scholarly journals Wave-equation Rayleigh-wave dispersion inversion using fundamental and higher modes

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. EN57-EN65 ◽  
Author(s):  
Zhen-Dong Zhang ◽  
Tariq Alkhalifah
Keyword(s):  
Wave Equation ◽  
Rayleigh Wave ◽  
Surface Waves ◽  
Wave Velocity ◽  
Minimum Problem ◽  
Velocity Spectrum ◽  
Local Similarity ◽  
Inversion Algorithm ◽  
S Wave ◽  
Near Surface

Recorded surface waves often provide reasonable estimates of the S-wave velocity in the near surface. However, existing algorithms are mainly based on the 1D layered-model assumption and require picking the dispersion curves either automatically or manually. We have developed a wave-equation-based inversion algorithm that inverts for S-wave velocities using fundamental and higher mode Rayleigh waves without picking an explicit dispersion curve. Our method aims to maximize the similarity of the phase velocity spectrum ([Formula: see text]) of the observed and predicted surface waves with all Rayleigh-wave modes (if they exist) included in the inversion. The [Formula: see text] spectrum is calculated using the linear Radon transform applied to a local similarity-based objective function; thus, we do not need to pick velocities in spectrum plots. As a result, the best match between the predicted and observed [Formula: see text] spectrum provides the optimal estimation of the S-wave velocity. We derive S-wave velocity updates using the adjoint-state method and solve the optimization problem using a limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Our method excels in cases in which the S-wave velocity has vertical reversals and lateral variations because we used all-modes dispersion, and it can suppress the local minimum problem often associated with full-waveform inversion applications. Synthetic and field examples are used to verify the effectiveness of our method.

Full-waveform matching of VP and VS models from surface waves

2019 ◽  
Vol 218 (3) ◽  
pp. 1873-1891 ◽  
Author(s):  
Farbod Khosro Anjom ◽  
Daniela Teodor ◽  
Cesare Comina ◽  
Romain Brossier ◽  
Jean Virieux ◽  
...  
Keyword(s):  
Surface Waves ◽  
Wave Velocity ◽  
Real Data ◽  
Test Site ◽  
P Wave ◽  
S Wave ◽  
Surface Wave Dispersion ◽  
Data Set ◽  
Near Surface ◽  
Velocity Models

SUMMARY The analysis of surface wave dispersion curves (DCs) is widely used for near-surface S-wave velocity (VS) reconstruction. However, a comprehensive characterization of the near-surface requires also the estimation of P-wave velocity (VP). We focus on the estimation of both VS and VP models from surface waves using a direct data transform approach. We estimate a relationship between the wavelength of the fundamental mode of surface waves and the investigation depth and we use it to directly transform the DCs into VS and VP models in laterally varying sites. We apply the workflow to a real data set acquired on a known test site. The accuracy of such reconstruction is validated by a waveform comparison between field data and synthetic data obtained by performing elastic numerical simulations on the estimated VP and VS models. The uncertainties on the estimated velocity models are also computed.

A comprehensive comparison between the refraction microtremor and seismic interferometry methods for phase-velocity estimation

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. EN99-EN108 ◽  
Author(s):  
Zongbo Xu ◽  
T. Dylan Mikesell ◽  
Jianghai Xia ◽  
Feng Cheng
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Wave Velocity ◽  
Velocity Estimation ◽  
Seismic Interferometry ◽  
S Wave ◽  
Noise Sources ◽  
Surface Wave Dispersion ◽  
Near Surface ◽  
Refraction Microtremor

