Surface wave tomography, using the fundamental Rayleigh wave velocities and those of higher modes between 1 and 4 and periods between 50 and 160 s, is used to image structures with a horizontal ...resolution of ∼250 km and a vertical resolution of ∼50 km to depths of ∼300 km in the mantle. A new model, PM_v2_2012, obtained from 3×106 seismograms, agrees well with earlier lower resolution models. It is combined with temperature estimates from oceanic plate models and with pressure and temperature estimates from the mineral compositions of garnet peridotite nodules to generate a number of estimates of SV(P,T) based on geophysical and petrological observations alone. These are then used to estimate the unrelaxed shear modulus and its derivatives with respect to pressure and temperature, which agree reasonably with values from laboratory experiments. At high temperatures relaxation occurs, causing the shear wave velocity to depend on frequency. This behaviour is parameterised using a viscosity to obtain a Maxwell relaxation time. The relaxation behaviour is described using a dimensionless frequency, which depends on an activation energy E and volume Va. The values of E and Va obtained from the geophysical models agree with those from laboratory experiments on high temperature creep. The resulting expressions are then used to determine the lithospheric thickness from the shear wave velocity variations. The resolution is improved by about a factor of two with respect to earlier models, and clearly resolves the thick lithosphere beneath active intracontinental belts that are now being shortened. The same expressions allow the three dimensional variations of the shear wave attenuation and viscosity to be estimated.
•A Vs model is obtained from Rayleigh waves from 3×106 earthquakes.•The model has resolutions of ∼300×∼30 km horizontally and vertically.•Temperature, viscosity and attenuation are calculated from Vs.•The activation energy and volume of the viscosity agree with laboratory values.•Active Asiatic mountain belts have lithospheric thicknesses of 200 km or more.
This work presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. Panoramic in scope, it includes discussions of how ocean waves are ...refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas.
Using data from more than 2000 seismic stations from multiple networks arrayed throughout China (CEArray, China Array, NECESS, PASSCAL, GSN) and surrounding regions (Korean Seismic Network, F-Net, ...KNET), we perform ambient noise Rayleigh wave tomography across the entire region and earthquake tomography across parts of South China and Northeast China. We produce isotropic Rayleigh wave group and phase speed maps with uncertainty estimates from 8 to 50 s period across the entire region of study, and extend them to 70 s period where earthquake tomography is performed. Maps of azimuthal anisotropy are estimated simultaneously to minimize anisotropic bias in the isotropic maps, but are not discussed here. The 3D model is produced using a Bayesian Monte Carlo formalism covering all of China, extending eastwards through the Korean Peninsula, into the marginal seas, to Japan. We define the final model as the mean and standard deviation of the posterior distribution at each location on a 0.5° × 0.5° grid from the surface to 150 km depth. Surface wave dispersion data do not strongly constrain internal interfaces, but shear wave speeds between the discontinuities in the crystalline crust and uppermost mantle are well determined. We design the resulting model as a reference model, which is intended to be useful to other researchers as a starting model, to predict seismic wave fields and observables and to predict other types of data (e.g. topography, gravity). The model and the data on which it is based are available for download. In addition, the model displays a great variety and considerable richness of geological and tectonic features in the crust and in the uppermost mantle deserving of further focus and continued interpretation.
