Modelling S-wave radiation for SP-waves in isotropic and anisotropic media

Utilizing shear-wave (S-wave) data acquired with compressional waves (P-waves) is becoming more common as joint imaging and inversion techniques improve. Interest in S-waves radiated from vertical sources and buried explosives exploits conversion to P-waves as primary reflections (SP-waves) for reducing acquisition costs and for application to legacy data. However, recent investigations overstate the extent of SP-wave illumination and show isotropic processing results with narrow bandwidth frequency and wavenumber data. I demonstrate that illumination with SP-waves is limited in general to near vertical polar angles up to around 30° or 35° for V_P/V_S of 2 or 3, respectively. At greater angles, S-waves are typically in the P-wave evanescent range and cannot excite SP-wave reflections. Contrary to recent claims, these sources for P-wave do not radiate S_H-waves polarized in horizontal planes in all azimuths. I show these properties for isotropic media with radiation expressions for amplitude derived in vector slowness coordinates. Also, I extend these expressions to transversely isotropic media with a vertical symmetry axis to show agreement with synthetic seismic data that only quasi S_V-waves are radiated and become more narrowly focused towards 45°. Furthermore, in orthorhombic media, synthetic data show that fast S₁- and slow S₂-waves polarized parallel and perpendicular to fractures may appear as S_V- and S_H-waves. For the partially saturated fracture model studied here, S₁-wave radiation has broader azimuthal illumination than slow S₂-waves, which are more narrowly focused in azimuth. These produce SP-wave splitting signatures on vertical component reflection data that are nearly identical to PS-wave signatures on radial horizontal component data. Separating these fast and slow SP-waves is an additional processing challenge.     

Radar experiments in isotropic and anisotropic geological formations (granite and schists)1

In order to understand various aspects of radar wave propagation, a survey of electromagnetic wave behaviour relative to the geological characteristics of the formations prospected was undertaken. The sites chosen for the tests were a granite quarry and an underground schist working. By investigating an electrically resistive isotropic site and a conductive anisotropic site, it was demonstrated that non-conventional use of a radar system (antennae raised, various orientations of the transmitter/receiver, etc.) could improve data quality, and could allow information other than reflector depth to be collected (volume scattering intensity, isotropy, etc.). By studying wave propagation velocities, we underlined the difficulties encountered in establishing a velocity versus depth law, despite recourse to seismic data processing, such as NMO corrections. The results of field experiments, complemented by laboratory measurements of dielectric permittivities, clearly showed anisotropy effects: in the case of a path that is perpendicular to the schistosity plane, an electromagnetic wave propagates more slowly and is more attenuated than a wave parallel to the schistosity plane.     

3-D isotropic and anisotropic tomography of P-wave travel times from the Anhui airgun experiment in the Yangtze River

The Middle-Lower Yangtze River is a typical transition region between the nearly NW-oriented Tethys and NE-trending Pacific tectonic regimes.Structures of different periods and directions overlap strongly during these processes.The NE-trending Yangtze River compound structural belt and NW-trending Tongling-Hangzhou struc-tural belt both control the magmatic activities and distribu-tions of the metallogenic belts in the area.Here,we obtain 3-D high-resolution isotropic and azimuthally anisotropic velocity structures at depths of 1-10 km using the first arrivals from airgun sources.The velocity maps correspond well with the tectonic structures,with high-velocity anomalies distributed in ore-concentrated districts and low-velocity anomalies distributed along the Yangtze River.The fast directions are generally consistent with the fault strike,indicating that the azimuthal anisotropy is mainly dominated by the fault and fracture trends in the upper crust.The complicated fast directions near the Luzong and Tongling ore deposits reveal complex deformations in the upper crust,which are mainly caused by the intersection of the Yangtze River compound and Tongling-Hangzhou structural belts.The magma intrusion beneath the two ore deposits(Luzong and Tongling)are connected at depths of 5-10 km.     

