Higher-mode Dispersion Curves Research Articles

Extracting Multimodal Surface-Wave Dispersion Curves from Ambient Seismic Noise Using High-Resolution Linear Radon Transform

Abstract In the past two decades or so, ambient noise tomography (ANT) has emerged as an established method for imaging subsurface seismic velocity structures. One of the key steps in ANT is to extract surface-wave dispersion curves. The predominant approach for subsurface shear-wave velocity structure inversion involves utilizing fundamental-mode surface waves in ANT. Nevertheless, a notable challenge encountered is the issue of nonuniqueness when employing the dispersion information of fundamental-mode surface waves to invert for shear-wave velocity models. The inclusion of higher-mode dispersion curves in the inversion offers several benefits, including the reduction of nonuniqueness, enhancement of inversion stability, and decreased dependence on the initial model. In this study, we illustrate the applicability of the high-resolution linear radon transform method (HRLRT) for extracting multimodal surface-wave dispersion energy from ambient seismic noise data. We apply HRLRT to both the synthetic noise data and real data recorded by USArray. Our results of applications show that the HRLRT method can extract multimodal surface-wave dispersion information. Compared with established methods such as the frequency–Bessel transform and multicomponent frequency–Bessel transform, the HRLRT exhibits an advantage in suppressing “crossed” artifacts and the second-/third-type artifacts caused by sparse spatial sampling, and the resulting dispersion energy from HRLRT has narrower peaks, meaning high resolution of dispersion curves based on the HRLRT method.

Observation of Higher-Mode Rayleigh Waves from Ambient Noise in the Tarim Basin, China

Abstract Higher mode surface waves, which can provide additional constraints on subsurface structures in addition to fundamental modes in surface-wave tomography, have been observed from ambient noise cross-correlation functions (CCFs) in sedimentary basins in oceans or near coastlines. However, few studies show that higher mode surface waves can be observed and extracted directly from ambient noise CCFs in inland basins. In this study, we report observations of high signal-to-noise ratio fundamental and the first higher mode Rayleigh waves at a period range of 0.2–1.90 s and 0.2–1.35 s, respectively, from ambient noise CCFs in the southeastern margin of the Tarim basin, the biggest inland basin in China. We confirm the credibility of the first higher mode surface waves by showing that the observed first higher mode dispersion curves are matched with predicted ones calculated from S velocity models solely constrained by fundamental-mode dispersion curves. After the verification of the credibility of the first higher mode surface waves, we demonstrate that the inclusion of the first higher mode dispersion curves helps image deeper structures with an increase of average depths from ∼0.73 to ∼1.24 km, which will be beneficial to future explorations of deep oil and gas resources in the Tarim basin.

Multi-Mode Imaging of Ambient Background Noise for Karst Detection in the Limestone Area Based on Frequency-Bessel Transform

In response to the challenges of karst geophysical exploration in an environment with strong external interference, this paper proposes a new method, namely the frequency-Bessel transform method, for extracting multi-order dispersion curves of surface waves from background noise to characterize karst. The observation noise data of the Wuhan karst development area are used as an example, where the dolomitic limestone and limestone mixed with dolomite of the Jialing River Formation of the middle lower Triassic are widely developed in the observation area. The frequency-Bessel transform method involves performing a Bessel integral transformation on the cross-correlation coefficient of background noise in the frequency domain. Firstly, by synthesizing theoretical noise data and comparing it with the spatial autocorrelation method—which is currently the main method for extracting the fundamental dispersion curve of surface waves—it is verified that the frequency-Bessel transform method can extract the higher-mode dispersion curve. Then, by taking the actual measured single-point noise data as an example, the effect of applying the frequency-Bessel transform to the actual noise data is tested, and the inversion of the fine structure of the strata by the addition of higher-mode dispersion, the use of the damped least squares inversion method, and the joint inversion of fundamental and higher-mode dispersion curves are analyzed. The higher-mode dispersion curve of Rayleigh surface wave extracted by the frequency-Bessel transform is much clearer, and the 2D shear wave velocity structure profile obtained from inversion explains the karst development area, karst strip area, and thickness of the Quaternary overburden. The inferred results match with the actual borehole data. Multi-mode imaging of background noise based on the frequency-Bessel method can be applied to depict karst in complex backgrounds, and has significant potentiality in the field of ambient seismic noise tomography, providing a new idea and method for karst detection in near-surface engineering.

Crustal S-Wave Velocity Structure Beneath the Northwestern Bohemian Massif, Central Europe, Revealed by the Inversion of Multimodal Ambient Noise Dispersion Curves

The northwestern Bohemian Massif and adjacent areas are a tectonically active region associated with complex geodynamic activities, that manifest as Quaternary volcanism, earthquake swarms in the upper and middle crust, degassing of CO2, and crustal fluid migration. The intricate tectonic evolution and activities of this region reflect the complexity of the crustal structure therein. However, the crustal models derived from previous studies in this area offer different, even contradictory information regarding the existence of a mid-crustal low-velocity zone (LVZ). In this study, we apply the frequency-Bessel transform (F-J) method to extract the fundamental-mode and up to five higher-mode Rayleigh wave dispersion curves from ambient seismic noise data recorded in the study area and perform multimodal ambient noise dispersion curves inversion. The addition of higher-mode dispersion curves enhances the vertical resolution of the velocity structure inversion results. Our models support the view that the general S-wave velocity level of the crust is high within the study area. We detect two S-wave LVZs beneath the study area that are distributed mainly in the middle crust rather than the lower crust, and these LVZs are separated by a high-velocity zone. Considering the results of previous studies in the area, we infer that these S-wave LVZs may be the consequence of crustal fluids, plastic deformation and even partial melting of the felsic middle crust at relatively high crustal temperatures. Furthermore, these S-wave LVZs could be responsible for the origin and foci depth distribution of earthquake swarms. S-wave low-velocity anomalies are also observed in the uppermost mantle beneath the study area. These S-wave models based on the joint inversion of multimodal dispersion curves can provide new references for understanding the tectonic activity and geodynamic evolution of the northwestern Bohemian Massif and adjacent areas.

