Rayleigh Wave Dispersion Curves Research Articles

Multiple inversions of Rayleigh wave dispersion curve for geotechnical site characterization using particle swarm optimization dan genetic algorithm

The inversion of the Rayleigh wave dispersion curve is a crucial step in the multi-channel analysis of surface waves (MASW) method, used to obtain the shear wave velocity (<em>Vs</em>) profile. The nonlinear and multimodal nature of the dispersion curve makes a global optimization approach, such as particle swarm optimization (PSO) and genetic algorithm (GA), the optimal choice for inversion. This study aims to compare the performance of multiple inversions of PSO (MI-PSO) and multiple inversions of GA (MI-GA) in solving the inversion problem of the Rayleigh wave dispersion curve. The test results indicate that the utilized MI-PSO outperforms MI-GA in terms of computational time and accuracy of the obtained model

Inversion of Rayleigh Wave Dispersion Curve Extracting from Ambient Noise Based on DNN Architecture

The inversion of the Rayleigh wave dispersion curve is a crucial step in obtaining the shear wave velocity (VS) of near-surface structures. Due to the characteristics of being ill-posed and nonlinear, the existing inversion methods presented low efficiency and ambiguity. To address these challenges, we describe a six-layer deep neural network algorithm for the inversion of 1D VS from dispersion curves of the fundamental mode Rayleigh surface waves. Our method encompasses several key advancements: (1) we use a finer layer to construct the 1-D VS model of the subsurface, which can describe a more complex near-surface geology structure; (2) considering the ergodicity and orderliness of strata evolution, the constrained Markov Chain was employed to reconstruct the complex velocity model; (3) we build a practical and complete dispersion curve inversion process. Our model tested the performance using a random synthetic dataset and the influence of different factors, including the number of training samples, learning rate, and the selection of optimal artificial neural network architecture. Finally, the field test dispersion data were used to further verify the method’s effectiveness. Our synthetic dataset proved the diversity and rationality of the random VS model. The results of training and predicting showed higher accuracy and could speed the inversion process (only ~15 s), and we proved the important effect of different factors. The outcomes derived from the application of this technique to the measured dispersion data in the Yellow River Delta exhibit a strong correlation with the outcomes obtained from the integration of the very fast simulated annealing method and the downhill simplex method, as well as the statistically derived shear wave velocity data of the sedimentary layers in the Yellow River Delta. From a long-term perspective, our method can provide an alternative for deriving VS models for complex near-surface structures.

Effects of surface topography and subsurface structural irregularities of river embankments on Rayleigh wave propagation

A numerical investigation of surface wave propagation in the surface wave exploration of river embankments is implemented using 3D shallow soil models with different subsurface shapes and S-wave velocities. The focus is on the effects of surface and subsurface irregularities on the propagation and dispersion characteristics of Rayleigh waves generated by a surface source and observed at points along the crest of the embankment. Rayleigh wave dispersion curves observed along the embankment crest are found to be contaminated by reflected waves, with the amount of contamination affected more by the position of the velocity boundary at the bottom edge of the embankment than the surface topography. When the velocity boundary is close to the ground surface, especially at the toe of the slope, the effect of reflected waves is sufficiently large to generate biases in the phase velocity estimates.Graphical

On the Accuracy of Surface-Wave Dispersion Measurements from Horizontal-Component Ambient Noise Cross Correlations

