Sensitivity Kernels Research Articles

Imaging of seismic discontinuities using an adjoint method

Summary For imaging of seismic discontinuities at depth, reverse time migration (RTM) is a powerful method to apply to recordings of seismic events. It is especially powerful when an extensive receiver array, numerous seismic sources, or both, permit adequate reconstruction of incident and scattered wavefields at depth. Reconstructing either the incident or scattered wavefield at depth becomes less accurate when relatively few recordings of seismic events are available. Here we explore an inverse scattering approach to imaging discontinuities based on an adjoint method, employing sensitivity kernels (Fréchet derivatives) that represent jumps in material properties across seismic-discontinuity surfaces. When combined with ray-based requirements on scattering geometry, it constitutes a powerful approach to determining the locations and amplitudes of the discontinuities, recovering only those properties that can be resolved by a spatially limited source and/or receiver distribution. This is illustrated by synthetic examples with local sources followed by a field example in a subduction zone setting.

Unveiling complex magnetic field configurations in red giant stars

The recent measurement of magnetic field strength inside the radiative interior of red giant stars has opened the way toward full 3D characterization of the geometry of stable large-scale magnetic fields. However, current measurements, which are limited to dipolar (ℓ = 1) mixed modes, do not properly constrain the topology of magnetic fields due to degeneracies on the observed magnetic field signature on such ℓ = 1 mode frequencies. Efforts focused toward unambiguous detections of magnetic field configurations are now key to better understand angular momentum transport in stars. We investigated the detectability of complex magnetic field topologies (such as the ones observed at the surface of stars with a radiative envelope with spectropolarimetry) inside the radiative interior of red giants. We focused on a field composed of a combination of a dipole and a quadrupole (quadrudipole) and on an offset field. We explored the potential of probing such magnetic field topologies from a combined measurement of magnetic signatures on ℓ = 1 and quadrupolar (ℓ = 2) mixed mode oscillation frequencies. We first derived the asymptotic theoretical formalism for computing the asymmetric signature in the frequency pattern for ℓ = 2 modes due to a quadrudipole magnetic field. To access asymmetry parameters for more complex magnetic field topologies, we numerically performed a grid search over the parameter space to map the degeneracy of the signatures of given topologies. We demonstrate the crucial role played by ℓ = 2 mixed modes in accessing internal magnetic fields with a quadrupolar component. The degeneracy of the quadrudipole compared to pure dipolar fields is lifted when considering magnetic asymmetries in both ℓ = 1 and ℓ = 2 mode frequencies. In addition to the analytical derivation for the quadrudipole, we present the prospect for complex magnetic field inversions using magnetic sensitivity kernels from standard perturbation analysis for forward modeling. Using this method, we explored the detectability of offset magnetic fields from ℓ = 1 and ℓ = 2 frequencies and demonstrate that offset fields may be mistaken for weak and centered magnetic fields, resulting in underestimating the magnetic field strength in stellar cores. We emphasize the need to characterize ℓ = 2 mixed-mode frequencies, (along with the currently characterized ℓ = 1 mixed modes), to unveil the higher-order components of the geometry of buried magnetic fields and to better constrain angular momentum transport inside stars.

Testing the volume integrals of travel-time sensitivity kernels for flows

Context. Helioseismic inversions largely rely on sensitivity kernels, in which 3D spatial functions describe how the changes in the solar interior translate into the change in helioseismic observables. These sensitivity kernels in most cases come from the forward modelling that is used in the most advanced solar models. Aims. We aim to test the sensitivity kernels by comparing their volume integrals with measured values from helioseismic travel times. Methods. By manipulating the tracking rate, we mimicked the additional zonal velocity in the Dopplergram datacubes. These datacubes were then processed by a standard travel-time measurements pipeline. We investigated the dependence of the east-west travel time averaged over a box around the disc centre on the implanted tracking velocity. The slope of this dependence is directly proportional to the total volume integral of the sensitivity kernel that corresponds to the travel-time geometry that is used. Results. The agreement between measurements and models for travel times that are computed with a ridge filtering is very good to acceptable. The dependence we sought to determine indeed resembles a linear function, and its slope agrees with the expected volume integral from the forward-modelled sensitivity kernel. The agreement is poorer for the phase-speed filtered datacubes. The disagreement is particularly strong for the slowest phase speeds (filters td1–td4). For the higher phase speeds, our result indicates that the measured kernel integrals are systematically larger than expected from the forward modelling. We admit our testing procedure may not be appropriate for high phase speeds and higher radial modes.