Modelling frequency-dependent seismic anisotropy in fluid-saturated rock with aligned fractures: implication of fracture size estimation from anisotropic measurements

Measurements of seismic anisotropy in fractured rock are used at present to deduce information about the fracture orientation and the spatial distribution of fracture intensity. Analysis of the data is based upon equivalent-medium theories that describe the elastic response of a rock containing cracks or fractures in the long-wavelength limit. Conventional models assume frequency independence and cannot distinguish between microcracks and macrofractures. The latter, however, control the fluid flow in many subsurface reservoirs. Therefore, the fracture size is essential information for reservoir engineers. In this study we apply a new equivalent-medium theory that models frequency-dependent anisotropy and is sensitive to the length scale of fractures. The model considers velocity dispersion and attenuation due to a squirt-flow mechanism at two different scales: the grain scale (microcracks and equant matrix porosity) and formation-scale fractures. The theory is first tested and calibrated against published laboratory data. Then we present the analysis and modelling of frequency-dependent shear-wave splitting in multicomponent VSP data from a tight gas reservoir. We invert for fracture density and fracture size from the frequency dependence of the time delay between split shear waves. The derived fracture length matches independent observations from borehole data.     

About the Efficiency of Numerical 1-D and 2-D Modelling of Site Effects in Basin Structures

—In the present study we compare results obtained from experimental estimates of local site amplification effects with those from numerical modelling using four different techniques. We benefit from an extremely precise knowledge of the near-surface structure and experimental estimates of the local amplification factors which are determined from seismic weak-motion data recorded by a dense array across a sedimentary basin at a European test-site in Northern Greece. The possibilities and limitations of the different modelling techniques (a 1-D technique, and three 2-D techniques) to model the effects of local amplification effects are tested. Amplifications calculated by the numerical techniques are only qualitatively compared with observed data from experimental studies in the time domain and directly in the frequency domain.¶As a result we conclude that, in the case of a complex subsurface geometry, 1-D modelling underestimates the amplification patterns in terms of absolute amplification level, and cannot correctly account for resonant frequencies, at least for modes higher than the fundamental mode. If a more realistic incident wave field than just a plane wave is taken into account, 2-D modelling reveals the fundamental frequency and shows adequate amplifications not only at the fundamental frequency but also at higher frequencies. The general trend of the amplifications at the lowest frequencies is well determined by the 2-D numerical modelling, and can therefore supply information for seismic risk analysis.     

Construction of regional and local seismic anisotropic structures from wide-angle seismic data: crustal deformation in the southeast of China

We present a method to obtain spatial distributions of seismic anisotropy associated with regional stress and local faulting in the crust from wide-angle seismic data. The method contains three steps. The first step consists of obtaining radial- and transverse-component seismic sections using a pre-stack depth migration algorithm from the S-wave velocity model determined by conventional interpretation of picked intra-crustal seismic events. In the second step, we compute time delays between split shear-waves and polarizations of fast split shear-waves by minimizing the transverse-component seismic energy. The time delay and polarization in each layer are derived using a layer-stripping method. The final step is to estimate the average splitting parameters along the whole profile. Thus, the average time delay and polarization can be regarded as caused by the effects owing to regional structure and stress fields, whereas the residual values of the splitting parameters are considered to be related to local structures and local faulting. Our method allows us to construct multi-layer anisotropic images, which may later be interpreted in terms of intra-layer coupling/decoupling or deformation. We present results from a set of three-component seismic data acquired by a controlled source experiment in the southeast region of China. The results demonstrate that the average polarizations and time delays are consistent with the direction and strength of the stress field, and their lateral variations related to local anisotropy match the spatial distribution of surface faulting crossing the acquisition seismic profile.     

Cross-field gradients: general concept, importance of multi-spacecraft measurements and study at 1 AU of the source intensity gradient for E>30 keV solar event electrons

Three main physical processes (and associated properties) are currently used to describe the flux and anisotropy time profiles of solar energetic particle events, called SEP profiles. They are (1) the particle scattering (due to magnetic waves), (2) the particle focusing (due to the decrease of the amplitude of the interplanetary magnetic field (IMF) with the radial distance to the Sun) and (3) the finite injection profile at the source. If their features change from one field line to another, i.e. if there is a cross IMF gradient (CFG), then the shape of the SEP profiles will depend, at onset time, on the relative position of the spacecraft to the IMF and might vary significantly on small distance scale (e.g. 10⁶ km). One type of CFG is studied here. It is called intensity CFG and considers variations, at the solar surface, only of the intensity of the event. It is shown here that drops of about two orders of magnitude over distances of 10⁴ km at the Sun (1° of angular distance) can influence dramatically the SEP profiles at 1 AU. This CFG can lead to either an under or overestimation of both the parallel mean free path and of the injection parameters by factor up to, at least, 2/3 and 18, respectively. Multi-spacecraft analysis can be used to identify CFG. Three basic requirements are proposed to identify, from the observation, the type of the CFG being measured.     