Passive-source seismic-noise-based surface-wave methods are now routinely used to investigate the near-surface geology in urban environments. These methods estimate the S-wave velocity of the near surface, and two methods that use linear recording arrays are seismic interferometry (SI) and refraction microtremor (ReMi). These two methods process noise data differently and thus can yield different estimates of the surface-wave dispersion, the data used to estimate the S-wave velocity. We have systematically compared these two methods using synthetic data with different noise source distributions. We arrange sensors in a linear survey grid, which is conveniently used in urban investigations (e.g., along roads). We find that both methods fail to correctly determine the low-frequency dispersion characteristics when outline noise sources become stronger than inline noise sources. We also identify an artifact in the ReMi method and theoretically explain the origin of this artifact. We determine that SI combined with array-based analysis of surface waves is the more accurate method to estimate surface-wave phase velocities because SI separates surface waves propagating in different directions. Finally, we find a solution to eliminate the ReMi artifact that involves the combination of SI and the [Formula: see text]-[Formula: see text] transform, the array processing method that underlies the ReMi method.

scholarly journals 3D wave-equation dispersion inversion of surface waves recorded on irregular topography

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. R147-R161 ◽  
Author(s):  
Zhaolun Liu ◽  
Jing Li ◽  
Sherif M. Hanafy ◽  
Kai Lu ◽  
Gerard Schuster
Keyword(s):  
Wave Equation ◽  
Surface Wave ◽  
Surface Waves ◽  
Wave Velocity ◽  
Field Data ◽  
P Wave ◽  
Topographic Effects ◽  
S Wave ◽  
Surface Wave Dispersion ◽  
Irregular Topography

Irregular topography can cause strong scattering and defocusing of propagating surface waves, so it is important to account for such effects when inverting surface waves for shallow S-wave velocity structures. We have developed a 3D surface-wave dispersion inversion method that takes into account the topographic effects modeled by a 3D spectral element solver. The objective function is the frequency summation of the squared wavenumber differences [Formula: see text] along each azimuthal angle of the fundamental mode or higher-order modes of Rayleigh waves in each shot gather. The wavenumbers [Formula: see text] associated with the dispersion curves are calculated using the data recorded along the irregular free surface. Numerical tests on synthetic and field data demonstrate that 3D topographic wave equation dispersion inversion (TWD) can accurately invert for the S-wave velocity model from surface-wave data recorded on irregular topography. Field data tests for data recorded across an Arizona fault demonstrate that, for this example, the 2D TWD model can be as accurate as the 3D tomographic model. This suggests that in some cases, the 2D TWD inversion is preferred over 3D TWD because of its significant reduction in computational costs. Compared to the 3D P-wave velocity tomogram, the 3D S-wave tomogram agrees much more closely with the geologic model taken from the trench log. The agreement with the trench log is even better when the [Formula: see text] tomogram is computed, which reveals a sharp change in velocity across the fault. The localized velocity anomaly in the [Formula: see text] tomogram is in very good agreement with the well log. Our results suggest that integrating the [Formula: see text] and [Formula: see text] tomograms can sometimes give the most accurate estimates of the subsurface geology across normal faults.

Near-surface velocity structure study using surface waves and first breaks in the middle segment of the Bangong-Nujiang suture zone, Tibetan Plateau

2020 ◽  
Author(s):  
Hui Zhang ◽  
Rizheng He ◽  
Zhiwei Liu
Keyword(s):  
Surface Waves ◽  
Wave Velocity ◽  
Velocity Structure ◽  
Dispersion Curves ◽  
Suture Zone ◽  
Surface Velocity ◽  
S Wave ◽  
Middle Segment ◽  
Near Surface ◽  
Order Dispersion