Detectability of Axisymmetric Magnetic Fields from the Core to the Surface of Oscillating Post-main-sequence Stars

Magnetic fields in the stellar interiors are key candidates to explain observed core rotation rates inside solar-like stars along their evolution. Recently, asteroseismic estimates of radial magnetic field amplitudes near the hydrogen-burning shell (H-shell) inside about 24 red giants (RGs) have been obtained by measuring frequency splittings from their power spectra. Using general Lorentz-stress (magnetic) kernels, we investigated the potential for detectability of near-surface magnetism in a 1.3 M ⊙ star of supersolar metallicity as it evolves from a mid subgiant to a late subgiant into an RG. Based on these sensitivity kernels, we decompose an RG into three zones—deep core, H-shell, and near-surface. The subgiants instead required decomposition into an inner core, an outer core, and a near-surface layer. Additionally, we find that for a low-frequency g-dominated dipolar mode in the presence of a typical stable magnetic field, ∼25% of the frequency shift comes from the H-shell and the remaining from deeper layers. The ratio of the subsurface tangential field to the radial field in the H-burning shell decides if subsurface fields may be potentially detectable. For p-dominated dipole modes close to νmax , this ratio is around two orders of magnitude smaller in subgiant phases than the corresponding RG. Further, with the availability of magnetic kernels, we propose lower limits of field strengths in crucial layers in our stellar model during its evolutionary phases. The theoretical prescription outlined here provides the first formal way to devise inverse problems for stellar magnetism and can be seamlessly employed for slow rotators.

Seismic Anisotropy From 6C Ground Motions of Ambient Seismic Noise

AbstractWe propose a new approach capable of measuring local seismic anisotropy from 6C (three‐component translation and three‐component rotation) amplitude observations of ambient seismic noise data. Our recent theory demonstrates that the amplitude ratio of 6C cross‐correlation functions (CCFs) enables retrieving the local phase velocity. This differs from conventional velocity extraction methods based on the travel time. Its local sensitivity kernel beneath the 6C seismometer allows us to study anisotropy from azimuth‐dependent CCFs, avoiding path effects. Such point measurements have great potential in planetary exploration, ocean bottom observations, or volcanology. We apply this approach to a small seismic array at Pion Flat Observatory (PFO) in southern California, array‐deriving retrieves rotational ground motions from microseismic noise data. The stress‐induced anisotropy is well resolved and compatible with other tomography results, providing constraints on the origin of depth‐dependent seismic anisotropy.

Comparing sensitivities of groundwater head to variations in hydraulic parameters under boundary conditions of river stage rise and tidal variation

The sensitivity of hydraulic head responses to spatially distributed hydraulic parameters is essential for uncertainty analysis, inverse modeling, and parameter estimation and interpretation. This study formulates the Fréchet sensitivity kernel of hydraulic head responses to a suddenly rising boundary and a sinusoidal head fluctuation boundary to variation of spatially distributed hydraulic parameters in a semi-infinite, one-dimensional (1-D), confined aquifer, and it then derives analytical solutions. Different from previous studies that derived expressions for Fréchet kernels in the time domain for a 2-D pumping test, this study is the first to derive the closed-form Fréchet kernels in time and frequency domains for a semi-infinite, 1-D, confined aquifer. This study uses the Fréchet kernels to investigate the nature of singularities in the spatial sensitivity functions around the observation location and boundary. The information content revealed by observation of head change or head fluctuation amplitude at a given specified location and time (or frequency) under the above two boundary conditions is different. When comparing Fréchet sensitivity kernels across various times or periods, multi-frequency information, much like multi-time information, can be instrumental for hydrogeological parameter inversion. The explicit-form Fréchet sensitivity kernels also identify the optimal time or period for obtaining measurements.

