Inversion Of Love Waves Research Articles

2D Gauss-Newton full waveform inversion of SH- and Love-waves in the time domain

Full waveform inversion (FWI) has become a popular and efficient tool for near-surface site characterization. SH- and Love-wave inversion has recently gained attention due to the good sensitivity to mass density and S-wave velocity and the computing advantage over Rayleigh-wave inversion. In this study, we present a new time-domain Gauss-Newton FWI (GN-FWI) method of SH- and Love-waves to extract both mass density and S-wave velocity of soil and rock. The advantage of Gauss-Newton optimization is that the inverse of the regularized Hessian matrix filters, balances, and regularizes the gradient vector to reduce shallow artifacts and resolve deeper structures. To overcome the main challenge of Gauss-Newton approach as high computing demand, we derive analytical formula to compute Jacobian matrix efficiently based on the virtual source and reciprocity theory. The presented method is demonstrated on realistic synthetic and field experiments. The synthetic experiment indicates that the method can characterize a challenging reverse profile with four variable layers of high and low mass density and S-wave velocity. The density and S-wave velocity values and layer interfaces are recovered. The field experiment reveals an 18-m depth subsurface profile, which includes a softer soil layer underlain by stiffer weathered limestone layer. Comparing to invasive Standard Penetration Tests (SPT), the trends of both density and S-wave velocity generally agree with the SPT N-values, including a weak soil zone and weathered limestone. To our best understanding, this is the first study of Gauss-Newton FWI on SH- and Love-waves at any scales.

Inversion of Love waves in earthquake ground motion records for two-dimensional S-wave velocity model of deep sedimentary layers

We propose a new waveform inversion method to estimate the 2D S-wave velocity structure of deep sedimentary layers using broadband Love waves. As a preprocessing operation in our inversion scheme, we decompose earthquake observation records into velocity waveforms for periods of 1 s each. Then, we include in the inversion only those periods for which the assumption of 2D propagation holds, which we propose to determine through a principal component analysis. A linearized iterative inversion analysis for the selected Love wave segments filtered for periods of 1 s each allows a detailed estimation of the boundary shapes of interfaces over the seismic bedrock with an S-wave velocity of approximately 3 km/s. We demonstrate the effectiveness of the technique with applications to observed seismograms in the Kanto Plain, Japan. The differences between the estimated and existing velocity structure models are remarkable at the basin edges. Our results show remarkable differences from previous existing structural models, particularly near the basin edges while being in good agreement with the surface geology. Since a subsurface structure at a basin edge strongly affects the earthquake ground motions in a basin with the generation of surface waves, our method can provide a detailed model of a complex S-wave velocity structure at an edge part for strong ground motion prediction.

Wave-equation dispersion inversion of Love waves

We present a theory for wave-equation inversion of Love-wave dispersion curves, in which the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to inversion of Rayleigh-wave dispersion curves, the complicated Love-wave arrivals in traces are skeletonized as simpler data, namely, the picked dispersion curves in the [Formula: see text] domain. Numerical solutions to the SH-wave equation and an iterative optimization method are then used to invert these dispersion curves for the S-wave velocity model. This procedure, denoted as wave-equation dispersion inversion of Love waves (LWD), does not require the assumption of a layered model or smooth velocity variations, and it is less prone to the cycle-skipping problems of full-waveform inversion. We demonstrate with synthetic and field data examples that LWD can accurately reconstruct the S-wave velocity distribution in a laterally heterogeneous medium. Compared with Rayleigh waves, inversion of the Love-wave dispersion curves empirically exhibits better convergence properties because they are completely insensitive to the P-velocity variations. In addition, Love-wave dispersion curves for our examples are simpler than those for Rayleigh waves, and they are easier to pick in our field data with a low signal-to-noise ratio.

