Scattering and anelastic attenuation of seismic energy in northern Greece

The relative contribution of scattering (Q _s ^–1 ) and intrinsic (Q _i ^–1 ) attenuation to the totalS-wave attenuation for the frequencies of 1.5, 3.0, 6.0 and 12.0 Hz has been studied by applying the radiative energy transfer theory, Data of local earthquakes which occurred in northern Greece and were recorded by the permanent telementered network of the Geophysical Laboratory of the University of Thessaloniki have been used. The results show that in this area the scattering attenuation is dominant over all frequencies while intrinsic attenuation is significantly lower. The estimatedQ _s ^–1 andQ _i ^–1 values have frequency dependences off ^–0.72 andf ^–0.45, respectively. The frequency dependence ofQ _s ^–1 is the same as that of the codaQ _c ^–1 , obtained by applying the single scattering model, which probably implies that the frequency dependence of the coda wave attenuation is attributed to the frequency dependence of the scattering attenuation.Q _c ^–1 values are very close to scattering attenuation for short lapse times, (10–20 sec), and intermediate between scattering and intrinsic attenuation for the longer lapse times, (50–100 sec). This difference is explained as the result of the depth-dependent attenuation properties and the multiple scattering effects.     

Improvement of Ground Penetrating Radar (GPR) Data Interpretability by an Enhanced Inverse Scattering Strategy

This paper is inserted into the framework of inverse scattering with application to Ground Penetrating Radar (GPR) data and is meant to provide a method helping to apply inverse scattering algorithms to electrically large investigation domains. In particular, we focus on the depth slices that are particularly important in application on cultural heritage and propose in relationship with the depth slices a strategy that we will call “shifting zoom” that is specifically a method to mitigate the effects of the limited view angle in the linear tomographic inversion applied to GPR data. In particular, this paper is an extended version of the contribution (Persico et al. in: Proceedings of Imeko international conference on metrology for archaeology and cultural heritage, Lecce, Italy, 2017a), published in the Proceedings of the conference metrology for archaeology 2017. We propose here a validation of the shifting zoom versus experimental data gathered in a controlled test site, and we will show the effect of the shifting zoom on depth slices achieved from these data after a linear inverse scattering processing has been applied for their focusing.     

一种新的实时电磁逆散射方法

为解决介质圆柱体逆散射问题,提出一种新的在线逆散射方法,通过支持向量机将逆散射问题转化成一个回归估计问题. 该方法可应用于各种逆散射方面, 尤其是目标的几何与电磁参数重构和埋地目标探测. 文中首次将支持向量机方法应用到该领域,设置多个散射场的观测点,通过提取散射场的不同信息作为样本信息训练支持向量机, 建立了介质圆柱体的逆散射模型, 利用该模型重构了介质圆柱体的电磁参数,同时探测了埋地位置. 数值结果显示了该方法的有效性和准确性,为目标的实时逆散射研究提供了一种有效方法.     

逆散射级数法去除自由表面多次波

压制多次波是地震资料处理过程中的重要环节之一,多次波去除的效果直接影响到最后成像的质量．本文研究的逆散射级数法以波动方程和Born级数为基础,构造一个与自由表面多次波相关的子序列来预测并消除多次波,该方法不需要知道地下的速度结构信息,适用于各种复杂的地下情况．在逆散射级数法的实现过程中,地震子波和近道波场是必不可少的信息,本文采用能量最低法则和带限抛物Radon变换法来弥补原始地震资料中所缺失的这些信息．合成资料和实际地震资料的处理结果表明,逆散射级数法能够在去除自由表面多次波的同时保留有效波的信息,对于地下复杂结构的情况同样有效．     

The interpretation of inverse isochron diagrams in Ar/Ar geochronology

The concepts involved in the construction and interpretation of inverse isochron diagrams used in ⁴⁰Ar/³⁹Ar geochronology are reviewed. The diagrams can be useful as a means of recognising atmospheric argon and excess ⁴⁰Ar, incorporated in the mineral lattice, which cannot be recognised from ⁴⁰Ar/³⁹Ar spectra. The age established using an inverse isochron plot, unlike that yielded by a spectrum, is not affected by trapped argon ⁴⁰Ar/³⁶Ar ratios that are different from the atmospheric argon ratio (e.g. due to excess ⁴⁰Ar), and may contribute to a better age interpretation. However, a heterogeneous distribution of excess ⁴⁰Ar or heterogeneous argon loss can cause ‘false’ isochrons, with axial intercepts indicating an incorrect age and an incorrect trapped argon composition. Inconsistency between the ages from a spectrum and from the associated inverse isochron plot may indicate the degree of inaccuracy of isochrons. However, it is possible that both the spectrum and inverse isochron yield the same incorrect age. The importance of considering all possible interpretations before assigning an age to a specimen is stressed.     