<p>The Bangong-Nujiang suture zone, located in the central Tibet, is one of several important geological boundaries in Qinghai-Tibet plateau. Abundant researches have been performed and most of them focused on deep tectonic structure and its dynamic mechanism through recent geophysical projects such as INDEPTH-III, Hi-CLIMB, ANTILOPE, SinoProbe, etc. (Zhao Wenjin et al., 2008; N´abelek et al. 2009; Gao Rui, et al., 2013;Zhao Junmeng et al. 2014; He Rizheng et al., 2014; Xu Qiang et al., 2017; Shang Xuefeng et al., 2017; Davlatkhudzha et al.,2018). Near-surface velocity study can not only obtain the physical parameters such as Vp and Vs in the area, but also improve seismic image quality of deep structure (Zhao Lingzhi et al., 2018). However, the velocity information obtained from passive seismic stations using either receiver function or ambient noise tomography is not enough to elaborate the near surface velocity structure of the Bangong-Nujiang suture zone. Besides, the active-source seismic reflection data usually doesn’t have sufficient offset density at near surface which poses a challenge to conventional near-surface velocity analysis methods.</p><p>This study makes full use of surface waves and first breaks to obtain near-surface P- and S-wave velocities based on a 2D deep seismic reflection survey data which was acquired by SinoProbe project in 2009 . We adopt the method of superposition of surface waves in common receiver domain to generate high quality F-K spectrum which enables us to obtain fundamental-order and high-order dispersion curves. First, a 2D layered model with an irregular topography was built and the 2D elastic finite difference modeling was executed to generate 161 synthetic seismic shot gathers which mimicking the actual acquisition geometry. These gathers contain surface waves, refractions, reflections and multiples energy, and the maximum offset is about 18 km. It is shown that the F-K spectrum quality has been improved for each receiver station using superposition of surface waves in the F-K domain by adding more shots. The S-wave velocity inverted from dispersion curves showed good agreement with the synthetic model. Second, high quality F-K spectrum generated from the above method enabled us to pick both fundamental and 1<sup>st</sup> order dispersion curves from the SinoProbe field data. The S-wave velocity was generated using three methods: 1) empirical equations based on dispersion curves; 2) fundamental order dispersion curves inversion; and 3) both fundamental and 1<sup>st </sup>order dispersion curves inversion. Results show that using higher order dispersion curves can generate a more reliable near-surface model. Third, first breaks were picked up to 18 km offset and diving wave tomography was applied to derive near-surface P-wave velocity from abundant first break information. It is shown that there is an excellent correlation between P- and S-wave velocities, the bottom of basin is clearly revealed, and over-thrusts are identified accordingly which is consistent with field geological survey in the middle segment of Bangong-Nujiang suture zone.</p><p>This study was financially supported by the CAGS Research Fund (grant YWF201907), and the National Natural Science Foundation of China (grant 41761134094). Data sources: SinoProbe-02 Project.</p>

Retrieval of shallow S-wave profiles from seismic reflection surveying and traffic-induced noise

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. EN105-EN117
Author(s):  
Kai Zhang ◽  
Hongyi Li ◽  
Xiaojiang Wang ◽  
Kai Wang
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Wave Velocity ◽  
Rayleigh Waves ◽  
Seismic Reflection ◽  
Seismic Energy ◽  
Dispersion Curves ◽  
S Wave ◽  
Near Surface ◽  
Wave Velocities

In urban subsurface exploration, seismic surveys are mostly conducted along roads where seismic vibrators can be extensively used to generate strong seismic energy due to economic and environmental constraints. Generally, Rayleigh waves also are excited by the compressional wave profiling process. Shear-wave (S-wave) velocities can be inferred using Rayleigh waves to complement near-surface characterization. Most vibrators cannot excite seismic energy at lower frequencies (<5 Hz) to map greater depths during surface-wave analysis in areas with low S-wave velocities, but low-frequency surface waves ([Formula: see text]) can be extracted from traffic-induced noise, which can be easily obtained at marginal additional cost. We have implemented synthetic tests to evaluate the velocity deviation caused by offline sources, finding a reasonably small relative bias of surface-wave dispersion curves due to vehicle sources on roads. Using a 2D reflection survey and traffic-induced noise from the central North China Plain, we apply seismic interferometry to a series of 10.0 s segments of passive data. Then, each segment is selectively stacked on the acausal-to-causal ratio of the mean signal-to-noise ratio to generate virtual shot gathers with better dispersion energy images. We next use the dispersion curves derived by combining controlled source surveying with vehicle noise to retrieve the shallow S-wave velocity structure. A maximum exploration depth of 90 m is achieved, and the inverted S-wave profile and interval S-wave velocity model obtained from reflection processing appear consistent. The data set demonstrates that using surface waves derived from seismic reflection surveying and traffic-induced noise provides an efficient supplementary technique for delineating shallow structures in areas featuring thick Quaternary overburden. Additionally, the field test indicates that traffic noise can be created using vehicles or vibrators to capture surface waves within a reliable frequency band of 2–25 Hz if no vehicles are moving along the survey line.