Abstract At present, both Rayleigh and Love waves can be extracted from cross-correlations of ambient noise in ambient noise tomography (ANT). It has been demonstrated that accurate Rayleigh-wave dispersion curves can be extracted from vertical-component noise when noise sources are evenly distributed in space. However, because the rotation of horizontal components alters the distributions of effective sources in horizontal–horizontal cross correlations between a pair of stations, it is still not completely sure if dispersion curves of Rayleigh and Love waves extracted from horizontal-component noise data are accurate for ANT. In this study, through numerical simulations, we demonstrate that surface-wave phase velocities extracted from the horizontal–horizontal cross-correlation functions (CCFs) systematically deviate from structural phase velocity even when noise sources are evenly distributed in space. The deviations of phase velocities quickly increase with decreasing station separations of CCFs when station separations are shorter than three wavelengths. Further analysis on field data recorded at seismic stations in the contiguous United States confirms the existence of the phase-velocity deviations of Rayleigh and Love waves when they are measured from horizontal–horizontal CCFs. Because the deviations become smaller with increasing station separations and are less than 0.25% at station separations longer than three wavelengths, we suggest that it is best to only select those CCFs with station separations longer than three wavelengths in ANT when measuring phase velocities of surface waves from horizontal-component CCFs, such as Love waves from radial–radial CCFs.

Shear Wave Velocities in the San Gabriel and San Bernardino Basins, California

AbstractWe construct a new shear velocity model for the San Gabriel, Chino and San Bernardino basins located in the northern Los Angeles area using ambient noise correlation between dense linear nodal arrays, broadband stations, and accelerometers. We observe Rayleigh and Love waves in the correlation of vertical (Z) and transverse (T) components, respectively. By combining Hilbert and Wavelet transforms, we obtain the separated fundamental and first higher mode of the Rayleigh wave dispersion curves based on their distinct particle motion polarization. Basin depths constrained by receiver functions, gravity, and borehole data are incorporated into the prior model. Our 3D shear wave velocity model covers the upper 3–5 km of the crust in the San Gabriel, Chino and San Bernardino basin area. The Vs model is in agreement with the geological and geophysical cross‐sections from other studies, but discrepancies exist between our model and a Southern California Earthquake Center community velocity model. Our shear wave velocity model shows good consistency with the CVMS 4.26 in the San Gabriel basin, but predicts a deeper and slower sedimentary basin in the San Bernardino and Chino basins than the community model.

In situ estimation of effective rock elastic moduli by seismic ambient vibrations

In this study, we performed a non-invasive ambient noise investigation of unsaturated rock structures in the Bohemian Paradise (Bohemian Cretaceous Basin, Czech Republic). Our study focused on two key topics: 1) An in situ elastic moduli estimate of competent, horizontally deposited sandstone layers using ambient noise array measurements. Recordings were processed using an f-k array analysis, from which frequency-dependent Love and Rayleigh wave dispersion curves, as well as Rayleigh wave ellipticity, were retrieved. Data were inverted for the P- and S-wave velocity profiles, from which Young's and shear moduli were successfully estimated. 2) A study of the local response of the Kapelník rock tower. We analysed a dataset of ambient noise recordings obtained from the top of the tower and its foot. Information regarding tower oscillation frequencies and directions, together with amplification ratios, were retrieved from a particle motion polarisation analysis and from site-to-reference spectral ratios. Euler-Bernoulli beam theory was also employed for interpreting measured data using elastic moduli estimated from noise array measurements.

Crustal Shear Wave Velocity Structure Using Dispersion of Rayleigh Wave Beneath Sumatra Stations

The structure of the earth's crust is a fundamental and very important topic in seismology, because the crustal structure can be used as initial information to study the surface conditions of an area. One method to determine the structure of the earth's crustal layers is by analyzing the dispersion of surface waves, because surface waves are very sensitive to S waves. The shear wave velocity as a result of Rayleigh wave velocity inversion can provide the information of the subsurface material properties in the earth that can be study the structure of the earth's crust. The inversion results using the SVAL program can provide the Rayleigh wave dispersion curve with group velocity which shows the station on the island of Sumatra is higher than the velocity on the island of Nias. The structure beneath the island of Sumatera was formed earlier than the island of Nias. The thickness of the crust varies in the Sumatra region, the thickness of the crust on the island of Sumatra (BKNI, LHMI, MNAI and PMBI) is 28 km and 33 km. Specifically on the island of Nias, the thickness of the crust is 19 km. S-wave velocity in the crust is 3.1 km/s to 3.7 km/s.