Multimodal surface wave inversion with automatic differentiation

SUMMARY Investigating subsurface shear wave velocity (vs) structures using surface wave dispersion data involves minimizing a misfit function that is commonly solved through gradient-based optimization. Sensitivity kernels for model updates are commonly estimated using numerical differentiation, variational methods or implicit functions which however, may involve numerical instability and computational challenges when dealing with complex velocity models and large data sets. In this study, we propose a novel surface wave inversion framework in which error-free gradients are calculated by automatic differentiation (AD) and forward modelling is implemented by convenient computational graphs in the state-of-the-art deep learning framework. The AD-based inversion approach is first validated using two synthetic data sets. Then, the subsurface structures at three distinct locations, namely the Great Plains and the Long Beach in the US and Tong Zhou in China, are also derived using this method with seismic ambient noise data, which show nice consistency with those obtained using traditional methods. With the significantly improved computational efficiency, a great number of initial models can be inverted simultaneously to mitigate the impact of local minima and to estimate the uncertainty in the invert models. We have developed a new surface wave inversion package named ADsurf based on automatic differentiation and computational graphs in the deep learning framework, and its computational efficiency is also compared with the traditional finite-difference-based gradient estimation approach. While a great number of intriguing studies on the geophysical inverse problems have been conducted recently using deep learning for end-to-end mapping, the use of AD provided in the in the deep learning frameworks to assist and expedite the gradient computations are still underexploited in geophysics. Thus, it is expected that various geophysical inverse problems in many different areas beyond the surface wave inversion can also be tackled with this new paradigm in the future.

Adjoint sensitivity kernels for free oscillation spectra

SUMMARY We apply the adjoint method to efficiently calculate sensitivity kernels for long-period seismic spectra with respect to structural and source parameters. Our approach is built around the solution of the frequency-domain equations of motion using the direct solution method (DSM). The DSM is currently applied within large-scale mode coupling calculations and is also likely to be useful within finite-element type methods for modelling seismic spectra that are being actively developed. Using mode coupling theory as a framework for solving both the forward and adjoint equations, we present numerical examples that focus on the spectrum close to four eigenfrequencies (the low-frequency mode, 0S2, and higher frequency modes, namely 2S2, 0S7 and 0S10 for comparison). For each chosen observable, we plot sensitivity kernels with respect to 3-D perturbations in density and seismic wave speeds. We also use the adjoint method to calculate derivatives of observables with respect to the matrices occurring within mode coupling calculations. This latter approach points towards a generalization of the two-stage splitting function method for structural inversions that does not rely on inaccurate self-coupling or group-coupling approximations. Finally, we verify through direct calculation that our sensitivity kernels correctly predict the linear dependence of the chosen observables on model perturbations. In doing this, we highlight the importance of non-linearity within inversions of long-period spectra.

One‐way waveform inversion: Real marine data application

AbstractThe reflection waveform inversion is a powerful technique to build a large‐scale velocity model of the subsurface by fitting the reflected recorded seismic waves. The reflection waveform inversion is designed based on the pillar concept of model and data‐scale separation. Therefore, its success is related to the ability of its forward modelling engine to separate reflected events distinctly from other propagation modes (diving waves, multiples, etc.). However, the standard Born modelling based on the two‐way wave equation may generate internal multiples in case of an insufficient smooth background model. These internal multiples may lead to a distorted sensitivity kernel, which adds more non‐linearity to the inverse problem. In addition, simulating the wave equation using two‐way propagators is still an overburden step of the algorithm especially in large three‐dimensional real surveys. In this proposal, we introduce an alternative to the two‐way wave equation by using a one‐way approach for the reflection waveform inversion. The Born modelling based on one‐way propagators significantly reduces the computational cost and I think it should be allows to relax the smooth background velocity model assumption by restricting the forward modelling to primary reflected waves. After a brief theoretical description of the one‐way waveform inversion, we present an application of the algorithm on the real marine dataset to review its promises and pitfalls. Our approach produces an acceptable large‐scale velocity model whose accuracy is confirmed by the migrated image and the offset gathers.

Research on the impact of sliding window and differencing procedures on the support vector regression model for load forecasting

Load forecasting is a critical aspect of energy management and grid operations. Machine learning techniques as support vector regression (SVR), have been widely used for load forecasting. However, the effectiveness of SVR is highly dependent on its hyperparameters, including the error sensitivity parameter, penalty factor, and kernel function. Furthermore, as the load data follows a time series pattern, the accuracy of the SVR model is influenced by the data's characteristics. In this regard, the present study aims to investigate the impact of combining the sliding window procedure and differencing the input data on the prediction accuracy of the SVR model. The study utilizes daily maximum load data from the Queensland and Victoria states in Australia. The analyses revealed that while the sliding window procedure had a minimal impact on the prediction results, the differencing of the input data significantly improved the accuracy of the predictions.

