‐randomly distributed stations as sources. Anisotropic phase velocity maps for Rayleigh waves in the period range from 10–40 s are obtained by training on observed traveltimes. Despite using only about 3% of the total stations as sources, our results show low uncertainties, good resolution and are consistent with results from conventional tomography.

Eikonal Tomography With Physics‐Informed Neural Networks: Rayleigh Wave Phase Velocity in the Northeastern Margin of the Tibetan Plateau

AbstractWe present a novel eikonal tomography approach using physics‐informed neural networks (PINNs) for Rayleigh wave phase velocities based on the eikonal equation. The PINN eikonal tomography (pinnET) neural network utilizes deep neural networks as universal function approximators and extracts traveltimes and velocities of the medium during the optimization process. Whereas classical eikonal tomography uses a generic non‐physics based interpolation and regularization step to reconstruct traveltime surfaces, optimizing the network parameters in pinnET means solving a physics constrained traveltime surface reconstruction inversion tackling measurement noise and satisfying physics. We demonstrate this approach by applying it to 25 s surface wave data from ChinArray II sampling the northeastern Tibetan plateau. We validate our results by comparing them to results from conventional eikonal tomography in the same area and find good agreement.

Integrating controlled-source and ambient noise seismic measures for archaeological prospection: the Scrovegni Chapel case

SUMMARY In this paper, we present the results of an analysis of passive seismic noise recorded around the Scrovegni Chapel in Padua (Italy), using a dense 2-D network with nearly 1500 autonomous seismic nodes. Surface wave tomography using the active records allowed the imaging of several structures located at a depth of few metres, while this study focuses on the processing of about 22 hr of continuous passive records. First, the ambient noise is characterized in terms of amplitude, frequency content and azimuthal distribution, in order to ensure the applicability of the interferometric method. Second, a cross-correlation analysis is performed to retrieve virtual source gathers. Third, traveltimes are extracted from virtual source gathers using the same processing sequence applied to active gathers. Fourth, Eikonal tomography is run to retrieve isotropic phase velocity maps and azimuthal anisotropy. We compare and discuss the results obtained from the active and the passive methods, and finally propose a strategy for the integration of passive and active information. The new quasi-3-D shear wave velocity model obtained from the joint active and passive analysis is more accurate at depth, due to the addition of the passive low-frequency information.

Restricted lithospheric extrusion in the SE Tibetan Plateau: Evidence from anisotropic Rayleigh-wave tomography

Constraining variations of lithospheric structure and deformation across southeastern Tibet and the surrounding region are crucial for understanding the lateral growth of the plateau. Using data from two dense seismic arrays in the SE Tibetan Plateau, we obtained fine-scale Rayleigh-wave phase velocity maps by Eikonal tomography, and further inverted for 3-D shear wave velocity and azimuthal anisotropy of the crust and upper mantle. High velocities and weak lithospheric anisotropy are revealed under Dianzhong Block (DZB), where is covered by the relics of the Emeishan Large Igneous Province, while strong anisotropy is imaged around. We propose that the DZB strengthened by the paleo igneous activity plays an essential role in the evolution along the southeastern plateau margin. On the one hand, the DZB obstructs the migration of plateau material to the southeast. On the other hand, strong deformation is localized along the DZB margins, while the stress due to the plate expansion is transferred further to the Xiaojiang fault, which induced significant deformation within the Yangtze Craton. Furthermore, the lithosphere of DZB deflects the mantle flow driven by the eastward Indian subduction under the northern Indochina block.

Eikonal surface wave tomography of central and eastern China

SUMMARY Eikonal tomography has become a key approach to image lithospheric structures with surface waves recorded by dense regional arrays. Its main advantage is that phase velocities can be determined directly from phase measurements without resolving a tomographic inverse problem. Here, we apply a new smoothing spline eikonal tomography approach to a selection of 40 large (Mw larger than 6.5) teleseismic events recorded by the permanent seismic stations of the CEArray. We first apply a time–frequency filter to isolate the fundamental mode of Rayleigh waves and cross-correlate the cleaned and isolated surface wave records to measure precise relative traveltimes. The phase measurements are then unwrapped and corrected for cycle skipping. Finally, we derive phase-velocity maps from the gradient of the reconstructed traveltime fields, using the eikonal equation. We obtain finely resolved phase-velocity maps from 25 to 150 s period that are inverted to obtain a 3-D shear wave velocity model which is in good agreement with previous tomographic studies. The lithospheric architecture emerging from the phase-velocity maps and 3-D S-wave velocities correlates with surface geology and major tectonic provinces. In particular, the architecture of the narrow rift systems, the South China Craton, and the North China Craton (NCC) are revealed with unprecedented details. The South China Craton is characterized by very high velocities beneath the Sichuan Basin. The NCC shows more complex structures with two high-velocity anomalies beneath the Ordos Basin and the southeastern NCC and low-velocity anomalies beneath the Cenozoic rift systems.