Lithospheric deformation in Mongolia revealed by anisotropic Rayleigh wave tomography: Implications for the mechanism of intracontinental orogeny

The Mongolian Plateau is situated in the eastern part of the Central Asian Orogenic Belt that was formed during the Paleozoic era. In the Cenozoic era, the plateau has been reactivated, leading to significant topographic uplift, volcanism, and seismic activity. Several destructive earthquakes, ranging from magnitudes 6 to 8, have occurred in the 20th century. But the mechanism of these neotectonics remains unclear. To better understand these processes, we determined S wave velocity and azimuthal anisotropy in the crust and upper mantle under Mongolia using Rayleigh wave dispersion curves. Our findings indicate that the lithosphere is dominated by NW-SE fast velocity directions (FVDs). However, we observed different patterns in two specific regions. The lithospheric anisotropy under the Hangay Dome is weak, suggesting that it is accompanied by significant mantle upwelling under the dome. On the other hand, the FVDs in the Gobi Desert exhibit a circular pattern that wraps around the Ordos Block, which may have been caused by past and present deformation imposed on the stable block. These results offer new insights into the lithospheric deformation and dynamics of the Mongolian Plateau.

Surface wave dispersion curve inversion using mixture density networks

SUMMARYIn many seismological, environmental and engineering applications a detailed S-wave velocity model of the shallow subsurface is required. This is generally achieved by the inversion of surface wave dispersion curves using various inversion methods. The classical inversion approaches suffer from several shortcomings, such as inaccurate solutions due to local minima or large computation times in case of a wide parameter space. A number of machine learning (ML) approaches have been suggested to tackle these problems, which however do not provide probabilistic solutions and/or constrain layer number and layer thickness to a fixed value. In this study, we develop a novel neural network (NN) approach in order to characterize the shallow velocity structure from Love and Rayleigh wave dispersion curves. The novelty of our method lies in the simultaneous estimation of layer numbers, layer depth and a complete probability distribution of the S-wave velocity structure. This is achieved by a two-step ML approach, where (1) a regular NN classifies the number of layers within the upper 100 m of the subsurface and (2) a mixture density network outputs the depth estimates together with a fully probabilistic solution of the S-wave velocity structure. We show the advantages of our ML approach compared to a conventional neighbourhood inversion and a Markov chain Monte Carlo algorithm. Our ML approach is then applied to dispersion curves extracted from recorded noise data in Munich, Germany. The resulting velocity profile is in accordance with lithologic information at the site, which highlights the potential of our approach.

Active and passive seismic methods for site characterization in Nuweiba, Gulf of Aqaba, Egypt

Nuweiba is located on the western coast of the Gulf of Aqaba (GoA), which represents the southern part of the Gulf of Aqaba - Dead Sea transform fault (GoA-DST). The GoA is characterized by high seismic activity and is the source of the November 22, 1995, Nuweiba earthquake, with a moment magnitude of Mw 7.3. This seismic unrest caused extensive damage in the city of Nuweiba due to the strong shaking caused by the earthquake. In addition, soil amplification triggered by the thick soft-sediments of the Wadi Watir delta beneath the city amplified the destructive power of the event. Therefore, an assessment of the effect of the Wadi Watir sediments on the ground motion at Nuweiba is very important for future construction, seismic hazard assessment, and seismic risk mitigation. Accordingly, the goal of the current study is to define the amplification characteristics of the Wadi Watir deposits using microtremor and surface wave data sets. The horizontal-to-vertical spectral ratio (HVSR) technique is applied to the microtremor data and Multichannel Analysis of Surface Waves (MASW) is applied to the surface wave data. The data are processed to obtain the distribution of the fundamental resonance frequency (F0), the depth of the geophysical bedrock using joint inversion of the Rayleigh wave dispersion curve and ellipticity peak, the shear wave velocity structure, the time-averaged shear-wave velocity in the topmost 30 m (Vs30), and the shear wave transfer function. The results of the HVSR show that F0 in the northern part of the city is 4.2–5.2 Hz and 0.5–0.8 Hz in the middle of the city. Bedrock depth is found to be in the range of 27 and 199 m. The one-dimensional velocity structure obtained from the MASW measurements has resolved two sedimentary layers within the upper 15 m. The Vs30 ranges between 207 and 556 m/s, according to the Vs30 the soil in the study area is categorized into soil classes B and C according to Eurocode 8. The obtained shear wave transfer functions show that the highest amplification factors are observed in the middle part of the study area.