Rayleigh wave attenuation tomography based on ambient noise interferometry: methods and an application to Northeast China

SUMMARY Although ambient noise interferometry has been extensively utilized for seismic velocity tomography, its application in retrieving attenuation remains limited. This study presents a comprehensive workflow for extracting Rayleigh wave amplitude and attenuation from ambient noise, which consists of three phases: (1) retrieval of empirical Green's functions (EGFs), (2) selection and correction of amplitude measurements and (3) inversion of attenuation, site amplification and noise intensity terms. Throughout these processes, an ‘asynchronous’ temporal flattening method is used to generate high-quality EGFs while preserving relative amplitudes between stations. Additionally, a novel ‘t-symmetry’ criterion is proposed for data selection along with the signal-to-noise ratio. Furthermore, 2-D sensitivity kernels are utilized to estimate the focusing/defocusing effect, which is then corrected in amplitude measurements. These procedures are designed to deliver reliable attenuation measurements while maintaining flexibility and automation. To validate the effectiveness of the proposed noise-based attenuation tomography approach, we apply it to a linear array, NCISP-6, located in NE China. The obtained results correlate reasonably well with known geological structures. Specifically, at short periods, high attenuation anomalies delineate the location of major sedimentary basins and faults; while at longer periods, a notable rapid increase of attenuation is observed beneath the Moho discontinuity. Given that attenuation measurements are more sensitive to porosity, defect concentration, temperature, melt and volatile ratio than seismic velocities, noise-based attenuation tomography provides important additional constraints for exploring the crustal and upper mantle structures.

Adjoint inversion of antipodal PKPab waveforms for P wave velocity anomaly at the base of the lower mantle

We perform an adjoint inversion by using antipodal PKPab phases to estimate the heterogeneous Vp structure at the base of the lowermost mantle. We have carefully examined antipodal stations with high S/N ratios during the past 30 years and selected 20 source-receiver pairs with the epicentral distances >179.0 degree and the Mw <7.0. We have used the spectral-element method on the Earth Simulator of JAMSTEC to calculate the synthetic seismograms for a heterogeneous mantle Vp model with the accuracy of period about 8 s (110 km wavelength at the CMB). We have set up the time window to retrieve the PKPab phase from the vertical component of both observed and computed seismograms to calculate the adjoint source to obtain the sensitivity kernels of Vp in the mantle. The computed Vp sensitivity kernel for each event shows the characteristic annulus pattern in the lowermost mantle, which covers a large area of the CMB. The twenty PKPab earthquake-station pairs in this antipodal study contribute the equivalent of about 3140 measurements at the CMB—compared with 1871 previously studied—and provide new data. Therefore, although the number of individual source-receiver pairs is not large, the summed sensitivity kernels of the PKPab phase for Vp structure at the base of the mantle may be sufficient to model heterogeneity of the Vp structure at the CMB. We summed each event kernel to set up a sensitivity kernel of Vp in the lowermost mantle and iterated the inversion to estimate a heterogeneous structure in D″. Although we have iterations that dominantly affect both South America and the South Pacific, the summary final model shows features within South of Africa, South Pacific, SE Australia, and Central & South America. Keeping the Vs model fixed, we map the CMB Vp heterogeneity measured by the parameter Rs,p = dlnVs/dlnVp and find qualitative, proximal correspondence with the degree-2 pattern of Large Low Velocity Shear Provinces observed in shear tomographic models: in the Pacific and Africa Rs,p > 2.0, whereas the surrounding edges of the edges of the Pacific show Rs,p < 2.0.

Reciprocal sensitivity kernels for receiver positioning

In their classical formulation, sensitivity kernels aim to evaluate the points where an infinitesimal variation in the properties of the medium would most affect a pressure (or displacement) measurement at a fixed location. These kernels feature typical cigar shapes, with characteristically low sensitivity on the direct path. In this presentation, the same approach is applied to the reciprocal problem, where we want to evaluate, at a constant source position, which points are the most (or least) sensitive to a given model change. These reciprocal kernels exhibit flared shapes centered on the areas where the model is perturbed. Applications to receiver positioning in acoustic are discussed.

