Inversion Of Dispersion Curves Research Articles

Radial Anisotropy of the Crust and Uppermost Mantle Beneath the Central North China Craton From Joint Inversion of Surface Wave Dispersion Curves and Ellipticity: Implications for the Mechanisms of Differential Rifting and Uplift

AbstractThe central North China Craton (NCC) acts as a transition zone between the stable western and reworked eastern NCC. It is characterized by high seismic activity and experienced volcanic activity with small magma volumes. To assess the dynamic processes of the central NCC, particularly in a zone marked by intense differential tectonic deformation, we have obtained a 3‐D radial anisotropic model of crust and uppermost mantle via joint inversion of Love‐ and Rayleigh‐wave dispersion curves and ellipticity measurements. Compared to models without Rayleigh‐wave ellipticity, our new model shows improved accuracy in crustal radial anisotropy. This refined model reveals two noteworthy geological features: (a) Most of the Shanxi Rift has pronounced positive radial anisotropy in the crust except for Linfen and Xinding Basins, as critical earthquake‐prone areas, which are characterized by weak positive to negative anisotropy with much thinner sediments. This observation suggests that differential rifting processes with uneven sedimentation and crustal deformation occur in these Cenozoic basins due to right‐lateral strike slip motion. (b) The crust in the Lvliang Mountains shows weak positive or negative anisotropy with a lower crustal low‐velocity layer beneath the northern parts, whereas the crust in the Taihang Mountains exhibits positive anisotropy. This implies that the Lvliang Mountains experienced uplift under compressional environments since the Yanshanion Orogeny. Furthermore, the magmatic underplating in the crust accelerated the uplift of the northern Lvliang Mountains. In contrast, the Taihang Mountains underwent relative uplift under extensional environments, along with the subsidence of the Bohai Bay Basin during the Cenozoic.

Using Crustal-Scale Refraction Data for Joint Inversions of Rayleigh-Wave Dispersion Curves and H/V Spectral Ratios for Atlantic Coastal Plain Velocity Structure, Eastern United States

Using Crustal-Scale Refraction Data for Joint Inversions of Rayleigh-Wave Dispersion Curves and H/V Spectral Ratios for Atlantic Coastal Plain Velocity Structure, Eastern United States

Nonlinear joint inversion of Rayleigh and Love wave dispersion curves based on Pearson correlation coefficient and thickness mean sharing

AbstractThe joint inversion of Rayleigh and Love waves plays a crucial role in mitigating the non‐uniqueness of surface wave inversion results and enhancing the stability of these inversions. Existing approaches to the joint inversion of Rayleigh and Love wave dispersion curves, which rely on conventional objective functions, often struggle with complex stratigraphic configurations and yield results of limited accuracy. This study introduces two novel nonlinear joint inversion techniques for Rayleigh and Love waves: Pearson correlation coefficient and thickness mean sharing. The Pearson correlation coefficient approach employs the Pearson correlation coefficient and alternating iterative objective functions to synchronize the shear wave velocity structures derived from Rayleigh and Love waves, thereby enhancing the accuracy of the joint inversion. Conversely, the thickness mean sharing method computes an average of the thickness values obtained in each iteration of the inversion, utilizing the traditional joint inversion objective function. Tests on three distinct stratigraphic structures—characterized by increasing velocity, high‐speed hard interlayers and low‐speed soft interlayers—as well as on measured data, demonstrate that the proposed methods significantly improve the stability and accuracy of nonlinear joint inversion.

Lithospheric Evolution of the South‐Central United States Constrained by Joint Inversion of Receiver Functions and Surface Wave Dispersion

AbstractIn the present study, we use broadband seismic data recorded by 190 stations of the EarthScope program's Transportable Array to construct a 3‐D shear wave velocity model for the upper 180 km using a non‐linear Bayesian Monte‐Carlo joint inversion of receiver functions (RFs) and Rayleigh wave dispersion curves. Ambient noise and teleseismic data are used for obtaining Rayleigh wave phase velocity dispersion curves. A resonance removal filtering technique is applied to the RFs contaminated by reverberations from the thick sedimentary layers that cover most of the region. Our observations of the higher crustal shear velocities (∼3.40 km/s) beneath the Sabine Block (SB), along with the estimated relatively thicker crust (∼34.0 km) and lower crustal Vp/Vs estimates (∼1.80) in comparison with the rest of the Gulf Coastal Plain (GCP) (∼3.10 km/s for crustal shear velocities, ∼29.0 km for crustal thickness, and ∼1.90 for crustal Vp/Vs estimates), indicating that this crustal block has different crustal properties from the surrounding coastal plain regions. The southern Ouachita Mountains have a thin crust (∼30.0 km) and low mean crustal Vp/Vs value (∼1.73), suggesting that lower crustal delamination has occurred in this region. Low velocities in the upper mantle beneath most of the GCP are interpreted as a combined result of thin lithosphere, higher‐than‐normal temperatures, and possibly compositional variations.