Two‐dimensional elastic full‐waveform inversion of Love waves in shallow vertically transversely isotropic media: synthetic reconstruction tests

ABSTRACTIn most shallow‐seismic applications of full‐waveform inversion, the subsurface is assumed to be isotropic, although near‐surface materials may exhibit strong seismic anisotropy. Ignoring anisotropy will lead to inexact solutions when simulating wave propagation or imaging the subsurface using full‐waveform inversion. For shallow structures, vertically transversely isotropic media provide a suitable approximation due to the fine horizontal layering of the sediments. We investigate the effects of anisotropy on surface waves and on shallow‐seismic full‐waveform inversion in vertically transversely isotropic media. The comparisons of seismograms calculated in isotropic and vertically transversely isotropic models show that the sensitivity of full‐waveform inversion towards anisotropy is significantly higher for Love waves than for Rayleigh waves. This observation indicates that it is more promising to perform full‐waveform inversion on Love waves rather than on Rayleigh waves to identify anisotropy of near‐surface materials. Therefore, we performed synthetic two‐dimensional reconstruction tests of anisotropic full‐waveform inversion using only shallow‐seismic Love waves. These tests revealed that the parameters describing vertical transverse isotropy can be accurately reconstructed by full‐waveform inversion. Although the inversion for density is still problematic, this does not affect the results for the seismic velocities in a significant way. The tests on synthetic data thus prove the general applicability and the benefits of an anisotropic inversion of shallow‐seismic Love waves, which can provide a more comprehensive subsurface characterization in shallow anisotropic media.

Novel depiction of love wave dispersion and inversion for inversely dispersive medium by full SH-wavefield reflectivity method – part II: field example

In this part we discussed field example of SH wave data recorded using horizontal component of the three-component geophone that might represent characteristic of the inversely dispersive medium. Extraction of the SH wavefield data, both for north- and south-source impact, using tau-pi transform showed increasing phase-velocity dispersion with the frequencies. Such patterns of “effective” dispersion curves illustrated the nature of the inversely dispersive medium. Inversions of the dispersion curves were carried out by utilizing a series of Love wave inversion approaches. These approaches included forward modelling of Love wave dispersion curve by full SH-wavefield method and partial derivatives of the Love wave phase velocity. The inversion procedures utilized a linearized inversion of Occam’s algorithm. Inversions of the Love wave real data, both for north- and south-source impact, confirm the presence of an inversely dispersive medium.

Near-surface anisotropic structure characterization by Love wave inversion for assessing ground conditions in Urban Areas

In many geophysical applications, neglecting of anisotropy is somehow an oversimplification. The mismatch between prediction based on isotropic theory and near-surface seismic observations indicates the need for the inclusion of medium anisotropy. In this paper, surface wave (Love wave) dispersion properties are used to estimate the anisotropic structure of the near-surface layered earth, which is modeled as media possess vertical transverse isotropy (VTI), a reasonable assumption for near-surface sedimentary layers. Our approach utilizes multi-mode surface waves to estimate both the velocity structure and the anisotropy structure. This approach consists of three parts. First, the dispersion analysis is used to extract dispersion curves from real data. Second, the forward modeling is carried out based on the dispersion equation of Love wave in a multi-layered VTI medium. Dispersion curves of multi-modes, which are the numerical solutions of the dispersion equation, are obtained by a graphic-based method. Finally, the very fast simulated annealing (VFSA) algorithm is used to invert velocity structure and anisotropy structure simultaneously. Our approach is verified by the synthetic dispersion curve generated by a VTI medium model. The estimation of shear wave velocity and anisotropy structure of surface wave data acquired at Rentschler Field, an urban center site on sediments in the Connecticut River valley reveals a simple structure of the sediment layer over a bedrock half space. The results are verified by other inversion results based on different data set obtained on the same site. The consistency of inversion results shows the feasibility and efficiency of the approach.