A 2-D Sensitivity Study of the Dynamic Behavior of a Volcanic Hill in the Azores Islands: Comparison with 1-D and 3-D Models

—?A 2-D and a 3-D finite element representation using Drucker-Prager cap model is employed in the study to determine the seismic response of a volcanic hill located in one of the islands in the Azores Archipelago. In order to test the applicability of these models we used the motion recorded at the base of the hill during an aftershock of the July 9, 1998 earthquake and compared the numerical response with the record obtained at the top of the hill. Several comparisons and sensitivity analyses were made to identify the most important dynamic parameters influencing the response. Even though the match is not yet adequate for any one of the representations, especially in time domain, the 3-D model showed a good fitting in terms of Fourier Spectrum. Up to a PGA of 0.24?g the behavior of the hill is approximately linear, with higher amplifications going upwards along a vertical interior column; beyond this limit, there is a clear nonlinear behavior.     

基于谱元-简正振型耦合方法的核幔边界D″区地震波波形模拟方法研究

本文拓展了一种模拟地震波在地球核幔边界D″区各向异性介质中传播的数值方法:谱元-简正振型耦合方法(CSEM).该方法通过在球对称各向同性介质空间采用简正振型方法,在各向异性的D″区采用谱元方法,并在两种介质的边界采用"DtN"算子耦合的策略计算一维模型PREM(见文献[1])或修改后的D″区横向各向同性VTI-PREM模型的理论地震图.模拟所得数值解结果与采用简正振型方法得到的解析解结果进行对比以验证方法的精度.在中国科学院地球深部结构重点实验室高性能计算机上使用128个CPU计算得到的结果显示,在10^-5～0.125 Hz的频率范围内谱元简正振型法得到的波形与简正振型方法能很好拟合.此外,对于VTI介质结构模型,谱元简正振型法能够准确模拟S波分裂现象,从而验证了谱元简正振型耦合方法对各向异性介质中地震波传播数值模拟是一种有效的方法.     

Design hydrograph estimation in small and ungauged watersheds: continuous simulation method versus event‐based approach

The proper assessment of design hydrographs and their main properties (peak, volume and duration) in small and ungauged basins is a key point of many hydrological applications. In general, two types of methods can be used to evaluate the design hydrograph: one approach is based on the statistics of storm events, while the other relies on continuously simulating rainfall‐runoff time series. In the first class of methods, the design hydrograph is obtained by applying a rainfall‐runoff model to a design hyetograph that synthesises the storm event. In the second approach, the design hydrograph is quantified by analysing long synthetic runoff time series that are obtained by transforming synthetic rainfall sequences through a rainfall‐runoff model. These simulation‐based procedures overcome some of the unrealistic hypotheses which characterize the event‐based approaches. In this paper, a simulation experiment is carried out to examine the differences between the two types of methods in terms of the design hydrograph's peak, volume and duration. The results conclude that the continuous simulation methods are preferable because the event‐based approaches tend to underestimate the hydrograph's volume and duration. Copyright © 2011 John Wiley & Sons, Ltd.     

Deep seismic soundings on the 1-AP profile in the Barents Sea: Methods and results

Profile 1-AP with a length of 1300 km intersects the Barents Sea from The Kola Peninsula to Franz Josef Land. The combined Common Depth Point (CDP) and Deep Seismic Sounding (DSS) seismic studies were carried out on this profile. The DSS measurements were conducted with the standalone bottom seismic stations with an interval of 5–20 km between them. The stations recorded the signals generated by the large air guns with a step of 250 m. Based on these data, the detailed P-velocity section of the Earth’s crust and uppermost mantle have been constructed for the entire profile and the S-velocity section for its southern part. The use of a variety of methods for constructing the velocity sections enabled us to assess the capabilities of each method from the standpoint of the highest reliability and informativity of the models. The ray tracing method yielded the best results. The 1-PR profile crosses two large basins—the South Barents and North Barents ones, with the thickness of the sediments increasing from 8 to 10 km in the south to 12–15 km in the north. The Earth’s crust pertains to the continental type along the entire profile. Its thickness averages 32 to 36 km and only increases to 43 km at the boundary between the two basins. The distinct change in the wave field at this boundary suggests the presence of a large deep fault in this zone. The high-velocity blocks are revealed in the crust of the South Barents basin, whereas the North Barents crust is characterized by relatively low velocities.     