Full Dispersion‐Spectrum Inversion of Surface Waves

AbstractNowadays, the most successful applications of full‐waveform inversion (FWI) involve marine seismic data under acoustic approximations. Elastic FWI of land seismic data is still challenging in theory and practice. Here, we propose a full dispersion spectrum inversion method and apply it to seismic data acquired in West Antarctica. Inspired by the conventional surface wave dispersion curve inversion method, we propose to invert the surface wave dispersion spectrum instead of the complicated waveforms. We compare the frequency‐velocity, frequency‐slowness, and frequency‐wavenumber spectra in terms of their ability to resolve dispersion modes and the feasibility of their adjoint updates and conclude that the frequency‐slowness spectrum is the best for our inversion objectives. We test four objective functions, subtraction, zero‐lag crosscorrelation, optimal transport, and the local‐crosscorrelation to quantify the spectrum mismatch and provide the corresponding adjoint source. We then theoretically analyze the convexity of the proposed objective functions and examine their convergence behavior using numerical examples. We also compare the proposed method with the classic FWI method and the traditional surface wave dispersion curve inversion method and discuss the strengths and weaknesses of each method. This technique is employed to evaluate the shallow velocity structures beneath a seismic array stationed in West Antarctica. Our proposed inversion scheme is also useful for more general applications such as imaging the shallow subsurface of the critical zones, like geothermal reservoirs, and CO2 storage sites.

Near-Surface Rayleigh Wave Dispersion Curve Inversion Algorithms: A Comprehensive Comparison

Near-Surface Rayleigh Wave Dispersion Curve Inversion Algorithms: A Comprehensive Comparison

Multi‐mode non‐linear inversion of Rayleigh wave dispersion curves with grey wolf optimization and cuckoo search algorithm

AbstractDispersion curve inversion is one of the core contents of Rayleigh wave data processing. However, the dispersion curve inversion has the characteristics of multi‐parameter, multi‐extremum as well as nonlinearity. In the face of Rayleigh wave data processing under complex seismic‐geological conditions, it is difficult to reconstruct an underground structure quickly and accurately apply a single global‐searching non‐linear inversion algorithm. For this reason, we proposed a strategy to invert multi‐order mode Rayleigh wave dispersion curves by combining with grey wolf optimization (GWO) and cuckoo search (CS) algorithms. On the basis of introducing the mechanism of iterative chaotic map with infinite collapses (ICMIC) and the strategy of dimension learning–based hunting (DLH), an improved GWO was developed that was called IDGWO (ICMIC and DLH GWO). After searching the near‐optimal region through IDGWO, the CS with a variable step‐size Lévy flight search mechanism was switched adaptively to complete the final inversion. The correctness of our method was verified by the multi‐order mode dispersion curve inversion of a six‐layer high‐velocity interlayer model. Then it was further applied to the processing of real seismic datasets. The research results show that our method fully utilizes the advantages of each of the two global‐searching non‐linear algorithms after integrating IDGWO and CS, while effectively balancing the ability between global search and local exploitation, further improving the convergence speed and inversion accuracy and having good anti‐noise performance.

Assessment of cortical bone phantom properties using ultrasonic guided waves transduced with a multi-element transducer

The past decade has seen extensive exploration of alternative methods for the early diagnosis of osteoporosis through the assessment of the the bone quality. Previous research on axial transmission of ultrasonic guided waves demonstrated their sensitivity to the intrinsic properties of elongated cortical bones. This study highlights the capacity of low-frequency guided waves to ascertain bone properties through the inversion of dispersion curves. The proposed inversion scheme relies on dispersion curves simulated using the semi-analytical iso-geometric analysis (SAIGA) method. The model incorporates the excitability of ultrasonic guided wave modes to ensure that the inversion uses both the dispersive trajectories and amplitudes of the modes. Two models were examined: (1) a cortical bone phantom plate covered with a soft tissue mimicking material and (2) a quasi-cylinder cortical bone phantom surrounded by a soft tissue mimicking material. A proprietary axial transmission multielement ultrasonic transducer, designed for exciting guided waves under 500 kHz, was employed to capture experimental dispersion curves on phantoms through the 2D-FFT. The mechanical properties of the bone phantoms were inferred by minimizing disparities between experimental and simulated dispersion curves. Inverse properties exhibited an error of less than 4% compared to reference values. The axial transmission probe demonstrated its proficiency in accurately measuring modes propagating inside the cortical layer.