scholarly journals Opportunities and pitfalls in surface-wave interpretation

2017 ◽  
Vol 5 (1) ◽  
pp. T131-T141 ◽  
Author(s):  
Gerard T. Schuster ◽  
Jing Li ◽  
Kai Lu ◽  
Ahmed Metwally ◽  
Abdullah AlTheyab ◽  
...  
Keyword(s):  
Surface Waves ◽  
Wave Velocity ◽  
Seismic Data ◽  
S Wave ◽  
Near Surface ◽  
Velocity Anomalies ◽  
The Common ◽  
The Many ◽  
Surface Geology ◽  
Depth Of Investigation

Many explorationists think of surface waves as the most damaging noise in land seismic data. Thus, much effort is spent in designing geophone arrays and filtering methods that attenuate these noisy events. It is now becoming apparent that surface waves can be a valuable ally in characterizing the near-surface geology. This review aims to find out how the interpreter can exploit some of the many opportunities available in surface waves recorded in land seismic data. For example, the dispersion curves associated with surface waves can be inverted to give the S-wave velocity tomogram, the common-offset gathers can reveal the presence of near-surface faults or velocity anomalies, and back-scattered surface waves can be migrated to detect the location of near-surface faults. However, the main limitation of surface waves is that they are typically sensitive to S-wave velocity variations no deeper than approximately half to one-third the dominant wavelength. For many exploration surveys, this limits the depth of investigation to be no deeper than approximately 0.5–1.0 km.

Numerical and Theoretical Investigation on the Origin of the Multiple Peaks of the H/V Ratio Curve

2021 ◽  
Author(s):  
Wanbo Xiao ◽  
Siqi Lu ◽  
Yanbin Wang
Keyword(s):  
Rayleigh Wave ◽  
Wave Velocity ◽  
Subsurface Layer ◽  
P Wave ◽  
Theoretical Formula ◽  
S Wave ◽  
Multiple Peaks ◽  
Ratio Curve ◽  
Multiple Layer ◽  
Wave Resonance

&lt;p&gt;Despite the popularity of the horizontal to vertical spectral ratio (HVSR) method in site effect studies, the origin of the H/V peaks has been controversial since this method was proposed. Many previous studies mainly focused on the explanation of the first or single peak of the H/V ratio, trying to distinguish between the two hypotheses &amp;#8212; the S-wave resonance and ellipticity of Rayleigh wave. However, it is common both in numerical simulations and practical experiments that the H/V ratio exhibits multiple peaks, which is essential to explore the origin of the H/V peaks.&lt;/p&gt;&lt;p&gt;The cause for the multiple H/V peaks has not been clearly figured out, and once was simply explained as the result of multi subsurface layers. Therefore, we adopted numerical method to simulate the ambient noise in various layered half-space models and calculated the H/V ratio curves for further comparisons. The peak frequencies of the H/V curves accord well with the theoretical frequencies of S-wave resonance in two-layer models, whose frequencies only depend on the S wave velocity and the thickness of the subsurface layer. The same is true for models with varying model parameters. Besides, the theoretical formula of the S-wave resonance in multiple-layer models is proposed and then supported by numerical investigations as in the cases of two-layer models. We also extended the S-wave resonance to P-wave resonance and found that its theoretical frequencies fit well with the V/H peaks, which could be an evidence to support the S-wave resonance theory from a new perspective. By contrast, there are obvious differences between the higher orders of the H/V ratio peaks and the higher orders of Rayleigh wave ellipticity curves both in two-layer and multiple-layer models. The Rayleigh wave ellipticity curves are found to be sensitive to the Poisson&amp;#8217;s ratio and the thickness of the subsurface layer, so the variation of the P wave velocity can affect the peak frequencies of the Rayleigh wave ellipticity curves while the H/V peaks show slight change. The Rayleigh wave ellipticity theory is thus proved to be inappropriate for the explanation of the multiple H/V peaks, while the possible effects of the Rayleigh wave on the fundamental H/V peak still cannot be excluded.&lt;/p&gt;&lt;p&gt;Based on the analyses above, we proposed a new evidence to support the claim that the peak frequencies of the H/V ratio curve, except the fundamental peaks, are caused by S-wave resonance. The relationship between the P-wave resonance and the V/H peaks may also find further application.&lt;/p&gt;

