Dispersion Inversion Research Articles

Numerical simulation and dispersion inversion of ground penetrating radar waveguide

Abstract Ground penetrating radar (GPR) is widely used in near-surface detection due to its non-destructive and high-efficiency advantages. Radar waves are continuously reflected in the waveguide structure, and dispersion will be formed. In order to find out the propagation regularity and characteristics of radar waves in waveguides, we use the simulation and field GPR waveguide data to test the radar wave dispersion characteristic. Then, the Dix-type inversion method is used to estimate the permittivity from the radar wave dispersion curve. The synthetic and field data tests show that the GPR waveguide dispersion inversion can accurately estimate the permittivity result.

Insight into intracontinental deformation and crustal reworking of ancient continents implied by crustal structure imaging of the Yangtze Craton

The crustal imprints from multistage tectonic activities in cratons offer valuable insights into continental evolution. Utilizing seismic data from two densely deployed, nearly perpendicular linear arrays, and a newly developed stepwise joint inversion of depth-domain receiver function and surface wave dispersion, we constructed a detailed crustal layering model for the Yangtze Craton. Our analysis revealed elongated double velocity reversal zones as salient features of the crust, which likely record ancient crustal reworking and juvenile crustal growth associated with Neoproterozoic rift-related magmatic processes. The interlayering of low- and high-velocity structures may contribute to the enduring stability of the Yangtze Craton. Additionally, superimposed layers separated by east-dipping interfaces and abrupt changes in crustal thickness in the boundary belts surrounding the Yangtze Craton document the crust's structural responses to intracontinental deformation during continent assembly.

Joint inversion of receiver function and surface wave dispersion based on the unscented Kalman inversion

SUMMARY Joint inversion, such as the combination of receiver function and surface wave dispersion, can significantly improve subsurface imaging by exploiting their complementary sensitivities. Bayesian methods have been demonstrated to be effective in this field. However, there are practical challenges associated with this approach. Notably, most Bayesian methods, such as the Markov Chain Monte Carlo method, are computationally intensive. Additionally, accurately determining the data noise across different data sets to ensure effective inversion is often a complex task. This study explores the unscented Kalman inversion (UKI) as a potential alternative. Through a data-driven approach to adjust estimated noise levels, we can achieve a balance between actual noise and the weights assigned to different data sets, enhancing the effectiveness of the inversion process. Synthetic tests of joint inversion of receiver function and surface wave dispersions indicate that the UKI can provide robust solutions across a range of data noise levels. Furthermore, we apply the UKI to real data from seismic arrays in Pamir and evaluate the accuracy of the joint inversion through posterior Gaussian distribution. Our results demonstrate that the UKI presents a promising supplement to conventional Bayesian methods in the joint inversion of geophysical data sets with superior computational efficiency.

Three-dimensional joint inversion of surface wave dispersion and gravity data using a petrophysical approach: an application to Los Humeros Geothermal Field

SUMMARY We present a method to jointly invert surface wave dispersion data and gravity measurements for 3-D shear wave velocity and density models. We implemented a petrophysical approach to combine the kernels of both methodologies in a single process. The synthetic experiments show that jointly inverted models recover shear wave velocity and density better than separate inversions. In particular, density models benefit from the good vertical resolution of surface wave dispersion data, while shear velocity models benefit from the good lateral resolution of gravity data. We also proposed two methods to stabilize the solution when using high-grade polynomials. We applied the methodology to the Los Humeros Geothermal area to demonstrate its applicability in a complex geological scenario. Compared with separate inversion, the joint inversion contributes to enhancing key aspects of the geothermal system by (i) delimitating better the geometry of the caldera deposits in the first 0–2.8 km deep by increasing the vertical resolution in density, (ii) delimitating better the lateral borders of low-Vs bodies at different depths interpreted as a part of a complex magmatic chamber system and (iii) estimating the local shear wave velocity–density relationship that conforms to other known relationships for sedimentary and igneous rocks but with some differences that bring us additional information.