Upper‐Mantle Anisotropy in the Southeastern Margin of Tibetan Plateau Revealed by Fullwave SKS Splitting Intensity Tomography

AbstractThe southeastern margin of the Tibetan Plateau has undergone complex deformation since the Cenozoic, resulting in a high level of seismicity and seismic hazard. Knowledge about the seismic anisotropy provides important insight about the deformation mechanism and the regional seismotectonics beneath this tectonically active region. In this study, we conduct fullwave multi‐scale tomography to investigate the seismic anisotropy in the southeastern margin of the Tibetan Plateau. Broadband records at 111 permanent stations in the region from 470 teleseismic events are used to obtain 5,216 high‐quality SKS splitting intensity (SI) measurements, which are then inverted in conjunction with 3D sensitivity kernels to obtain an anisotropic model with multi‐scale resolution. Resolution tests show that our data set recovers anisotropy anomalies reasonably well on the scale of 1° × 1° horizontally and ∼100 km vertically. Our result suggests that in the southeastern margin of the Tibetan Plateau the deformation in the lithosphere and asthenosphere are decoupled. The anisotropy in the lithosphere varies both laterally and vertically as a result of dynamic interactions of neighboring blocks as well as lithospheric reactivation. The anisotropy in the asthenosphere largely follows the direction of regional absolute plate motion. The SKS splittings observed at the surface are shown to be consistent with the vertical integral of our depth‐dependent anisotropy model over lithospheric and asthenospheric depths.

Quantification of Shortwave Surface Albedo Feedback Using a Neural Network Approach

Radiative transfer is a nonlinear process. Despite this, most current methods to evaluate radiative feedback, such as the kernel method, rely on linear assumptions. Neural network (NN) models can emulate nonlinear radiative transfer due to their structure and activation functions. This study aims to test whether NNs can be used to evaluate shortwave radiative feedbacks and to assess their performance. This study focuses on the shortwave radiative feedback driven by surface albedo. An NN model is first trained using idealized cases, simulating truth values from a radiative transfer model via the partial radiative perturbation method. Two heuristic cases are analyzed: univariate feedback, perturbing the albedo; and bivariate feedback, perturbing the albedo and cloud cover concurrently. These test the NN’s ability to capture nonlinearity in the albedo–flux and albedo–cloud–flux relationships. We identify the minimal NN structure and predictor variables for accurate predictions. Then, an NN model is trained with realistic radiation flux and atmospheric variable data and is tested with respect to its predictions at different order levels: zero-order for the flux itself, first-order for radiative sensitivity (kernels), and second-order for kernel differences. This paper documents the test results and explains the NN’s ability to reproduce the complex nonlinear relationship between radiation flux and different atmospheric variables, such as surface albedo, cloud optical depth, and their coupling effects.

SItomo – A toolbox for splitting intensity tomography and application in the Eastern Alps

The tomographic inversion of shear wave splitting data for upper mantle anisotropy has been a longstanding challenge. This is due to the ray-based approximation of classical approaches and the near-vertical incidence of the core-mantle converted phases such as SKS that are often used. Recent developments include the calculation of finite-frequency sensitivity kernels for SKS splitting intensity observations, which allows us to accurately take into account the sensitivity to anisotropic structure with depth. A requirement of this tomographic technique is a dense station spacing, which results in overlapping sensitivity kernels at depth and allows for the localization of anisotropic structure. This is satisfied by a growing number of temporary seismic deployments, which motivates the desire to image anisotropic complexities with depth. Here, we introduce and make available a toolbox for the MATLAB environment that facilitates the application of finite-frequency splitting intensity tomography to dense seismic arrays. Our implementation includes several key features, including: 1) A forward calculation of splitting intensities and sensitivity kernels for a complex anisotropic model space. 2) Consideration of the dominant period of the wave, allowing for multiple-frequency analysis, as well as the incoming wave’s non-vertical incidence. 3) The inversion can be based on a classical gradient descent, on a form of the conjugate gradient method known as the BFGS algorithm, or on a gradient-informed stochastic reversible jump algorithm, allowing for a data-driven parametrization of the model space. 4) Importing splitting intensity measurements from waveforms processed in SplitRacer allows for fast pre-processing of large data sets due to its fully automatic design. To illustrate our method, we present both synthetic tests and an application to real data. We apply our inversion procedure to data from the Swath-D network, which densely covers the transition of the Central to the Eastern Alps. Previous studies showed evidence for an abrupt lateral change of layered seismic anisotropy that had been attributed to an opening for channeled asthenospheric flow. Using an SKS splitting intensity tomography approach, we can confirm previous inferences while providing additional constraints on the distribution of anisotropy laterally and with depth.