Currently, using the finite difference method to simulate millimeter-sized fractures in formations requires intensive calculations. However, only the time domain characteristics of the calculated ...borehole acoustic signal are often analysed, while the frequency domain characteristics are ignored. This study aims to obtain the time-frequency characteristics of full acoustic waveforms in different types of fractured formations while reducing operational time and to analyze more comprehensively the influence of fractures on time-frequency characteristics. Therefore, the variable grid finite difference method is used to simulate full acoustic waveforms in boreholes in formations with millimeter-sized horizontal fractures to reduce the computational time of the finite difference method. Afterwards, the wavelet transform is used to analyze the influence of fracture width, fracture number, and radial extension length on the waveform time-frequency characteristics. The results show that with increasing fracture width or number, the P- and S-wave arrival times are delayed, amplitude attenuation is enhanced, and the dominant frequency increases gradually. The frequency and amplitude attenuation of each Stoneley wave component also increases, and the arrival time of the 20–28 kHz high-frequency Stoneley wave is delayed. When the fracture radial length is limited, an increase in radial length delays the P- and S-wave arrival times, and the amplitude attenuation increases. The main S-, Stoneley, and pseudo-Rayleigh wave frequencies increase, and the Stoneley wave and pseudo-Rayleigh wave amplitude attenuation increases. When the fracture radial length is infinite, the P-wave and pseudo-Rayleigh wave amplitude attenuation increases, whereas that of the S-wave and Stoneley wave decreases. This study reveals the influence of fractures on the time-frequency characteristics of full acoustic waveforms in boreholes, provides a theoretical basis for the time-frequency analysis of full acoustic waveforms, and is significant for further clarification of the propagation characteristics of borehole acoustic waves in fractured formations.
SUMMARY
The core–mantle boundary (CMB) is the most abrupt internal discontinuity in the Earth, marking the solid–fluid boundary between mantle and outer core that strongly affects the dynamics of the ...Earth’s interior. However, good agreement between models of CMB topographic variations is still lacking. This is probably due to difficulties relating to observations on seismograms and to the lack of good models of lowermost mantle velocity structure. Using spectral-element synthetic seismograms and adjoint methods, we perform traveltime analyses of seismic waves interacting with the CMB. We focus on reflected and refracted P and S waves. We select some of the most important and routinely used seismic phases: ScS, SKS, SKKS, PcP, PKP, PKKP and PcS, given their path through mantle and core and their interaction with the CMB. These seismic waves have been widely deployed by seismologists trying to image CMB topography and lowermost mantle structure. To analyse the reliability of measuring their traveltimes to infer CMB topography, we perform experiments in two ways. First, we compute synthetic seismograms with a dominant period of T ≈ 11s, for computational efficiency, using existing models of CMB topography. We compare traveltime perturbations measured by cross-correlation on the synthetics to those predicted using ray theory. We find deviations from a perfect agreement between ray theoretical predictions of time shifts and those measured on synthetics with and without CMB topography. Second, we calculate Fréchet sensitivity kernels of traveltimes with respect to shear and compressional wave speeds. We also explicitly compute boundary sensitivities with respect to the CMB interface. We observe that the overall sensitivity of the traveltimes is mostly due to volumetric velocity structure and that imprints of CMB on traveltimes are less pronounced. Our study explains the observed difficulties relating to inferring CMB topography using traveltimes and provides a suite of finite frequency sensitivity kernels computed with the adjoint method. The kernels allow us to qualitatively explain the behaviour of measured traveltimes and understand the trade-off between velocity and CMB topography. They can also serve as reference of finite frequency effects on traveltimes of observed seismic phases. From our analyses we conclude that: i) traveltime anomalies measured on Swaves are more in accord with ray theoretical predictions, ii) PcP, PKP, ScS and SKS phases have more pronounced sensitivity to the boundary and iii) separating the greater effects of velocity from those due to the boundary structure is difficult, as they intricately affect the traveltime. We propose that jointly inverting for CMB topography and lowermost mantle velocity structure using full-waveform synthetics and adjoint sensitivity kernels can progress our understanding of deep Earth structure and finite frequency effects on observed waveforms.