New findings in high-frequency surface wave method

Multi channel Analysis of Surface Waves (MASW) analyzes high-frequency Rayleigh waves to determine near-surface shear (S)-wave velocities. This method is getting increasingly attention in the near-surface geophysics and geotechnique community in the past 20 years because of its non-invasive, non-destructive, efficient, and low-cost advantages. They are viewed by near-surface geophysics community as one of most promise techniques in the future. We introduce some research results about propagation and applications of high-frequency surface waves proposed by near-surface geophysical research group at China University of Geosciences (Wuhan) in recent years. Non-geometric wave exists uniquely in near-surface materials, especially in unconsolidated sediments. It is valuable for a quick and accurate estimation of S-wave velocity of the surface layer. Our study shows that non-geometric waves are leaky waves and they are dispersive. Leaky surface wave could cause misidentification when treating the leaky-wave energy as fundamental or higher modes Rayleigh wave. Such misidentification will result in wrong inversion results. By obtaining Rayleigh-wave Green's function after separating fundamental- and higher-mode Rayleigh waves, we verify the feasibility of virtual source method in Rayleigh-wave survey, which could tremendously decreases the cost of field works. Compared to Rayleigh waves, a fewer parameters are involved in Multichannel Analysis of Love Waves (MALW), which makes Love-wave dispersion curves simpler than Rayleigh waves. As a result, inversion of Love waves is more stable and the degree of non-uniqueness is reduced. Images of Love-wave energy are usually sharper and of higher resolution than those from Rayleigh waves. This make picking Love-wave phase velocities much easier and more accurate. Analysis on relationship between surface-wave wavelength and penetrating depth by using Jacobian matrix shows that: as for fundamental mode with the same wavelength, Rayleigh wave can see 1.3~1.4 times deeper than Love waves, however, their penetrating depths are similar for higher modes. We also make some attempts on time-domain Love-wave waveform inversion. We divide the subsurface model into different sizes of blocks according to resolution of Love waves. We remove the source effect by deconvolution, and achieve an appropriate subsurface S-wave velocity model via updating S-wave velocity of each block to fit observed waveforms. This method does not need horizontal-layered-model assumption, and can be applied to any kind of 2D media.

Advantages of Using Multichannel Analysis of Love Waves (MALW) to Estimate Near-Surface Shear-Wave Velocity

As theory dictates, for a series of horizontal layers, a pure, plane, horizontally polarized shear (SH) wave refracts and reflects only SH waves and does not undergo wave-type conversion as do incident P or Sv waves. This is one reason the shallow SH-wave refraction method is popular. SH-wave refraction method usually works well defining near-surface shear-wave velocities. Only first arrival information is used in the SH-wave refraction method. Most SH-wave data contain a strong component of Love-wave energy. Love waves are surface waves that are formed from the constructive interference of multiple reflections of SH waves in the shallow subsurface. Unlike Rayleigh waves, the dispersive nature of Love waves is independent of P-wave velocity. Love-wave phase velocities of a layered earth model are a function of frequency and three groups of earth properties: SH-wave velocity, density, and thickness of layers. In theory, a fewer parameters make the inversion of Love waves more stable and reduce the degree of nonuniqueness. Approximating SH-wave velocity using Love-wave inversion for near-surface applications may become more appealing than Rayleigh-wave inversion because it possesses the following three advantages. (1) Numerical modeling results suggest the independence of P-wave velocity makes Love-wave dispersion curves simpler than Rayleigh waves. A complication of “Mode kissing” is an undesired and frequently occurring phenomenon in Rayleigh-wave analysis that causes mode misidentification. This phenomenon is less common in dispersion images of Love-wave energy. (2) Real-world examples demonstrated that dispersion images of Love-wave energy have a higher signal-to-noise ratio and more focus than those generated from Rayleigh waves. This advantage is related to the long geophone spreads commonly used for SH-wave refraction surveys, images of Love-wave energy from longer offsets are much cleaner and sharper than for closer offsets, which makes picking phase velocities of Love waves easier and more accurate. (3) Real-world examples demonstrated that inversion of Love-wave dispersion curves is less dependent on initial models and more stable than Rayleigh waves. This is due to Love-wave’s independence of P-wave velocity, which results in fewer unknowns in the MALW method compared to inversion methods of Rayleigh waves. This characteristic not only makes Love-wave dispersion curves simpler but also reduces the degree of nonuniqueness leading to more stable inversion of Love-wave dispersion curves.