Nonlinear two‐dimensional elastic inversion of multioffset seismic data

Geophysics ◽  
1987 ◽  
Vol 52 (9) ◽  
pp. 1211-1228 ◽  
Author(s):  
Peter Mora
Keyword(s):  
Wave Equation ◽  
Wave Velocity ◽  
A Priori ◽  
Gaussian Model ◽  
Wave Impedance ◽  
P Wave ◽  
S Wave ◽  
Elastic Wave Equation ◽  
Gradient Direction ◽  
P Wave Velocity

The treatment of multioffset seismic data as an acoustic wave field is becoming increasingly disturbing to many geophysicists who see a multitude of wave phenomena, such as amplitude‐offset variations and shearwave events, which can only be explained by using the more correct elastic wave equation. Not only are such phenomena ignored by acoustic theory, but they are also treated as undesirable noise when they should be used to provide extra information, such as S‐wave velocity, about the subsurface. The problems of using the conventional acoustic wave equation approach can be eliminated via an elastic approach. In this paper, equations have been derived to perform an inversion for P‐wave velocity, S‐wave velocity, and density as well as the P‐wave impedance, S‐wave impedance, and density. These are better resolved than the Lamé parameters. The inversion is based on nonlinear least squares and proceeds by iteratively updating the earth parameters until a good fit is achieved between the observed data and the modeled data corresponding to these earth parameters. The iterations are based on the preconditioned conjugate gradient algorithm. The fundamental requirement of such a least‐squares algorithm is the gradient direction which tells how to update the model parameters. The gradient direction can be derived directly from the wave equation and it may be computed by several wave propagations. Although in principle any scheme could be chosen to perform the wave propagations, the elastic finite‐ difference method is used because it directly simulates the elastic wave equation and can handle complex, and thus realistic, distributions of elastic parameters. This method of inversion is costly since it is similar to an iterative prestack shot‐profile migration. However, it has greater power than any migration since it solves for the P‐wave velocity, S‐wave velocity, and density and can handle very general situations including transmission problems. Three main weaknesses of this technique are that it requires fairly accurate a priori knowledge of the low‐ wavenumber velocity model, it assumes Gaussian model statistics, and it is very computer‐intensive. All these problems seem surmountable. The low‐wavenumber information can be obtained either by a prior tomographic step, by the conventional normal‐moveout method, by a priori knowledge and empirical relationships, or by adding an additional inversion step for low wavenumbers to each iteration. The Gaussian statistics can be altered by preconditioning the gradient direction, perhaps to make the solution blocky in appearance like well logs, or by using large model variances in the inversion to reduce the effect of the Gaussian model constraints. Moreover, with some improvements to the algorithm and more parallel computers, it is hoped the technique will soon become routinely feasible.

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