Translithospheric magma plumbing system fossilized in the Emeishan large igneous province

Lighting up the magma plumbing system beneath a large igneous province (LIP) is challenging because the complex magma migration paths are often covered by flood basalts and sediments. Here, we present a three-dimensional seismic image of the Permian Emeishan LIP in Southwest China, constructed by joint inversion of Rayleigh wave dispersions and receiver functions. The results outline a cylindrical, high-velocity anomaly extending to ~135 km depth below the inner zone of this continental LIP. The geometry and magnitude of the high-velocity anomaly suggest that it represents culminated crystallized materials of primary magmas, thereby mirroring a magma plumbing system fossilized in the lithosphere. Furthermore, our geodynamic models illustrate that the nearly vertical plumbing system was controlled by slow plate motion during the magma emplacement. The plume head beneath a nearly static plate has higher thermal buoyancy and thus promotes more intensive magma emplacement. This phenomenon may apply to other LIPs throughout Earth’s history

Crustal thicknesses in Uruguay from joint inversion of receiver functions and surface wave dispersion

The development of a seismic network in Uruguay in recent years has enabled studies of crustal structure in a region with few seismological studies of this type. In this work, we update the crustal thicknesses and Vp/Vs ratios calculated by H-k stack and present S-wave velocity models based on joint inversion of receiver functions and Rayleigh wave group velocity dispersion curves.Some interesting results are the presence of a lower crust with a high S-wave velocity of 4.1 km/s below one of the stations located on the Río de la Plata Craton and the existence of a transitional Moho in Uruguay's northernmost station on the Paraná Basin, perhaps suggesting the presence of localized underplated material. A relatively thick crust, 41.8 km, compared to surrounding stations, was found beneath the Sierra Ballena Shear Zone in the Dom Feliciano Belt. We confirm the decrease in crustal thickness when approaching the oceanic coast, reaching a Moho depth of 36.3 km in SE Uruguay. Finally, the calculated Poisson's ratio allows inferring a crust of felsic to intermediate composition beneath most of Uruguay.

Uncertainty Quantification in Radial Anisotropy Models Based on Transdimensional Bayesian Inversion of Receiver Functions and Surface-Wave Dispersion: Case Study Sri Lanka

ABSTRACT In geophysical inference problems, quantification of data uncertainties is required to balance the data-fitting ability of the model and its complexity. The transdimensional hierarchical Bayesian approach is a powerful tool to evaluate the level of uncertainty and determine the complexity of the model by treating data errors and model dimensions as unknown. In this article, we take account of the uncertainty through the whole procedure, thus developing a two-step fully Bayesian approach with coupled uncertainty propagation to estimate the crustal isotropic and radial anisotropy (RA) model based on Rayleigh and Love dispersion as well as receiver functions (RFs). First, 2D surface-wave tomography is applied to determine period-wise ambient noise phase velocity maps and their uncertainty for Rayleigh and Love waves. Probabilistic profiles of the isotropic average VS and RA as a function of depth are then derived at station sites by inverting the local surface-wave dispersion and model errors and RFs jointly. The workflow is applied to a temporary seismic broadband array covering all of Sri Lanka. The probabilistic results enable us to effectively quantify the uncertainty of the final RA model and provide robust inferences. The shear-wave velocity results show that the range of Moho depths is between 30 and 40 km, with the thickest crust (38–40 km) beneath the central Highland Complex. Positive RA (VSH>VSV) observed in the upper crust is attributed to subhorizontal alignment of metamorphic foliation and stretched layers resulting from deformation. Negative RA (VSV>VSH) in the midcrust of central Sri Lanka may indicate the existence of melt inclusions and could result from the uplift and folding process. The positive RA in the lower crust could be caused by crustal channel flow in a collision orogeny.

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.