水平层状介质中基于DTA的三维电磁波逆散射快速模拟算法

为提高水平层状介质中三维电磁波散射和逆散射数值模拟的效率,在对角张量近似(DTA)的基础上根据不同回代方式得到了求解积分方程的DTA1和DTA2两种近似. 这两种近似可以作为计算积分方程稳定型双共轭梯度快速Fourier变换(BCGS-FFT)算法的初始猜测值和预条件因子,从而形成效率更高的混合DTA-BCGS算法. 散射实例说明了DTA2的高精度和混合DTA-BCGS算法尤其是混合DTA2-BCGS算法的高效率. 由于DTA2近似程度更高,将DTA2与变型Born迭代反演方法(DBIM)相结合形成了一种对三维异常体进行重构的快速电磁波逆散射技术. 文中的逆散射实例说明所开发的逆散射技术对重构水平层状介质中的任意三维异常体是非常有效的.     

Scattering ofP andS waves by a spherically symmetric inclusion

Scattering of an arbitrary elastic wave incident upon a spherically symmetric inclusion is considered and solutions are developed in terms of the spherical vector system of Petrashen, which produces results in terms of displacements rather than displacement potentials and in a form suitable for accurate numerical computations. Analytical expressions for canonical scattering coefficients are obtained for both the cases of incidentP waves and incidentS waves. Calculations of energy flux in the scattered waves lead to elastic optical theorems for bothP andS waves, which relate the scattering cross sections to the amplitude of the scattered fields in the forward direction. The properties of the solutions for a homogeneous elastic sphere, a sphere filled by fluid, and a spherical cavity are illustrated with scattering cross sections that demonstrate important differences between these types of obstacles. A general result is that the frequency dependence of the scattering is defined by the wavelength of the scattered wave rather than the wavelength of the incident wave. This is consistent with the finding that the intensity of thePS scattering is generally much stronger than theSP scattering. When averaged over all scattering angles, the mean intensity of thePS converted waves is2V _p ² /V _s ⁴ times the mean intensity of theSP converted waves, and this ratio is independent of frequency. The exact solutions reduce to simple and easily used expressions in the case of the low frequency (Rayleigh) approximation and the low contrast (Rayleigh-Born) approximation. The case of energy absorbing inclusions can also be obtained by assigning complex values to the elastic parameters, which leads to the result that an increase in attenuation within the inclusion causes an increased scattering cross section with a marked preference for scatteredS waves. The complete generality of the results is demonstrated by showing waves scattered by the earth's core in the time domain, an example of high-frequency scattering that reveals a very complex relationship between geometrical arrivals and diffracted waves.     

Disproportionation of spinels to mixed oxides: significance of cation configuration and implications for the mantle

Experimental study of the phase boundary for the disproportionation of the inverse spinel Mg₂SnO₄ into its isochemical mixed oxides indicates a slope dP/dT = 40 ± 10bars/°K. This positive slope is consistent with the large entropies of inverse (relative to normal) spinels predicted from high-temperature entropy-molar volume systematics. Thermodynamic data do not support the existence of a distinctly negative slope for the proposed disproportionation of Mg₂SiO₄ normal spinel. Evidence from X-ray and phase equilibria studies suggests the possibility that Si⁴⁺, Mg²⁺, and Fe²⁺ share the octahedral sites in silicate spinels under mantle conditions. The consequences of this partial inverse character are a positive slope for the postulated spinel-mixed oxide phase boundary near 650 km depth, removal of a widely accepted constraint on mantle-wide convection, and anomalous elasticity-density behaviour within the transition zone.     