四川及其三个分区的地震平静指标及其预测效能的研究--不同层次地震平静异常预测效能的研究之一

作为不同层次地震平静异常预测效能的研究之一,本文针对四川及其三个分区,利用过去积累的30多年地震资料,经过多种方案试算、评分检验,明确了平静指标和预测规则,找到了合适的研究平静预测的震级下限M0、预测震级M1、平静异常时间T1与预测时间T2等最佳参数组合,可以取T2等最佳参数组合,可以取得高于置信水平为97.5%的区别随机瞎报的阈值R0的R评分值。     

Ground penetrating radar inversion in 1-D: an approach for the estimation of electrical conductivity, dielectric permittivity and magnetic permeability

This paper presents a method for inverting ground penetrating radargrams in terms of one-dimensional profiles. We resort to a special type of linearization of the damped E-field wave equation to solve the inverse problem. The numerical algorithm for the inversion is iterative and requires the solution of several forward problems, which we evaluate using the matrix propagation approach. Analytical expressions for the derivatives with respect to physical properties are obtained using the self-adjoint Green's function method. We consider three physical properties of materials; namely dielectrical permittivity, magnetic permeability and electrical conductivity. The inverse problem is solved minimizing the quadratic norm of the residuals using quadratic programming optimization. In the iterative process to speed up convergence we use the Levenberg–Mardquardt method. The special type of linearization is based on an integral equation that involves derivatives of the electric field with respect to magnetic permeability, electrical conductivity and dielectric permittivity; this equation is the result of analyzing the implication of the scaling properties of the electromagnetic field. The ground is modeled using thin horizontal layers to approximate general variations of the physical properties. We show that standard synthetic radargrams due to dielectric permittivity contrasts can be matched using electrical conductivity or magnetic permeability variations. The results indicate that it is impossible to differentiate one property from the other using GPR data.     

Chemical changes in spring waters at Tacaná volcano, Chiapas, Mexico: A possible precursor of the May 1986 seismic crisis and phreatic explosion

Local seismic activity consisting of sharp earthquakes accompanied by thunderous noise was reported starting in late December 1985 around Tacaná volcano (15.13°N, 92.10°W). Portable seismic stations were established in the area by late January 1986 and sampling of the only known thermal spring on the volcano flanks started at the same time. A marked increase in SO₄²⁻ concentration in the spring water preceded by two months the occurrence of a seismic swarm crisis and a small phreatic explosion. A model involving a crystalline basement fractured by tectonic stresses is proposed to explain the chemical and seismic anomalies, and the consequences on risk of volcanic activity are briefly discussed in terms of the observed behaviour.     

Site effects in 3D basins using 1D and 2D models: an evaluation of the differences based on simulations of the seismic response of Euroseistest

Site effects are one of the most predictable factors of destructive earthquake ground motion but results depend on the type of model chosen. We compare simulations of ground motion for a 3D model of the Mygdonian basin in northern Greece (Euroseistest) using different approximation for this basin. Site effects predicted using simple 1D models at many points inside the basin are compared to site effects predicted using four different 2D cross sections across the basin and with results for a full 3D simulation. Surface topography was neglected but anelastic attenuation was included in the simulations. We show that lateral heterogeneity may increase ground motion amplification by 100 %. Larger amplification is distributed in a wide frequency range, and amplification may occur at frequencies different from the expected resonant frequencies for the soil column. In contrast, on a different cross section, smaller conversion of incident energy into surface waves and larger dispersion leads to similar amplitudes of ground motion for 2D and 1D models. In general, results from 2D simulations are similar to those from a complete 3D model. 2D models may overestimate local surface wave amplitudes, especially when the boundaries of the basin are oblique to the selected cross section. However, the differences between 2D and 3D site effects are small, especially in regard of the difficulties and uncertainties associated to building a reliable 3D model for a large basin.