Understanding the structure of crust and shallow upper mantle beneath western Tibet through the joint inversion of Rayleigh wave group velocity dispersion with interpolated receiver functions

We present the 3-D shear wave velocity variationin the crust and upper mantle structure of western Tibet using a joint inversion of Rayleigh wave group velocity dispersion and interpolated receiver function. The lateral sampling of the receiver function and the surface wave dispersion is equalized by the interpolation scheme. This new method of spatial interpolation eliminates difficulties caused by back azimuthal variation in the receiver function. We have jointly inverted these interpolated receiver functions with the Rayleigh wave group velocity dispersions obtained from the earthquake and ambient noise tomography to map the tectonic structure of western Tibet. The study reveals remarkable variation of the seismic characteristics in the crust and shallow upper mantle of western Tibet. The mapped Moho depth is ~74 km in the northern part of the plateau, whereas it is ~69 km in the southern part. A thick mid-crustal slow-velocity zone from ~10km up to ~40 km depth has been observed, which could be attributed to partial melt. A noteworthy finding is the variation in slower crustal velocity between the south and north of the Lhasa Block (LB). We interpret this as the Indian crust that has been underthrusted beneath the Tibetan plateau, and the northern limit of the Indian lithosphere extends to the southern part of the LB.

Joint Inversion of Surface-Wave Dispersions and Receiver Functions Based on Deep Learning

Abstract We proposed a deep learning (DL) method to derive VS models from joint inversion of Rayleigh-wave dispersions and receiver functions, which is based on multilabel convolutional neural network and recurrent neural network. We used a spline-based approach to generate synthetic models instead of directly using existing models to build the training data set, which improves the generalization of the method. Unlike the traditional methods, which usually set a fixed VP/VS ratio, our method makes full use of the powerful data mining ability of DL to invert the VS models assuming different VP/VS ratios. A loss function is specially designed that focuses on key features of the model space, for example, the shape and depth of Moho. Synthetic tests demonstrate that the proposed method is accurate and fast. Application to the southeast margin of the Tibetan Plateau shows results consistent with the previous joint inversion with P constraints, indicating the proposed method is reliable and robust.

Seismic Evidence for Crustal Magmatic Intrusion Beneath the Southern Part of the Eastern North American Margin

AbstractThe southern portion of the eastern North American margin (SENAM) is an archetypical volcanic passive margin formed during Mesozoic rifting. How past magmatic events affect the evolution of the SENAM remains an open question of fundamental importance. To better understand this question, here we construct a high‐resolution 3‐D crustal velocity model from the oceanic side to the continental interior with a combination of multimodal dispersion inversion and full‐waveform ambient noise tomography. Our new model reveals an oceanic‐continental transitional crust over a short horizonal distance of 100–150 km across the SENAM, with a local‐scale lower‐than‐surrounding velocity anomaly directly beneath the transitional crust. Furthermore, the new model shows three intra‐crustal higher‐than‐average velocity anomalies beneath the SENAM continent. We suggest that the magmatism assisted the Mesozoic rifting process to form the narrow ocean‐continent transitional crust along the coastline. The underplating of magma beneath the transitional crust led to a reduction of seismic velocity of the uppermost mantle. In addition, it is probable that the emplacement of the Central Atlantic Magmatic Province caused widespread magmatic intrusions within the continental crust of the SENAM, which were later solidified into intra‐crustal high‐velocity plutons. Our findings provide new insights into crustal modification history at the passive margin.

Determination of the VS profile at a “noisy” industrial site via active and passive data: The critical role of Love waves and the opportunities of multicomponent group velocity analysis