Prevention of earthquake disaster is critical in the densely populated Kanto Basin, Japan, because of the presence of thick sediments that amplify strong ground motion. For this, a high‐resolution ...three‐dimensional S‐wave velocity model is essential to understand the complex amplification of strong ground motion. We constructed a three‐dimensional S‐wave velocity model using the joint inversion of multimodal dispersion curves of Rayleigh and Love waves. Inclusion of higher modes significantly improved the accuracy and precision of the surface‐wave inversion by more than 50% compared to using only fundamental mode. Our proposed model revealed a low‐velocity anomaly of sediments toward the east and a curved velocity contour of the basement rock, thereby better explaining the observed complex surface‐wave dispersion curves that have been unexplained in past homogeneous multilayered models. Estimated S‐wave velocity model better reflected subsurface heterogeneity, providing vital information for hazard assessment in a metropolitan area where huge earthquakes are expected.
Plain Language Summary
The Kanto Basin where the capital of Japan is located comprises large‐scale thick soft sediments which amplify seismic waves. Constructing an accurate underground structure model is important to reveal the propagation properties of seismic waves, and provide better hazard assessment. We constructed a highly accurate and precise underground structure model by using surface waves. Usually, only fundamental tone of surface waves is used to estimate underground structure model. In this study, we separated fundamental and over tones of surface waves, and jointed speed information of both tones to estimate underground structure model. Inclusion of overtones of surface waves significantly improved the accuracy and precision by more than 50%. Our proposed model better explains observed surface‐wave properties that previous models have not been able to explain. Our high‐precision underground structure model better reflected subsurface shapes, providing vital information for hazard assessment in a metropolitan area where huge earthquakes are expected.
Key Points
A three‐dimensional S‐wave velocity model was estimated by joint inversion of multimodal Rayleigh and Love waves
Inclusion of higher modes significantly improved the accuracy and precision of the inverted solutions by at least 50% in the simulation test
Estimated model better explains observed surface‐wave properties that previous model has not been able to explain
SUMMARY
In this paper, the 3-D theoretical seismogram at the free surface of an elastic half-space with ‘vertical transverse isotropy (VTI)’ and an ‘elliptic anisotropy‘ is synthesized via ...semi-analytical formulation. To this end, the time-domain solution is obtained via the Hankel and Laplace integral transforms and the Cagniard contour integration scheme. The formulations include complete Green's functions expressed in compact and elegant formulations in terms of some elementary line integrals over the finite interval (0, π/2), due to the general point force and point double-couple source of arbitrary orientation, varying with time as Heaviside step function. This solution is further implemented to model seismic waves generated from moment tensor source with a ramp-type slip function. The solution clearly delineates compressional P waves, shear SV waves and SH waves, diffracted SPwaves and surface Rayleigh waves, with two critical distances in which the mode conversion happens. The first marks the conversion of the total reflection of SV wave into the diffracted SPwave travelling on the free surface with the velocity of compressional wave. The second, however, marks a location where the order of arrival times of SP and SH waves is reversed. The interesting phenomenon of shear wave splitting by the apparent time lag between the arrivals of SV and SHwaves is further demonstrated. Studied also is the effect of non-double-couple (non-DC) components of the moment tensor of the shear fault. Particularly, it is shown that non-DC components may lead to large amplitude of the P wave in the presence of anisotropy, resulting in the changed polarity of P wave at the onset of the motion. It is found that for the elliptic anisotropy, and for oblique-thrust faults, the isotropic moment (ISO) is always negative if the elastic constants satisfy C11 > C33 and C44 > C66, whereas it is always positive if C11 < C33 and C44 < C66 (for oblique-reverse faults, the situation is reversed). It is shown that for some sedimentary rocks, the decomposition of moment tensor in the general VTI and in its elliptic approximation are close to each other, and that the moment tensor decomposition in VTI media is very sensitive to the elastic coefficients, such that a small change in the elastic constants may lead to a remarkable change in the moment tensor decomposition. Particularly, the effect of elastic constant C13 is shown to be significant. While the time-domain solution obtained in this paper can be also degenerated to the solution in the corresponding isotropic half-space, the Mathematica code of the solution provided can be served as benchmark to other numerical solutions, applicable for the computation of the theoretical seismogram in the involved media.