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.

The higher order leaky Lamb wave sensitivity of a notch in a fluid-immersed plate

We present an ultrasonic method of detecting cracks in pipelines based on using normally incident transducers in a pitch-catch setup, which can only excite Lamb modes of higher order than the fundamental modes A0 and S0 commonly used in crack detection applications. By excitation and measurements of the Lamb modes S1, S2, and A3, in a steel plate immersed in fluid with and without a notch (to emulate a crack), the performance of the modes towards crack detection is quantified by assessing whether it returns a high leaky component and whether the notch has a large impact on the leaky component. In order to narrow the scope of measurements necessary to investigate notch sensitivity for different system parameters, and to potentially optimize the system setup, we present a computationally efficient theoretical model based on angular spectrum method (ASM) and the theoretical sensitivity kernel formulation from the field of seismology that accounts for a scatterer in the wave path between the transmitter and receiver. The model is compared against measurements, which show that the frequency components of the S2 mode has both the largest leaky frequency component in the given setup and the largest sensitivity at a frequency close to the maximum leaky frequency such that a difference caused by the notch is easily measured. By using the measurements and the validation calculation as baseline reference, we calculate the expected S2 mode sensitivity and leaky components for larger plate thicknesses and larger standoffs, which exemplifies how the model can be applied in measurement system design and optimization.

Converted-wave reflection traveltime inversion with free-surface multiples for ocean-bottom-node data

Advancements in ocean-bottom-node (OBN) technologies have enabled the recording of high-quality multicomponent seismic data, which can provide crucial information about subsurface properties through elastic seismic imaging. However, imaging multicomponent data is challenging due to the requirement for P- and S-wave velocity models. Conventional processing relies on estimating the S-wave velocity model using a primary converted wave (C wave) because the pure S-wave primaries are not available if using standard air-gun sources. When a free surface is present, the C waves recorded with geophones can be contaminated by source-side P-wave multiples, especially water-layer reverberations, which are difficult to remove even using state-of-the-art wavefield decomposition methods. These C-wave multiples can cause significant mismatches between synthetic and observed data during reflection traveltime or waveform inversion if only primary P-to-S (PS) conversions are simulated. To address these issues and reliably build an S-wave velocity model for PS imaging, we develop a C-wave reflection traveltime inversion method that takes source-side free-surface multiples into account. The traveltime misfit of C-wave data is extracted using dynamic image warping to ensure a better match between the synthetic and observed data. The functional gradient of the objective function is derived using the adjoint state method. Based on sensitivity kernel analyses, a convenient gradient preconditioning strategy is developed to robustly separate the contribution of primary and multiple C waves during backpropagation. This strategy can effectively mitigate the high-wavenumber crosstalk associated with nonphysical wavepaths in the gradient and thus allow more accurate updating for the S-wave velocity model. The synthetic data and shallow-water OBN data from the East China Sea indicate that this approach can reliably recover the S-wave macrovelocity structures for PS imaging.

Adjoint‐State Teleseismic Traveltime Tomography: Method and Application to Thailand in Indochina Peninsula

AbstractWe propose a novel framework for teleseismic traveltime tomography that requires no ray tracing. The tomographic inverse problem is formulated as an Eikonal equation‐constrained optimization problem, aiming at the determination of a slowness model that minimizes the difference between observational and predicted differential traveltimes. Two improvements have been made over previous ray‐based methods. First, the traveltimes from the source outside the study region to any positions within the study region are computed using a hybrid approach. This involves solving a 2D Eikonal equation to obtain the traveltimes from the source to the boundary of the study region and solving a 3D Eikonal equation to compute the traveltimes from the boundary to any positions within the study region. Second, we compute the sensitivity kernel using the adjoint‐state method. This method avoids the computation of ray paths and makes the computational cost nearly independent of the number of receivers. We apply our new method in Thailand and adjacent regions. The final velocity model reveals a thick lithosphere beneath the Khorat Plateau and two mantle upwelling branches beneath its southern and western margins. The mantle upwelling may result from the mantle convection triggered by surrounding subduction systems and/or a slab window of the Indian Plate. The presence of the mantle upwelling corresponds to the source zone of the erupted Cenozoic basalts in the Khorat Plateau, indicating lithospheric modification beneath the plateau. The insightful tomographic result verifies our method and provides new perspectives on the structural heterogeneities and dynamics of the Indochina Block.