Along‐Strike Variations of Alaska Subduction Zone Structure and Hydration Determined From Amphibious Seismic Data

AbstractWe develop a 3‐D isotropic shear velocity model for the Alaska subduction zone using data from seafloor and land‐based seismographs to investigate along‐strike variations in structure. By applying ambient noise and teleseismic Helmholtz tomography, we derive Rayleigh wave group and phase velocity dispersion maps, then invert them for shear velocity structure using a Bayesian Monte Carlo algorithm. For land‐based stations, we perform a joint inversion of receiver functions and dispersion curves. The forearc crust is relatively thick (35–42 km) and has reduced lower crustal velocities beneath the Kodiak and Semidi segments, which may promote higher seismic coupling. Bristol Bay Basin crust is relatively thin and has a high‐velocity lower layer, suggesting a dense mafic lower crust emplaced by the rifting processes. The incoming plate shows low uppermost mantle velocities, indicating serpentinization. This hydration is more pronounced in the Shumagin segment, with greater velocity reduction extending to 18 ± 3 km depth, compared to the Semidi segment, showing smaller reductions extending to 14 ± 3 km depth. Our estimates of percent serpentinization from VS reduction and VP/VS are larger than those determined using VP reduction in prior studies, likely due to water in cracks affecting VS more than VP. Revised estimates of serpentinization show that more water subducts than previous studies, and that twice as much mantle water is subducted in the Shumagin segment compared to the Semidi segment. Together with estimates from other subduction zones, the results indicate a wide variation in subducted mantle water between different subduction segments.

Method of automated extracting dispersion curves based on time-frequency distribution of seismic data

This paper discusses examples of testing a new implementation of the method of multi-channel surface wave analysis on synthetic data computed for elastic media with complex boundary geometry. The new implementation of the method includes developed algorithms for noise-resistant spectral analysis based on time-frequency domain filtering of seismograms and inversion of dispersion curves of phase velocities based on determination of ranges of possible transverse wave velocity models and application of artificial neural networks. Based on the results of synthetic data processing, the accuracy, lateral resolution limitations and applicability limits of the method under consideration are evaluated.

Joint wave-equation inversion of Rayleigh and Love dispersion curves

Wave-equation dispersion (WD) inversion techniques for surface waves have proven to be a robust way to invert the S-wave velocity model. Unlike 1D dispersion curve inversion, WD method obviates the need for a layered model assumption and reduces the susceptibility to cycle-skipping issues in surface wave full-waveform inversion. Previous WD inversion experiments conducted on Rayleigh and Love waves have highlighted that inverting Love waves yields better stability due to their independence from the P-wave velocity model. Nevertheless, Rayleigh waves possess the advantage of greater penetration depth compared with Love waves with similar wavelengths. Therefore, combining the two types of surface waves is a feasible way to improve the accuracy of S velocity tomograms. In light of this, we develop a novel approach: a joint WD inversion encompassing Rayleigh and Love waves. This innovative technique adjusts the weighting of individual WD gradients using the sensitivity factor of an equivalent layered model, offering a significant advancement in subsurface characterization. Synthetic model tests demonstrate that the joint WD inversion method can generate a more accurate S-wave velocity model, particularly in the presence of complex low-velocity layers or high-velocity layers, when compared with individual wave WD inversion techniques. Simultaneously, the results of field tests validate the effectiveness of the proposed joint WD inversion strategy in producing a more dependable S-wave velocity distribution that aligns closely with the actual geologic structure.

Use of model substitution in the inversion of dispersion curves in weak subsurface layers