A Local Seismic Project near the Dalk Glacier Area, Larsemann Hills, East Antarctica: Toward Subice Imaging and Icequake Monitoring

Abstract During the 2019–2020 field season of the 36th Chinese National Antarctic Research Expedition, two seismic arrays were deployed in the Dalk Glacier area of Larsemann Hills, East Antarctica. The arrays consisted of 100 short-period nodal stations and were intended to investigate the physical properties and seismic events in the region, with the goal of enhancing our understanding of the glacier’s structure and dynamics. With these data, we use horizontal-to-vertical spectral ratio (HVSR) analysis to estimate the ice thickness. Noise cross-correlation functions and multimode dispersion curves of Rayleigh waves were extracted from the vertical-component ambient noise data to illuminate near-surface glacial structures. Teleseismic events with Mw >5.5 and two typical kinds of icequakes were observed via visual inspection. These initial results improve the understanding of the physical properties of the ice sheet as well as the glacial seismicity in Dalk Glacier.

Tectonic Activities Description in the Ongoing Collision Zone of the Eurasia-Arabia Plates Using 2D Surface Waves Tomography

In order to better understand the regional tectonic activities of the continent-continent ongoing collision-compressed edge zone of the Eurasian-Arabic plates, 2D tomography maps of the Caucasus territory using the Rayleigh waves were generated. The 2D tomography images of this study, illustrate the large variety in surface wave propagation velocity in different complex geologic units of the Caucasus. To draw the 2D tomography maps, we accomplished a 2D-linear inversion procedure on the Rayleigh wave dispersion curves for the periods of 5 to 70 s (depth= ~180 km). To conduct this, local-regional data from ~1300 earthquakes (M≥3.9) recorded by the 49 broadband stations from 1999 to 2018 in a wide area with complicated tectonic units were used. In comparison with results of previous studies in Caucasus, the tomography maps for the long-periods (T= 50-70 s; depth ~180 km) are more influenced by the velocity structure of the uppermost mantle which demonstrate the ultralow and ultrahigh-velocity anomalies. The results for the medium-periods (30≤T≤45 s), the low-velocity zones coincide with areas thought to be correlated with underplating of the lower crust (e.g. shallow LAB), while, the high-velocity zones are usually demonstrating the presence of a normal continental crust over a stable and thick or oceanic-like lid. Short-periods (5≤T≤25 s) are more influenced by the ever-evolving deformations of the geological units, sedimentary basins, volcanic complexes, uplifts, and reveals a low-velocity small zone, on the NW slope of the Aragats volcano (depth= ~7 km), which is different from the results of other studies.

Structure Along the Martian Dichotomy Constrained by Rayleigh and Love Waves and Their Overtones

AbstractUsing seismic recordings of event S1222a, we measure dispersion curves of Rayleigh and Love waves, including their first overtones, and invert these for shear velocity (VS) and radial anisotropic structure of the Martian crust. The crustal structure along the topographic dichotomy is characterized by a fairly uniform vertically polarized shear velocity (VSV) of 3.17 km/s between ∼5 and 30 km depth, compatible with the previous study by Kim et al. (2022), https://doi.org/10.1126/science.abq7157. Radial anisotropy as large as 12% (VSH > VSV) is required in the crust between 5 and 40 km depth. At greater depths, we observe a large discontinuity near 63 ± 10 km, below which VSV reaches 4.1 km/s. We interpret this velocity increase as the crust‐mantle boundary along the path. Combined gravimetric modeling suggests that the observed average crustal thickness favors the absence of large‐scale density differences across the topographic dichotomy.