To define the procedures necessary to unambiguously define the subsurface model, a comprehensive set of active and passive seismic data was collected in an industrial area characterized by an extremely high level of background microtremors. Passive data are recorded to define three observables: the dispersion curve of the vertical component of Rayleigh waves via miniature array analysis of microtremors, the Love-wave dispersion curve via extended spatial autocorrelation, and the horizontal-to-vertical spectral ratio (HVSR). Active data used for the holistic analysis of surface waves are extracted from data recorded through a hybrid acquisition procedure accomplished with only two 3C geophones used to simultaneously define the HVSR at two points. Defined observables are combined according to three different approaches: the joint analysis of Rayleigh waves and HVSR, the joint analysis of Rayleigh and Love waves together with the HVSR, and the joint analysis of multicomponent group velocities together with the HVSR and Rayleigh-wave particle motion (RPM) curves. In agreement with the theory, data indicate that, in general, surface-wave modeling cannot be performed considering modal dispersion curves: dispersion obtained from passive data needs to be modeled considering the effective curve, whereas group velocity obtained from active data can be analyzed using the full velocity spectrum technique. Results indicate that joint inversion of Rayleigh-wave dispersion and HVSR does not necessarily ensure the correctness of the obtained S-wave velocity ([Formula: see text]) profile and that Love waves represent a key observable to fully constrain an unambiguous inversion procedure. However, the joint analysis of multicomponent group velocity spectra (from active multicomponent single-offset data) together with the HVSR and RPM curves is a further efficient way to obtain robust [Formula: see text] profiles through the active and passive data obtained by a single 3C geophone.

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.

Electroseismic Scholte‐wave analysis: A potential method for estimating shear‐wave velocity structure of shallow‐water seabed sediments

AbstractThe potential application of conducting Scholte‐wave analysis using electroseismic pressure fields excited by an electric current source due to the electrokinetic effect in fluid‐saturated porous seabed sediments is investigated. First, we develop a numerical modelling algorithm by combining the Luco–Apsel–Chen generalized reflection and transmission method with the peak‐trough averaging method to simulate the electroseismic wave fields in stratified fluid/porous media. The modelling results show that the electroseismic pressure signals recorded on the seafloor are mainly composed of evanescent electroseismic waves, and Scholte waves are the dominant wave pattern. Their amplitudes are generally within the order of magnitudes capable of being detected by current seismic instruments. Then, the modified frequency–Bessel transform method is extended to extract the Scholte‐wave dispersion curves from electroseismic pressure fields. Results demonstrate that Scholte‐wave dispersion curves extracted from electroseismic records are superior to those extracted from conventional seismic wave fields excited by an airgun source under the same source–receiver geometry because they contain many overtones and are almost free from the interferences of dispersive guided waves. Furthermore, the Scholte‐wave dispersion inversion results obtained by employing the Levenberg–Marquardt method show that the shear‐wave velocity model inverted by Scholte‐wave dispersion curves extracted from the electroseismic pressure field is more accurate than those obtained by dispersion curves extracted from the seismic wave fields with the guided‐wave removal. The above results indicate that the electroseismic Scholte‐wave analysis method has the potential to evaluate the shear‐wave velocities of shallow‐water seabed sediments.

JointNet: A Multimodal Deep Learning-Based Approach for Joint Inversion of Rayleigh Wave Dispersion and Ellipticity

ABSTRACT Joint inversion of multitype datasets is an effective approach for high-precision subsurface imaging. We present a new deep learning-based method to jointly invert Rayleigh wave phase velocity and ellipticity into shear-wave velocity of the crust and uppermost mantle. A multimodal deep neural network (termed JointNet) is designed to analyze these two independent physical parameters and generate outputs, including velocity and layer thicknesses. JointNet is trained using random 1D models and corresponding synthetic phase velocity and ellipticity, resulting in a low cost for the training dataset. Evaluation using synthetic and observed data shows that JointNet produces highly comparable results compared to those from a Markov chain Monte Carlo-based method and significantly improves inversion speed. Training using synthetic data ensures its generalized application in various regions with different velocity structures. Moreover, JointNet can be easily extended to include additional datatypes and act as a joint inversion framework to further improve imaging resolution.