The primary concern for advanced geological prediction in tunnels is the weak layer, which can be explained by its properties based on the shear wave velocity. Ordinarily, the conventional technique of estimating longitudinal and transverse wave velocities using the reflection-wave theory has low precision and strong ambiguities, resulting in inaccurate predictions. To overcome this problem, surface waves can accurately predict multiparameter constraints and achieve high precision. However, the phenomenon of “mode kissing” is common during the surface wave dispersion mode of weak layers, leading to misinterpretation and escalating dangers during tunnel construction.Therefore, this study conducted numerical simulations of Rayleigh and Love waves using various weak-layer models and observation systems for low-speed weak layers. In addition, we analyzed the relationship between the dispersion curves obtained using the model substitution method and numerical models. We suggest a novel approach by employing the simplex method simulated annealing algorithm (ASSA) and the model-substitution method for inverting actual weak layer models and measurement data.Our findings demonstrate that the model substitution method can effectively delineate the “mode kissing” in the fundamental and higher modes of Rayleigh and Love waves. However, inconsistencies exist when characterizing the “mode kissing” frequency dispersion of Rayleigh waves when the low-speed layer velocity is equal to the surface velocity. Additionally, the model substitution method can accurately invert the velocity structure of various types of weak layer models. However, for low-sensitivity strata parameters, the accuracy improvement is limited. Therefore, we used coordinate rotation and model substitution to analyze the development of weak layers in front of the palm surface using spatial measurement data obtained from the tunnels. Our findings showed good agreement with the results of advanced drilling, verifying the effectiveness of using the model substitution method to invert the velocity structures of weak layers and providing a new approach for predicting geological features using surface- and reflection-wave methods.

Optimal Recovery of Rayleigh‐Wave Overtones by Multi‐Directional Acquisition

AbstractRayleigh waves are ubiquitously used for subsurface characterization through dispersion curve inversion, whose quality depends on the number of useable overtones. Traditional analysis is based on vertical receivers and, for active surveys, sources. However, for layered media, eigenfunction theory shows that optimal recovery of any given dispersion mode and frequency can be achieved by either vertical source‐vertical receiver or radial source‐radial receiver configurations, with source directivity being more dominant. Multi‐directional near‐surface wave‐equation modeling and field examples, including distributed acoustic sensing data, validate these predictions. Statistical analysis of compaction‐type near‐surface models shows that overtones are better recovered for radial‐radial surveys in large portions of the useable spectrum, extending beyond 60% for the second and above modes. We conclude that incorporating radial‐radial data acquisition is beneficial and should become standard procedure in active surveying, as well as analyzing the radial component in ambient noise and earthquake‐induced Rayleigh waves.

Simultaneous Estimation of P- and S-Wave Velocities by Integrated Inversion of Guided-P and Surface Wave Dispersion Curves

Simultaneous Estimation of P- and S-Wave Velocities by Integrated Inversion of Guided-P and Surface Wave Dispersion Curves

Multigrid Spatially Constrained Dispersion Curve Inversion for Distributed Acoustic Sensing (DAS)

Multigrid Spatially Constrained Dispersion Curve Inversion for Distributed Acoustic Sensing (DAS)

Joint Inversion of Rayleigh Wave Dispersion and Ellipticity Based on Deep Learning

The joint inversion of Rayleigh wave dispersion curves and ellipticity curves is an important method to obtain information about the velocity structure of the stratum, which has the advantages of high resolution and speed. However, there are problems in the application of this technique, such as complicated data, low inversion efficiency, and large influence factors of nonlinear inversion. Deep learning has excellent nonlinear approximation capability, which can compensate for most of the above defects, and has higher efficiency and accuracy compared with traditional methods. In this paper, in order to obtain the near-surface stratigraphic structure quickly and accurately, we propose to introduce the deep learning method into the joint inversion, use the CNN-LSTM network to perform the joint inversion of Rayleigh wave dispersion curves and ellipticity curves. And in order to expand the variety of data set, we propose to add noise to the sample data set, through which the empirical risk can be reduced, and the generalization performance of the network can be increased. Model experiments show that the deep learning network can effectively and accurately perform the joint inversion of Rayleigh waves, and adding noise to the training set is an effective way to improve the generalization and stability of the network.

Trans-Dimensional Bayesian Inversion of Rayleigh Wave Dispersion Curves for Shallow Surface Two-Dimensional Imaging

In this study, we achieve 2-D spatial structure directly from dispersion measurements using the reversible jump Markov chain Monte Carlo (rj-McMC) algorithm with a fully 2-D model parameterization. New parsimonious parameterization with low dimensional representation is introduced, which enable us to accurately reproduce the wave velocity field and the associated uncertainties. Field data test demonstrates that the proposed method estimates directly the shear-wave velocity profile with better lateral resolution. The associated uncertainties provide directly interpretable uncertainty on structures of interest.