Surface wave tomography using dense 3D data around the Scrovegni Chapel in Padua, Italy

A dense single-node 3D seismic survey has been carried out around the Scrovegni Chapel in Padua (Italy), in order to give new insights about the archaeological setting of the area. The survey made use of nearly 1500 vertical nodes deployed over two rectangular grids. 38 shot positions were fired all around the two receiver patches. The fundamental mode Rayleigh wave signal is here analysed: traveltimes are directly inferred from the signal phases, and phase velocity maps are obtained using Eikonal tomography. Also surface wave amplitudes are used, to produce autospectrum gradient maps. The joint analysis of phase velocity and autospectrum gradient allowed the identification of several buried features, among which possible remains of radial walls of the adjacent Roman amphitheater, structures belonging to a medieval convent, and the root area of an eradicated tree. Finally, depth inversion of 1D dispersion curves allowed the reconstruction of a quasi-3D shear-wave velocity model.

Eikonal tomography with physics informed neural networks: Rayleigh wave phase velocity in the northeastern margin of the Tibetan Plateau

Eikonal tomography with physics informed neural networks: Rayleigh wave phase velocity in the northeastern margin of the Tibetan Plateau

Eikonal tomography with physics informed neural networks: Rayleigh wave phase velocity in the northeastern margin of the Tibetan Plateau

Eikonal tomography with physics informed neural networks: Rayleigh wave phase velocity in the northeastern margin of the Tibetan Plateau

Eikonal surface wave tomography with smoothing splines—application to Southern California

SUMMARY The densification of both permanent and temporary seismic networks has raised new interest in surface wave eikonal tomography from which phase velocity maps can be obtained without resolving a tomographic inverse problem. However, eikonal tomography requires to reconstruct traveltime surfaces from a discrete number of measurements obtained at the station locations, which can be challenging. We present a new method to reconstruct these traveltime surfaces with smoothing splines discretized in a regular 2-D Cartesian grid. We impose Neumann boundary conditions so that the phase gradients on the edges of the grid are equal to the apparent slownesses of the average plane wave along the normal direction measured by beamforming. Using the eikonal equation, phase velocity maps are then derived from the norm of the gradient of the interpolated traveltime maps. The method is applied to Rayleigh waves recorded by the Southern California Seismic Network to derive phase velocity surfaces. Robust, stable and finely resolved phase velocity maps at 25 and 33 s period are obtained after averaging the phase velocity maps derived from the analysis of a selection of recent large (Mw ≥ 6.5) teleseismic events. The phase velocity map at 25 s mainly constrains the thickness of the Southern California crust, with results that are in excellent agreement with previous tomographic studies.

Surface and underground seismic characterization at Terziet in Limburg—the Euregio Meuse–Rhine candidate site for Einstein Telescope

We present a detailed characterization of surface and underground seismic noise measured at Limburg in the south of the Netherlands. This location is the Euregio Meuse–Rhine candidate for hosting Einstein Telescope, a future observatory for gravitational waves. Seismic noise measurements were performed with an array of seismometers installed on the surface. Passive seismic methods like beamforming were used to extract the propagation wave types of ambient seismic noise and the Rayleigh-wave dispersion in the region. Subsurface shear-wave models sensitive to depths of 300 m were derived by using the Rayleigh-wave dispersion and ellipticity. Subsurface P-wave velocities to depths of 200 m were obtained from an active seismic survey. Wavepath Eikonal tomography was used on the source-receiver refracted-wave travel-times to obtain a subsurface P-wave velocity model. Both the passive and the active seismic data analysis point to the presence of a layered geology with a soft-soil to hard-rock transition occurring at a shallow depth of about 25 to 40 m. The surface arrays are complemented by two permanent tri-axial seismometers installed on the surface and in a borehole at 250 m depth. Their data are used to interpret the surface-wave and body-wave contributions to the observed seismic noise. We use a cross-correlation analysis and compute the theoretical surface-wave eigenfunctions to understand the contributions of the different wave types at different frequencies. We observe that below 4 Hz in the horizontal component and 9 Hz in the vertical component, the seismic noise at depth is dominantly due to surface waves. Above these frequencies a significant contribution can be attributed to both nearby and far-away body-wave sources. At a depth of 250 m we find that the surface noise power has been damped by up to a factor 104 above about 2 Hz. The Limburg geology with soft-soil on top of hard-rock efficiently damps the anthropogenic noise produced at the surface. This implies that Einstein Telescope’s test masses are shielded from anthropogenic seismic noise and construction at greater depth will not bring significant further improvements in this regard. A body-wave background has been identified that contributes about half of the total underground seismic noise at 250 m depth for frequencies above 4 Hz. It remains to be studied if subtraction schemes for Newtonian noise originating from this body-wave background will be necessary. Finally, we estimate an interferometer downtime of about 3% due to regional and teleseismic earthquakes. We believe this is acceptable as it is comparable to current experience at the LIGO and Virgo interferometer sites.