Estimation of the Intrinsic Absorption and Scattering Attenuation in Northeastern Venezuela (Southeastern Caribbean) Using Coda Waves

—Northeastern Venezuela has been studied in terms of coda wave attenuation using seismograms from local earthquakes recorded by a temporary short-period seismic network. The studied area has been separated into two subregions in order to investigate lateral variations in the attenuation parameters. Coda-Q ^?1 (Q _c ^?1) has been obtained using the single-scattering theory. The contribution of the intrinsic absorption (Q _i ^?1) and scattering (Q _s ^?1) to total attenuation (Q _t ^?1) has been estimated by means of a multiple lapse time window method, based on the hypothesis of multiple isotropic scattering with uniform distribution of scatterers. Results show significant spatial variations of attenuation the estimates for intermediate depth events and for shallow events present major differences. This fact may be related to different tectonic characteristics that may be due to the presence of the Lesser Antilles subduction zone, because the intermediate depth seismic zone may be coincident with the southern continuation of the subducting slab under the arc.     

利用解析法有效快速估计将来GRACE Follow-On地球重力场的精度

本文首次利用解析法有效快速估计了将来GRACE（Gravity Recovery and Climate Experiment） Follow-On地球重力场的精度. 第一,基于功率谱原理分别建立了新的GRACE Follow-On卫星激光干涉星间测量系统星间速度、GPS接收机轨道位置和轨道速度以及加速度计非保守力误差影响累计大地水准面的单独和联合解析误差模型. 第二,利用提出的GRACE卫星关键载荷匹配精度指标和美国喷气推进实验室（JPL）公布的GRACE Level 1B实测精度指标的一致性,以及估计的GRACE累计大地水准面精度和德国波兹坦地学研究中心（GFZ）公布的EIGEN-GRACE02S地球重力场模型实测精度的符合性,验证了本文建立的解析误差模型是可靠的. 第三,论证了GRACE Follow-On卫星不同关键载荷匹配精度指标和轨道高度对地球重力场精度的影响. 在360阶处,利用轨道高度250 km、星间距离50 km、星间速度误差1×10^-9m/s、轨道位置误差3×10^-5m、轨道速度误差3×10^-8m/s和非保守力误差3×10^-13m/s²,基于联合解析误差模型估计累计大地水准面的精度为1.231×10^-1 m. 本文的研究不仅为当前GRACE和将来GRACE Follow-On地球重力场精度的有效快速确定提供了理论基础和计算保证,同时对国际将来GRAIL（Gravity Recovery and Interior Laboratory）月球卫星重力测量计划的成功实施具有重要的参考意义.     

Weak-contrast approximation of the elastic scattering matrix in anisotropic media

The plane-wave reflection and transmission coefficients at a plane interface between two anisotropic media constitute the elements of the elastic scattering matrix. For a 1-D anisotropic medium the eigenvector decomposition of the system matrix of the transformed elasto-dynamic equations is used to derive a general expression for the scattering matrix. Depending on the normalization of the eigenvectors, the expressions give scattering coefficients for amplitudes or for vertical energy flux.Computing the vertical slownesses and the corresponding polarizations, the eigenvector matrix and its inverse can be found. We give a simple formula for the inverse, regardless of the normalization of the eigenvectors. When the eigenvectors are normalized with respect to amplitudes of displacement (or velocity), the calculation of the scattering matrix for amplitudes is simplified.When the relative changes in all parameters are small, a weak-contrast approximation of the scattering matrix, based on the exactly determined polarization vectors in an average medium, is obtained. The same approximation is also derived directly from the transformed elasto-dynamic equations for a smooth vertically inhomogeneous medium, proving the consistency of the approximation.For monoclinic media, with the mirror symmetry plane parallel to the interface, the approximative scattering matrix is given in terms of analytic expressions for the non-normalized eigenvectors and vertical slownesses. For transversely isotropic media with a vertical axis of symmetry (VTI) and isotropic media, explicit solutions for the weak-contrast approximations of the scattering matrices have been obtained. The scattering matrix for amplitudes for isotropic media is well known. The scattering matrix for vertical energy flux may have applications in AVO analysis and inversion due to the reciprocity of the reflection coefficients for converted waves.Numerical examples for monoclinic and VTI media provide good agreement between the approximative and the exact reflection matrices. It is, however, expected that the approximations cannot be used when the symmetry properties of the two media are very different. This is because the approximation relies on a small relative contrast between the eigenvectors in the two media.Presented at the Workshop Meeting on Seismic Waves in Laterally Inhomogeneous Media, Castle of Trest, Czech Republic, May 22–27, 1995.     