Multi-objective particle swarm optimization for multimode surface wave analysis

Obtaining S-wave velocity profiles by inverting Rayleigh wave dispersion curves is crucial for the Rayleigh wave exploration method. Rayleigh wave inversion is a highly nonlinear and multi-extremum problem; therefore, global optimization algorithms are superior to local optimization methods for this inversion problem. Higher modes of dispersion curves have deeper penetration, which can improve the inversion quality. This study utilizes the multi-objective particle swarm optimization (MOPSO) algorithm, rather than a traditional single-objective optimization algorithm, to obtain S-velocity profiles from Rayleigh wave multimode phase velocity dispersion curves. The uncertainty of the inversion parameters is evaluated through the morphology of the Pareto front and the standard deviation of the Pareto optimal solution set. This is the first application of MOPSO in solving the multimode Rayleigh wave phase velocity dispersion curves joint inversion problem. It inverts three synthetic datasets, compares the inversion results with the synthetic data, and then conducts a comparative analysis with the particle swarm optimization (PSO) algorithm and the multi-objective grey wolf optimization (MOGWO) algorithm in one of these synthetic models to evaluate the accuracy and stability of MOPSO to the joint inversion. In addition, this research inverts observed data from an expressway roadbed in Henan, China, to examine the applicability of MOPSO for the joint inversion of multimode dispersion curves. The MOPSO inversion closely yields S-wave velocity profiles that match the borehole data. The synthetic and observed data inversion results indicated that the MOPSO algorithm accurately inverts multimode dispersion curves.

Characteristics of inverse dispersion curve of Rayleigh wave in pavement shallow structure with engineering application

The inverse dispersion curve depicts the dispersion characteristics of inverse layered models, in the layer velocity decreases with depth. To reveal the inverse dispersion characteristics of Rayleigh-wave propagation in pavement, we established a method to determine the dispersion curve of Rayleigh-wave multimodal coupling superposition in pavement structure by decomposing the contribution of multi-mode phase velocity to the vertical displacement of road surface, which was verified by the velocity-stress finite difference scheme. On this basis, further comparative calculations found that the generalized reflection and transmission coefficient method for solving the Rayleigh wave fundamental dispersion curve can fully demonstrate the dispersion characteristics of the coupling superposition of multi-mode dispersion curves of Rayleigh wave in pavement structure, which is suitable for the calculation of Rayleigh-wave inverse dispersion characteristics. Meanwhile, the analysis of dispersion characteristics shows that when the frequency is higher than 5000 Hz, the phase velocities are determined by surface materials. In the low frequency band with frequency <10 Hz, the phase velocities are determined by soil-based deepest materials. And with the increase of the thickness of the intermediate layer, the phase velocity range of dispersion curve moves to the low frequency. In this regard, through sensitivity calculation, an optimization method for Rayleigh wave testing and inversion of elastic modulus of pavement structural layers was established by combining Levenberg-Marquardt and adaptive genetic algorithm. Through the comparative test on the scale model of three-layer pavement structure in laboratory, the results show that the elastic modulus of each layer of pavement structure can be successfully evaluated from the inverse dispersion characteristics of Rayleigh wave in pavement structure.

A look at the blind Kumamoto experiment: combining active and passive seismic observations to avoid Rayleigh-wave mode misidentification