A method for transforming aliased modes to true modes based on density clustering and Riemann sheets selection in acoustic logging dispersion inversion

Dispersion curves obtained from well logs provide crucial formation information around the borehole. An essential step in the inversion of such curves is to eliminate aliased modes, which can potentially interfere with true modes at higher frequencies. The traditional approach involves manually matching the inversion slowness values with the corresponding wave modes at each frequency, which is time consuming and labor intensive. In addition, the traditional method is applicable for the elimination of the aliased modes that are far from true modes, but it is ineffective in resolving aliased modes that approach or even intersect with the true modes. To address these limitations, a novel method is developed to transform aliased modes into true modes. The proposed method involves two key steps. First, the slownesses of individual modes are automatically picked by the density clustering algorithm. Second, based on the Riemann sheets selection of slowness, aliased modes are transformed into true modes by using the single valuedness of the wave-mode spectra and the correspondence between the amplitude spectrum and the slowness. In addition, a theoretical background is provided by introducing the concept of Riemann sheets to explain the origin of aliased modes in the computation. The proposed method can obtain comprehensive and precise dispersion curves, even in cases for which the true modes are interfered with or crossed by aliased modes. The accuracy of the method is validated by comparing the inversion results with the forward model’s dispersion curves. Furthermore, the robustness of the approach is determined by applying it to synthetic waveforms with noise and field waveforms.

Rayleigh Wave Dispersion and Inversion for Shallow Surface with a High-velocity Rigid Pavement

We investigate the rigid pavement influence on phase velocity dispersion of the Rayleigh wave by using numerical modeling. An overestimation of Rayleigh wave phase velocity is observed more than 10% deviation caused by high-velocity rigid pavement. Based on the generalized reflection and transmission (R/T) coefficient method, the linear eigenvalue problem is solved for vertically heterogeneous media with a rigid pavement structure. The secular function demonstrates the multi-valuedness which is different phase velocity at the same frequency for the single Rayleigh mode. To address mode misidentification problem, we adopt a new misfit function for multimodal dispersion inversion. A Markov chain Monte Carlo (MCMC) sampling algorithm is used to solve dispersion inversion. The synthetic test shows that Rayleigh wave dispersion inversion incorporating a pavement layer can improve estimation accuracy of shear wave velocity.

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.

Cryptic Magma Chamber in the Deccan Traps Imaged Using Receiver Functions and Surface Wave Dispersion

AbstractAn anomalous crust and lithospheric mantle in the Deccan Volcanic Province are imaged below a 160 km long W‐E profile through the joint inversion of receiver functions and surface wave dispersion. The upper crust has an unusually low S‐wave velocity (Vs ∼ 3.3–3.5 km/s) at 8–17 km depth, underlying a 4 km thick high‐velocity layer (Vs > 3.8 km/s). The low velocity possibly represents the frozen magma reservoir, the source for the magma eruption at ∼65 Ma due to the interaction of the Reunion plume with India. The shallow, high‐velocity layer could be basaltic mafic intrusions responsible for the production of massive CO2 degassing. The Moho deepens beneath the west coast to ∼45 km due to 10–15 km of magma underplating. The mantle plume scar is seen as thinned lithosphere (80–100 km), with the presence of long‐lived low‐velocity layers in the shallow mantle attributed to the presence of sulfide melts.

Dispersion inversion for P- and S-wave velocities based on guided P and Scholte waves

Inversion based on dispersion curves is widely used for the estimation of subsurface velocity structures. However, conventional surface-wave dispersion inversion usually uses normal modes, and only the S-wave velocities are retrieved. To retrieve P-wave velocities, the dispersion of guided P waves should be considered. We develop an inversion scheme that uses the guided-P-wave and Scholte-wave modes to implement an integrated inversion for P- and S-wave velocity structures of shallow marine sediments. The forward modeling of dispersion curves is based on the spectral-element method and the perfectly matched layer technique. A quantitative sensitivity analysis of guided P modes is then carried out, which not only confirms the capability of guided P modes for estimating the P-wave velocity but also indicates that guided P modes can be combined with Scholte modes to better constrain the S-wave velocity. Based on the Levenberg-Marquardt algorithm, a joint inversion scheme that uses guided P and Scholte modes is developed. The validity of the inversion scheme is assessed by testing synthetic and field ocean-bottom seismometer data obtained in shallow marine environments. The results demonstrate the effectiveness of the joint inversion for retrieving the P- and S-wave velocity structures of shallow marine sediments.