Velocity and Azimuthal Anisotropy Structures Beneath the Dianzhong Block and its Vicinity, Se Tibetan Plateau, Revealed by Eikonal Equation-Based Traveltime Tomography

Velocity and Azimuthal Anisotropy Structures Beneath the Dianzhong Block and its Vicinity, Se Tibetan Plateau, Revealed by Eikonal Equation-Based Traveltime Tomography

Topography-dependent eikonal tomography based on the fast-sweeping scheme and the adjoint-state technique

First-arrival traveltime tomography has been widely used for upper crustal velocity modeling, but it usually suffers from the problem of complex surface topography. To overcome this problem, we have developed a new topography-dependent eikonal tomography scheme that combines a developed accurate and efficient traveltime modeling method and introduces a flexible and robust adjoint inversion scheme in the presence of irregular topography. A surface-flattening scheme is used to handle the irregular surface, where the real model is discretized by curvilinear grids and the irregular free surface is mathematically flattened through the transformation from Cartesian to curvilinear coordinates. Based on this parameterization, the forward traveltime modeling is conducted by a monotone fast-sweeping method that discretizes the factored topography-dependent eikonal equation with a point-source condition. This algorithm can circumvent the source-singularity problem and decrease the numerical error in the vicinity of a point source in the curvilinear system. Then, the gradient-based inversion is used to minimize the misfit function, which is achieved by a matrix-free adjoint-state method without cumbersome ray tracing and explicit estimation of the Fréchet derivative matrix in the curvilinear coordinate system. The new tomographic scheme is evaluated through numerical examples with different seismic structures with complex topography, and then applied to a wide-angle profile acquired in the northeastern Tibetan Plateau. The results validate the effectiveness and efficiency of our tomography scheme in constructing shallow crustal velocity models with irregular topography.

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.

High‐Resolution 3‐D Shear Wave Velocity Model of Northern Taiwan via Bayesian Joint Inversion of Rayleigh Wave Ellipticity and Phase Velocity With Formosa Array

AbstractThe Formosa array, with 137 broadband seismometers and ∼5 km station spacing, was deployed recently in Northern Taiwan. Here by using eight months of continuous ambient noise records, we construct the first high‐resolution three‐dimensional (3‐D) shear wave velocity model of the crust in the area. We first calculate multi‐component cross‐correlations to extract robust Rayleigh wave signals. We then determine phase velocity maps between 3 and 10 s periods using Eikonal tomography and measure Rayleigh wave ellipticity at each station location between 2 and 13 s periods. For each location, we jointly invert the two types of Rayleigh wave measurements with a Bayesian‐based inversion method for a one‐dimensional shear wave velocity model. All piecewise continuous one‐dimensional models are then used to construct the final 3‐D model. Our 3‐D model reveals upper crustal structures that correlate well with surface geological features. Near the surface, the model delineates the low‐velocity Taipei and Ilan Basins from the adjacent fast‐velocity mountainous areas, with basin geometries consistent with the results of previous geophysical exploration and geological studies. At a greater depth, low velocity anomalies are observed associated with the Linkou Tableland, Tatun Volcano Group, and a possible dyke intrusion beneath the Southern Ilan Basin. The model also provides new geometrical constraints on the major active fault systems in the area, which are important to understand the basin formation, orogeny dynamics, and regional seismic hazard. The new 3‐D shear wave velocity model allows a comprehensive investigation of shallow geologic structures in the Northern Taiwan.