A widespread mid-crustal low-velocity layer beneath Northeast China revealed by the multimodal inversion of Rayleigh waves from ambient seismic noise

In this study, we re-examined the crustal and uppermost mantle shear velocity structure beneath Northeast China using the broadband ambient seismic noise data from several temporary and permanent arrays in this region. By employing our newly developed interferometric analysis method (F-J method) for array noises and the corresponding multi-mode dispersion curve inversion approach, we obtained an integrated crustal and uppermost mantle shear velocity model of this region. We divided the study area into 39 overlapping sub-areas and then applied the F-J method to each sub-area to obtain a 3D shear velocity model. We extracted the fundamental mode and up to 4 higher-mode dispersion curves of Rayleigh waves in frequencies ranging 0.02–0.45 Hz from the ambient seismic noise data, inverted multi-mode dispersion curves, and obtained local 1D shear velocity model for each sub-area. By integrating all 1D shear velocity models of the 39 overlapping sub-areas, we obtained a 3D crustal and upper mantle model of Northeast China. Our integrated 3D model shows a widely distributed low-velocity zone at a depth of approximately 10–20 km located beneath the northern part of Xing-Mong orogenic belt and Songliao basin and the Changbaishan Mountain. Moreover, a large high-velocity zone underneath the region around the northern edge of Songliao basin is observed at a depth of approximately 40–50 km depth. These results provide evidence to improve our understanding of the tectonics of Northeast China.

Utilization of multimode surface wave dispersion for characterizing roadbed structure

Accurate measurement of shear (S)-wave velocity in a roadbed subsurface with a velocity reversal is crucial as well as challenging. A high frequency Rayleigh wave survey was carried out on a roadbed site from Henan, China to determine S-wave velocities to approximately 15 m depth. The phase shift approach was used to directly construct a high-resolution image of multimode dispersion curves in the frequency–velocity ( f– v) domain from a multi-channel raw shot gather with a high signal-to-noise (S/N) ratio. The measured fundamental and two higher-mode dispersion curves were then inverted by genetic algorithms to reconstruct the fine structure of the tested roadbed subsurface. Our case study demonstrates that an inversion performed with only fundamental mode data with a limited resolution and a high degree of error may yield an unrealistic model. A better agreement with direct borehole measurements, however, is obtained when the second-mode data are inverted simultaneously with the fundamental mode data, which clearly reveals a 1-m thick softer soil layer between two stiff soil layers in the tested roadbed. A higher accuracy S-wave velocity profile is achieved by simultaneously incorporating the three modes of data into the inversion process. This representative case study highlights advantages of fully exploiting intrinsic multimodal properties of Rayleigh waves and greatly enhances our confidence of accurately imaging and characterizing a complex subsurface.

Possible effects of misidentified mode number on Rayleigh wave inversion

Surface wave dispersion data obtained in field surveys are inherently incomplete. Poorly constrained dispersion curves and inclusion of data from higher-mode dispersion curves can be shown to produce erroneous inversion results. The present study evaluates the effects of cross-mode data mixing, and limited data and frequency range on inversion models. Multimodal dispersion curves were generated from synthetic velocity profiles using the forward modeling method. Subsets of the data points obtained by sampling the resulting dispersion curves using different sample intervals, frequency ranges, and by mixing fundamental-mode data with portion of the data from the higher-mode dispersion curves were inverted. The inversion results show that small sample intervals over a wide frequency range and an unambiguous identification of the fundamental-mode dispersion curve are essential factors for the reconstruction of accurate inversion models. The penetration range and accuracy of the inversion models are particularly sensitive to phase velocities at low frequencies of the dispersion curve. The theoretical results were tested with data from a roadbed survey in northern China. Ground model obtained from dispersion data derived by using the F-K method, which contained many cross-mode data points, was found to deviate substantially from the borehole record. A better agreement with the geotechnical record was obtained by inverse modeling of the dispersion data obtained from the fundamental-mode curve of the MASW spectral image.

Normal modes of continental surface waves

Abstract When the path between epicenter and station traverses only continental structure, the dispersion of the entire train of directly arriving seismic surface waves can be explained as the result of normal mode propagation in a crust-mantle system in which the velocity increases in some manner with depth within the crust. At least four modes, the Rayleigh mode, Sezawa's M2 mode, and the first two Love waves, may appear prominently on the seismogram. The characteristics of the higher-mode dispersion curves permit the explanation of the Lg phase of Press and Ewing, B䳨's Lg1 and Lg2, and, in some cases, Caloi's Sa without recourse to a low-velocity layer in the crust or mantle. Speculation on changes in these curves for less simplified models indicates that the remaining cases of Sa as well as Leet's C or coupled wave may be explained by classical theory. The occurrence of the higher-mode waves is widespread; they are found on the four continents for which data are available. Higher-mode data, particularly when combined with information from the fundamental modes, make surface-wave dispersion, previously a useful tool, a much more potent method for the study of crustal structure.