The neural network approximation method for solving multidimensional nonlinear inverse problems of geophysics

The iterative approximation neural network method for solving conditionally well-posed nonlinear inverse problems of geophysics is presented. The method is based on the neural network approximation of the inverse operator. The inverse problem is solved in the class of grid (block) models of the medium on a regularized parameterization grid. The construction principle of this grid relies on using the calculated values of the continuity modulus of the inverse operator and its modifications determining the degree of ambiguity of the solutions. The method provides approximate solutions of inverse problems with the maximal degree of detail given the specified degree of ambiguity with the total number of the sought parameters ~n × 10³ of the medium. The a priori and a posteriori estimates of the degree of ambiguity of the approximated solutions are calculated. The work of the method is illustrated by the example of the three-dimensional (3D) inversion of the synthesized 2D areal geoelectrical (audio magnetotelluric sounding, AMTS) data corresponding to the schematic model of a kimberlite pipe.     

Evaluation of Monod kinetic parameters in the subsurface using moment analysis: Theory and numerical testing

The spatial moments of a contaminant plume undergoing bio-attenuation are coupled to the moments of microbial populations effecting that attenuation. In this paper, a scalable inverse method is developed for estimating field-scale Monod parameters such as the maximum microbial growth rate (μ^max), the contaminant half saturation coefficient (K_s), and the contaminant yield coefficient (Y_s). The method uses spatial moments that characterize the distribution of dissolved contaminant and active microbial biomass in the aquifer. A finite element model is used to generate hypothetical field-scale data to test the method under both homogeneous and heterogeneous aquifer conditions. Two general cases are examined. In the first, Monod parameters are estimated where it is assumed a microbial population comprised of a single bacterial species is attenuating one contaminant (e.g., an electron donor and an electron acceptor). In a second case, contaminant attenuation is attributed to a microbial consortium comprised of two microbial species, and Monod parameters for both species are estimated. Results indicate the inverse method is only slightly sensitive to aquifer heterogeneity and that estimation errors decrease as the sampling time interval decreases with respect to the groundwater travel time between sample locations. Optimum conditions for applying the scalable inverse method in both space and time are investigated under both homogeneous and heterogeneous aquifer conditions.     

基于逆散射级数法的鬼波压制方法

鬼波问题是影响海上地震资料分辨率和保真度提高的最重要因素之一.详细论述了逆散射级数理论和逆散射级数法鬼波压制原理,说明了逆散射级数方法进行鬼波压制理论的完善性和对鬼波描述的精确性.实现了基于逆散射级数理论的鬼波压制方法,方法以波动方程和Lippmann-Schwinger方程为基础,在频率-波数-波数域内构造与鬼波相关的压制算子,在不需要对地下介质作任何假设条件下实现地震数据驱动鬼波压制,并通过改善消除鬼波的压制算子,提高算法的稳定性.资料处理试验与处理结果分析表明,基于逆散射级数鬼波压制方法能在实现鬼波压制的同时较好保留有效反射波的信息,从而补偿地震资料低频损失和提高地震数据的保真度.数据处理试验还表明,研究方法能对低信噪比的地震资料进行有效的鬼波压制处理.建立了基于逆散射级数鬼波压制处理流程.     

An alternative method for density variation modeling of the crust based on 3-D gravity inversion

In this paper we are proposing an alternative method for determination of density variations of the crust from constrained inversion of the terrestrial gravity data. The main features of the method can be summarized as follows: (i) Constructing a band-pass filter to remove the long and short wavelength signals from the terrestrial gravity data. (ii) Using an iterative method for stabilization and solution of the inverse problem. The mentioned regularization method is first validated by simulated gravity data and next the methodology is used for development of a new regional density variation model of the crust in three layers based on real gravity data in geographical area of Iran. Application of the band-pass filter to the latter data resulted the residual gravitation variations in the range of − 300 to 50 (mGal) which next based on the iterative method resulted following ranges for residual densities: −120 to 40 (kg/m³) in first layer, −40 to 40 (kg/m³) in second layer, and − 40 to 40 (kg/m³) in third layer.     