Near-Surface Geothermal Reservoir Imaging based on the Customized Dense Seismic Network

Exploration of geothermal resources has become one of the major drivers for urbanization and economic transformation in southeast China, and it calls for temporal and spatial resolution improvements on conventional geophysical techniques under complex near-surface conditions. A dense seismic network including 192 sensors, with its aperture around 4.8 km, was deployed to record ambient noise for local-scale geothermal reservoir imaging in central Zhejiang Province, southeast China. With the ultrashort (less than 5 days) observation, a subset of the total station pairs was extracted to conduct seismic interferometry and dispersion measurements. This customized subnet was qualified to be an overdetermined system to achieve similar performance of entire network for the eikonal tomography with higher efficiency. The recorded high-frequency noise sources turned out to be rather homogeneous distributions, except for the dominant direction of northern Jinhua urban area. Azimuthal effects and wavelength restriction of dispersion measurements were quantified by simulating source–receiver responses under non-equipartitions of energy. The azimuth–velocity variations of field dataset verified that phase velocity measurements using the tested wavelength restriction were robust under different source–receiver orientations. The obtained phase velocity maps were comparable with the geological map. Furthermore, the inverted body wave velocities coincide well with the borehole data. Shear wave velocity profiles revealed corresponding fracture and depression structures of the reservoir. Finally, multiple geophysical properties delineate the shallow geothermy to be karst fissure water heated at certain earth temperature gradient.

Layered crustal azimuthal anisotropy beneath the northeastern Tibetan Plateau revealed by Rayleigh-wave Eikonal tomography

The uplift of the Tibetan Plateau in the Cenozoic has greatly affected the tectonics in Asia. But the evolution of the plateau is still unclear. The northeastern Tibetan Plateau is under ongoing expansion and is therefore essential for understanding the tectonic evolution of the plateau. Using data from 675 stations deployed by the ChinArray project, we obtained an anisotropic shear-wave velocity model by Rayleigh-wave phase-velocity Eikonal tomography and further investigated layered anisotropy and deformation patterns in the northeastern Tibetan Plateau. In the upper crust (<20 km depth), the fast directions are parallel with major strike-slip faults. In the lower crust, the fast directions are mostly margin-parallel along the plateau margin (at depths of ∼20 km to Moho), but they are perpendicular to the plateau margin while parallel to the topographic gradient under the high plateau (at depths of ∼40 km to Moho). Our result indicates that there is lower crustal flow under the high plateau due to the differential lateral gravity potential. However, the deep crustal flow is blocked by the surrounding blocks, which results in pure shear along the plateau margin in the northeastern Tibetan Plateau.

Surface wave tomography using 3D active-source seismic data

Surface wave tomography (SWT) is a powerful and well-established technique to retrieve 3D shear-wave (S-wave) velocity models at the regional scale from earthquakes and seismic noise measurements. We have applied SWT to 3D active-source data, in which higher modes and heterogeneous spatial sampling make phase extraction challenging. First, synthetic traveltimes calculated on a dense, regular-spaced station array are used to test the performance of three different tomography algorithms (linearized inversion, Markov chain Monte Carlo [MCMC], and eikonal tomography). The tests suggest that the lowest misfit to the input model is achieved with the MCMC algorithm, at the cost of a much longer computational time. Then, real phases were extracted from a 3D exploration data set at different frequencies. This operation included an automated procedure to isolate the fundamental mode from higher order modes, phase unwrapping in two dimensions, and the estimation of the zero-offset phase. These phases are used to compute traveltimes between each source-receiver couple, which are input into the previously tested tomography algorithms. The resulting phase-velocity maps show good correspondence, highlighting the same geologic structures for all three methods. Finally, individual dispersion curves obtained by the superposition of phase-velocity maps at different frequencies are depth inverted to retrieve a 3D S-wave velocity model.

On the validity of the eikonal equation for surface-wave phase-velocity tomography

SUMMARYThe phase velocity of surface waves can be directly determined from the amplitude and phase of the regional wavefield using the Helmholtz equation. However, the Helmholtz equation involves estimating the Laplacian of the amplitude field, a challenging operation to perform on noisy and sparsely sampled seismic data. For this reason, the amplitude information is often discarded. In that case, phase-velocity maps are reconstructed with the eikonal equation, which relates the local phase slowness to the gradient of the phase. Here, we derive analytical expression of the errors arising from neglecting the amplitude of the wavefield in eikonal tomography. In general, these errors are quite strong but they vary sinusoidally with the wave propagation direction. Consequently, if the azimuthal coverage is good, they will average out, and unbiased phase-velocity maps can be obtained with eikonal tomography. We numerically validate these results with a synthetic tomography experiment.