We present our pathway through participation in the blind Kumamoto exercise, particularly the Step 1 of site characterization. The combination of passive and active seismic imaging techniques is used to image the velocity profile beneath the KUMA site. The estimation of the broadband Rayleigh wave dispersion curve is based on cross-correlations of ambient seismic noise and analysis of active seismic shots. We calculate correlations from the entire time series (only vertical components) of each seismic array after classical pre-processing of ambient noise data. Then, a passive seismic section is constructed using all available stations pairs and stacking the cross-correlation traces with similar interstation distances. The obtained passive seismic section is analyzed using a high-resolution Radon transform to obtain the dispersion image of Rayleigh waves traveling through the KUM-LL, KUM-M and KUM-SM arrays. Then, the information is merged and interpolated to obtain the final broadband dispersion curve. In addition, active source seismic data are used with the high-resolution Radon technique to constrain the model at shallow depths (< 30 m). Then, a broadband dispersion image is constructed with significant energy from 0.9 Hz to 45 Hz. The final dispersion curve is inverted using the non-linear neighborhood algorithm. Using just the fundamental mode Rayleigh wave, a first model with normal velocity variation in depth is obtained that corresponds well with the preferred model provided by the organizing committee. The addition of a mHVSR curve in a joint inversion better constrains the deeper part of the model (> 1 km). After comparison of the submitted dispersion curve to the theoretical dispersion curve for the preferred model (Step 4 of the blind test), the authors note that there was a clear misinterpretation in the fundamental mode of their submitted results, especially at frequencies higher than 5 Hz. Using both fundamental (only visible in the passive data set) and first overtones of Rayleigh waves (only visible in the active seismic data set) a refined velocity model could have been inferred, but we decided to keep our first submitted result. This detailed interpretation should be further studied as dispersion images from forward and backward hammer shots are quite different, which may indicate strong variations in the geometry and/or shear-wave velocities of the first meters of the subsurface.Graphical

Defining the Yangtze–Cathaysia suture zone in South China using ambient noise tomography

SUMMARYThe South China Craton formed after collision between the Yangtze and Cathaysia Blocks. The suture zone between these two blocks is the crux of understanding the geological evolution of South China. Due to the relative paucity of high-resolution subsurface data, the location of the suture zone in the southwestern region remains uncertain. To find the suture zone, we created a high-resolution model of the crust and upper mantle structure using 27 months of continuous waveform data acquired from 457 stations in South China. The model uses extracted phase velocity dispersion curves of Rayleigh waves at 4–40 s from ambient noise cross-correlation functions, to perform a direct inversion for an azimuthal anisotropic VSV model. In the crust a prominent belt of strong azimuthal anisotropy exists between the Yangtze and Cathaysia Blocks. The fast polarization axes in this belt correspond to the NE-trending orogen between the two blocks. In the deeper crust of the Cathaysia Block we image multiple areas of diffuse low-velocity anomalies. As defined by the margins of the strongly anisotropic belt, the Yangtze–Cathaysia suture zone is delineated by lines that traverse: Shaoxing–Jiangshan–Pingxiang–Longsheng–Hechi and Shitai–Jiujiang–Yueyang–Dayong–Jishou. Further analysis of the seismic data links deep low velocities with widespread Late Mesozoic magmatism in the Cathaysia Block. The deep low velocities are likely a result of dehydration of the subducting Pacific Plate causing mantle upwelling and underplating.

New constraints on the seismotectonics and crustal structure of the Eastern Trans-Mexican Volcanic Belt based on local seismicity, focal mechanisms and a preliminary state of stress evaluation