Surface-wave analysis has been widely used for near-surface geophysical and geotechnical studies by using the dispersive characteristic of surface waves (Rayleigh or Love waves) to determine ...subsurface model parameters. Unlike Rayleigh waves, the dispersive nature of Love waves is independent of P-wave velocity in 1D models, which makes Love-wave dispersion curve interpretation simpler than Rayleigh waves. This reduces the degree of nonuniqueness leading to more stable inversion of Love-wave dispersion curves. To estimate the near-surface shear-wave velocities (Vs) using multichannel analysis of Rayleigh (MASW) and Love waves (MALW) for hydrologic characterization, we conducted an experiment at the Boise Hydrogeophysical Research Site (BHRS, an experimental well field located near Boise, Idaho, USA). We constructed the pseudo-3D velocity structures at the BHRS using both the MASW and MALW methods and compared the results to borehole measurements. We used the 3D Vs distribution to identify and resolve the extent of a relatively low-velocity anomaly caused by a sand channel. The Vs structure and anomaly boundaries were delineated at the meter scale and confirmed by the ground-penetrating radar surveys. The differences in shear-wave velocity determined by MASW, MALW and borehole measurements were discussed and interpreted to reflect the near-surface anisotropy associated with the hydrologic characteristics at the BHRS. Our results demonstrated that the combination of MALW and MASW can be a powerful tool for near-surface characterization.
SUMMARY
In this paper, the global stiffness matrix K and the Fourier–Bessel series methods are proposed to derive the accurate Green's function and dynamic response in a form that is directly related ...to the dispersion curve and experimental dispersion spectrum. Detailed analyses are carried out for the two-layered half-space with different velocity profiles, including the homogeneous half-space as a special case. Our studies indicate that, in Rayleigh wave analysis, the original Rayleigh equation, instead of the rationalized Rayleigh equation as previously derived and used, should be used since the latter would contain extra non-physical roots. We further reveal and characterize three distinct types of leaky waves: the intrinsic surface leaky wave, the apparent Rayleigh mode with a frequency gap associated with a low-velocity half-space and the fast-guided P–SV wave in the layered medium with a high VS contrast between the upper layer and the lower half-space. All leaky modes can be captured by local minima of |detK| instead of tracing complex roots in other existing approaches. In the experimental estimation of dispersion curves for practical applications, we have observed that the truncation effect is the major source of uncertainty regardless of the wavefield transformation method utilized. Furthermore, the truncation effect is both location- and model-dependent, without a unique optimal near offset. As such, in order to reduce the uncertainty from the truncation effect, the receiver layout should be considered in the inversion of dynamic response, instead of relying on ensuring a minimum near offset. This becomes possible with the present fast and accurate complete dynamic Green's function by which all wave phenomena (including different types of leaky waves) and receiver locations can be considered in the wavefield transformation.
We explore the thesis that resonances in trees result in forests acting as locally resonant metamaterials for Rayleigh surface waves in the geophysics context. A geophysical experiment demonstrates ...that a Rayleigh wave, propagating in soft sedimentary soil at frequencies lower than 150 Hz, experiences strong attenuation, when interacting with a forest, over two separate large frequency bands. This experiment is interpreted using finite element simulations that demonstrate the observed attenuation is due to bandgaps when the trees are arranged at the sub-wavelength scale with respect to the incident Rayleigh wave. The repetitive bandgaps are generated by the coupling of the successive longitudinal resonances of trees with the vertical component of the Rayleigh wave. For wavelengths down to 5 meters, the resulting bandgaps are remarkably large and strongly attenuating when the acoustic impedance of the trees matches the impedance of the soil. Since longitudinal resonances of a vertical resonator are inversely proportional to its length, a man-made engineered array of resonators that attenuates Rayleigh waves at frequency ≤10 Hz could be designed starting from vertical pillars coupled to the ground with longitudinal resonance ≤10 Hz.
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