Application of Deep Learning in Rayleigh Dispersion Curves Inversion

The inversion of the Rayleigh wave dispersion curve is a fundamental step in determining the shear wave velocity profile. However, existing inversion methods, such as linear and nonlinear approaches, have inherent limitations. In order to overcome these challenges and enhance the speed and accuracy of the inversion, this paper proposes a novel deep learning-based approach. We establish a method to construct sample data that ensures ergodicity and evolutive orderliness of the near-surface velocity profile using a constrained Markov decision process to address these limitations. We then design a deep learning model to capture the nonlinear mapping relationship between the dispersion sequence data and velocity structure. Training the model on the generated sample data accurately predicts the subsurface velocity profile based on the dispersion curve. The proposed method is evaluated through theoretical model experiments, demonstrating high computational accuracy.

Joint Inversion of SPREE Receiver Functions and Surface Wave Dispersion Curves for 3‐D Crustal and Upper Mantle Structure Beneath the U.S. Midcontinent Rift

AbstractBroadband seismograms from the EarthScope Transportable Array and Superior Province Rifting EarthScope Experiment (SPREE) deployments are used to map the crust and uppermost mantle structures beneath the failed Midcontinent Rift (MCR) of Minnesota/Wisconsin, USA. The results suggest the existence of a variable zone of mafic underplating that is up to 20 km thick (40–60 deep). We jointly invert receiver functions and Rayleigh wave dispersion curves to quantify the region's crustal and mantle shear‐wave velocity structure. Basin sediment thicknesses are mildly asymmetric about the rift axis, with thickest regions immediately beneath the rift. 3‐D modeling shows anomalous lower crust and crust‐mantle transitions beneath the MCR. Sub‐MCR crustal thicknesses are generally >50 km with lower crust Vs of 4.0–4.2 km/s. Away from the MCR, the crust is typically ∼40 km thick. Strong variations in apparent crustal thickness are found along the MCR, increasing significantly in places. An additional layer of shear velocities intermediate between typical lower crust and upper mantle velocities (4.1–4.6 km/s) exists beneath most of the MCR which is thickest beneath the rift axis and pinches out away from the rift. This structure corroborates previous proposals of the presence of an underplated layer near the Moho. Results cannot distinguish between different mechanisms of emplacement (e.g., mafic interfingering within a subsequently down‐dropped lower crust vs. development of a high‐density pyroxenitic residuum at the top of the mantle). Also observed are anomalously high (>4.7 km/s) sub‐rift shear‐wave velocities at ∼70–90‐km depths, suggesting the presence of cold, depleted upper mantle material.

Structure of the crust-uppermost mantle beneath the Ethiopian volcanic province using ambient seismic noise and teleseismic P wave coda autocorrelation

The Ethiopian-Yemen plateaus have been affected by plume-related magmatism for at least 40 My, yet the nature and distribution of intrusive magmas and their relation to subsequent East Africa rifting remain poorly characterized. This paper presents a 3D shear (S) - wave velocity structure of the crust and uppermost mantle beneath the northern sectors of the East African rift and the dynamically-supported Ethiopian Plateau. We apply a Bayesian inversion of group and phase velocity dispersion curves for periods 5–40 s extracted from the ambient noise tomography of data from over 125 broadband seismic stations, and we identify seismic discontinuities using autocorrelation of P-wave coda. The resulting crustal structure affecting much of the Main Ethiopian Rift (MER) indicates a pronounced low S-wave velocity lower crust (∼3.6 km/s) that becomes thinner towards the northeast rising to almost the same depth level (∼20 km) as the base crust beneath the Afar triple junction zone. We also find high velocity features in the crust and uppermost mantle beneath the Afar rift axes, the current locus of strain and volcanism, that may indicate voluminous new basaltic crust. Our Moho-depth map indicates that the entire Afar Depression is underlain by crust thinner than 25 km, whereas the MER and central Ethiopian plateau are underlain by low S-wave velocity crust thicker than 35 km. These patterns suggest active underplating beneath the largely unfaulted plateau, in contrast to the efficient magmatic feeder system supplying a narrow zone of incipient seafloor spreading in the Afar depression. Within the uppermost mantle we report evidence of a localized asthenospheric upwelling beneath the western part of the plateau southeast of Lake Tana, overlying a cooled magma body within the upper crust. A broader low-velocity uppermost mantle underlies the crust beneath the Western Plateau. These observations attest to active mantle upwelling, heating, and melt intrusion at relatively different length scales beneath the plateau in agreement with the ongoing active strains reported away from the rift zones. At 45–60 km depth beneath the rift and its shoulders, we observe a fast lid (4.2–4.4 km/s). Beneath the plateau, upper mantle velocity highs that are at least 5 km below the Moho are observed. These areas have most likely experienced prolonged magma extraction and may mark highly depleted areas.