After the occurrence of unusual upper crustal seismic activity within the eastern sector of the Trans-Mexican Volcanic Belt (TMVB) in 2019, an area of generally low seismicity, an effort was made to interpret the origin. Concerns leading to the careful analysis presented here, were manifold: Shallow clustered seismicity can indicate active volcanism or related processes, as well as hydrothermalism. Additionally, the area was struck by a major earthquake (Mw 6.4) on January 4, 1920, which had devastating effects on the area's complex geological features and caused hundreds of deaths and significant material damage. As a result, several events of the 2019 sequence of unusual seismic activity have been relocated to precisely know the location. The 34 earthquakes of the 2019 seismic sequence occur in a relatively small area of less than 1600 km2. The seismic sequence can be further subdivided into 2 clusters, separated by the Pico de Orizaba – Cofre de Perote volcanic chain, which itself separates two tectonostratigraphic terranes, is a topographic divide and represents the limit to a considerable topographic drop. We also used the seismic sequence to constrain further the state of local stress and henceforth observe the tectonic regime of the area. For this purpose, focal mechanisms of the events with Mc > 4 (this sequence and previous data) were determined and the inversion of the stress tensor of this group was carried out. Similarly, the state of stress for the central zone of the TMVB was recalculated to establish its possible variations towards the eastern part of the TMVB. We show that the state of stress of the Eastern/Easternmost TMVB presents a transtensional regime, similar to the central TMVB, which has been suggested is mainly caused and controlled by the geometry of the subduction of the Cocos plate beneath the North American plate. A review of Rayleigh wave dispersion curves, calculated through interferometry of ambient seismic noise, a change is observed that suggests some variation in the structure of the eastern and easternmost areas. This contribution is relevant because little is known about the seismotectonics of the TMVB's eastern sector, in part because of the low cortical seismicity reported along the TMVB, the reduced coverage of seismic stations in this region and the distance from the trench Middle American Trench (MAT), where most of the important tectonic processes in Mexico take place. Recently, with the incorporation of a regional seismic network, the detection of small-magnitude events in the study area has significantly been improved.

Imaging the lithospheric structure and plumbing system below the Mayotte volcanic zone

Teleseismic receiver-functions and Rayleigh-wave dispersion curves are jointly inverted for quantifying S-wave velocity profiles beneath the active volcanic zone off Mayotte. We show that the lithosphere in the east-northeast quadrant is composed of four main layers, interpreted as the volcanic edifice, the crust with underplating, the lithospheric mantle, and the asthenosphere, the latter two presenting a main low-velocity zone. The depths of the old (10–11 km) and new Moho (28–31 km) coincide with the two magma reservoirs evidenced by recent seismological and petrological methods. We propose that the main magma reservoir composed of mush with an increasing amount of liquid extends down to 54 km depth. This magma storage develops from a rheological contrast between the ductile lower and brittle upper lithospheric mantle and accounts for most of the volcanic eruption-related seismicity. Finally, the abnormally small thickness of the lithospheric mantle (33 km) is likely a result of a thermal thinning since the onset of Cenozoic magmatism.

Rapid construction of Rayleigh wave dispersion curve based on deep learning

Introduction:The dispersion curve of the Rayleigh-wave phase velocity (VR) is widely utilized to determine site shear-wave velocity (Vs) structures from a distance of a few metres to hundreds of metres, even on a ten-kilometre crustal scale. However, the traditional theoretical-analytical methods for calculating VRs of a wide frequency range are time-consuming because numerous extensive matrix multiplications, transfer matrix iterations and the root searching of the secular dispersion equation are involved. It is very difficult to model site structures with many layers and apply them to a population-based inversion algorithm for which many populations of multilayers forward modelling and many generations of iterations are essential.Method:In this study, we propose a deep learning method for constructing the VR dispersion curve in a horizontally layered site with great efficiency. A deep neural network (DNN) based on the fully connected dense neural network is designed and trained to directly learn the relationships between Vs structures and dispersion curves. First, the training and validation sets are generated randomly according to a truncated Gaussian distribution, in which the mean and variance of the Vs models are statistically analysed from different regions’ empirical relationships between soil Vs and its depth. To be the supervised dataset, the corresponding VRs are calculated by the generalized reflection-transmission (R/T) coefficient method. Then, the Bayesian optimization (BO) is designed and trained to seek the optimal architecture of the deep neural network, such as the number of neurons and hidden layers and their combinations. Once the network is trained, the dispersion curve of VR can be constructed instantaneously without building and solving the secular equation.Results and Discussion:The results show that the DNN-BO achieves a coefficient of determination (R2) and MAE for the training and validation sets of 0.98 and 8.30 and 0.97 and 8.94, respectively, which suggests that the rapid method has satisfactory generalizability and stability. The DNN-BO method accelerates the dispersion curve calculation by at least 400 times, and there is almost no increase in computation expense with an increase in soil layers.