On the use of the Norwegian Geotechnical Institute's prototype seabed-coupled shear wave vibrator for shallow soil characterization - II. Joint inversion of multimodal Love and Scholte surface waves

Seismic data generated by a novel, seabed-coupled, shear-wave vibrator (prototype) and recorded by a densely-populated, multicomponent ocean-bottom cable allowed several modes of propagation of Love and Scholte waves to be retrieved in a relatively wide frequency band. Both global dispersion curves and local dispersion curves are extracted in the frequency–wavenumber (f–k) domain and inverted with a multimodal joint Scholte and Love wave inversion algorithm. Monte Carlo inversion is used for a estimating the global S-wave velocity profile of the seabed sediments whereas laterally constrained inversion is used to detect lateral variations of the layer interface depths. The results are in agreement and allowed consistent full-waveform simulation to be performed. The investigation depth is limited to around 40 m due to the low shear wave velocities within the shallow clay layer.

Finite-Difference Modeling and Dispersion Analysis of High-Frequency Love Waves for Near-Surface Applications

Love-wave propagation has been a topic of interest to crustal, earthquake, and engineering seismologists for many years because it is independent of Poisson’s ratio and more sensitive to shear (S)-wave velocity changes and layer thickness changes than are Rayleigh waves. It is well known that Love-wave generation requires the existence of a low S-wave velocity layer in a multilayered earth model. In order to study numerically the propagation of Love waves in a layered earth model and dispersion characteristics for near-surface applications, we simulate high-frequency (>5 Hz) Love waves by the staggered-grid finite-difference (FD) method. The air–earth boundary (the shear stress above the free surface) is treated using the stress-imaging technique. We use a two-layer model to demonstrate the accuracy of the staggered-grid modeling scheme. We also simulate four-layer models including a low-velocity layer (LVL) or a high-velocity layer (HVL) to analyze dispersive energy characteristics for near-surface applications. Results demonstrate that: (1) the staggered-grid FD code and stress-imaging technique are suitable for treating the free-surface boundary conditions for Love-wave modeling, (2) Love-wave inversion should be treated with extra care when a LVL exists because of a lack of LVL information in dispersions aggravating uncertainties in the inversion procedure, and (3) energy of high modes in a low-frequency range is very weak, so that it is difficult to estimate the cutoff frequency accurately, and “mode-crossing” occurs between the second higher and third higher modes when a HVL exists.

Full SH-wavefield modelling and multiple-mode Love wave inversion

Full SH-wavefield modelling by the reflectivity method is developed for Love wave inversion. The modelling simulates field tests, first by generating time-distance shot gathers, followed by standard plane-wave transform to extract Love wave phase-velocity dispersion. All SH surface wave modes, plus body waves and wavefront spreading are accurately simulated.When a thin low-velocity layer (LVL) is underlain by a much stiffer layer, Love wave modes are well separated and fundamental-mode identification is more straightforward than the equivalent Rayleigh waves. However, when the LVL is thicker and bounded by equally stiff layers, multiple dominant higher modes propagate, and their correct identification and inversion is essential to resolve the soft layer.A first field test shows how multimode Love wave inversion can resolve a 2 m thick clay layer at 1 m depth in the lithological log when only both the fundamental and first higher modes are incorporated. A second field test, where a much thicker LVL, interpreted as a mud plume, is present, shows how several higher modes are required to resolve the soft layer LVL, whereas use of the fundamental or effective mode only fails.