Unified approach to amplitude attenuation and coda excitation in the randomly inhomogeneous lithosphere

A unified model is proposed for explaining the frequency dependent amplitude attenuation and the coda wave excitation on the basis of the single scattering process in the randomly inhomogeneous lithosphere. Adopting Birch's law and a direct proportion between density and wave velocity, we statistically describe the inhomogeneous medium by one random function characterized by the von Karman autocorrelation function. We calculate the amplitude attenuation from the solid angle integral of scattered wave energy on the basis of the Born approxiimation after subtracting the travel-time fluctuation effect caused by slowly varying velocity inhomogeneities. This subtraction is equivalent to neglect energy loss by scattering within a cone around the forward direction. The random inhomogeneity of the von Karman autocorrelation function of order 0.35 with the mean square fractional fluctuation of 7.2×10^–3 1.3×10^–2 and the correlation distance of 2.15.1 km well explains observed backward scattering coefficientg and the ratioQ _P ^–1 /Q _S ^–1 , and observed and partially conjecturedQ _S ^–1 for frequencies between 0.5 Hz and 30 Hz.     

Paleomagnetic results from lakes Victoria and albert,Uganda

Summary Unfortunately most of the cores taken from Salisbury Channel, Lake Victoria which contained discrete pieces of wood suitable for¹⁴C dating were organic-rich and therefore showed a considerable scattering of the remanent magnetic direction plots resulting in poorly defined oscillations. However, the cores from Pilkington Bay as well as core C5 from Salisbury Channel, Lake Victoria and the cores from Lake Albert show well-defined paleodeclination and paleoinclination logs. Several cores from Pilkington Bay and Lake Albert with some¹⁴C control can be used to verify the isochronous correlation of the paleodeclination and paleoinclination oscillations. Core C5, from Salisbury Channel, Lake Victoria, which did not contain any discrete pieces of plant or shell material has been dated by correlation with other cores which had¹⁴C control. This core which shows the best-defined paleodeclination and paleoinclination logs of this study would appear to have bottomed in sediments in excess of 6000 years BP age and with the work of Maley et al. (1990) from the Cameroons provides a complete record of the Holocene for Central Africa.     

Seismic Wave Attenuation in the Greater Cairo Region, Egypt

In the present study, a digital waveform dataset of 216 local earthquakes recorded by the Egyptian National Seismic Network (ENSN) was used to estimate the attenuation of seismic wave energy in the greater Cairo region. The quality factor and the frequency dependence for Coda waves and S-waves were estimated and clarified. The Coda waves (Q _c) and S-waves (Q _d) quality factor were estimated by applying the single scattering model and Coda Normalization method, respectively, to bandpass-filtered seismograms of frequency bands centering at 1.5, 3, 6, 12, 18 and 24?Hz. Lapse time dependence was also studied for the area, with the Coda waves analyzed through four lapse time windows (10, 20, 30 and 40?s). The average quality factor as function of frequency is found to be Q _c?=?35?±?9f ^0.9±0.02 and Q _d?=?10?±?2f ^0.9±0.02 for Coda and S-waves, respectively. This behavior is usually correlated with the degree of tectonic complexity and the presence of heterogeneities at several scales. The variation of Q _c with frequency and lapse time shows that the lithosphere becomes more homogeneous with depth. In fact, by using the Coda Normalization method we obtained low Q _d values as expected for a heterogeneous and active zone. The intrinsic quality factor (Q _i ^?1 ) was separated from the scattering quality factor (Q _s ^?1 ) by applying the Multiple Lapse Time Domain Window Analysis (MLTWA) method under the assumption of multiple isotropic scattering with uniform distribution of scatters. The obtained results suggest that the contribution of the intrinsic attenuation (Q _i ^?1 ) prevails on the scattering attenuation (Q _s ^?1 ) at frequencies higher than 3?Hz.     

Seismic inversion with generalized Radon transform based on local second-order approximation of scattered field in acoustic media

Sound velocity inversion problem based on scattering theory is formulated in terms of a nonlinear integral equation associated with scattered field. Because of its nonlinearity, in practice, linearization algorisms (Born/single scattering approximation) are widely used to obtain an approximate inversion solution. However, the linearized strategy is not congruent with seismic wave propagation mechanics in strong perturbation (heterogeneous) medium. In order to partially dispense with the weak perturbation assumption of the Born approximation, we present a new approach from the following two steps: firstly, to handle the forward scattering by taking into account the second-order Born approximation, which is related to generalized Radon transform (GRT) about quadratic scattering potential; then to derive a nonlinear quadratic inversion formula by resorting to inverse GRT. In our formulation, there is a significant quadratic term regarding scattering potential, and it can provide an amplitude correction for inversion results beyond standard linear inversion. The numerical experiments demonstrate that the linear single scattering inversion is only good in amplitude for relative velocity perturbation ( \( \delta_{c}/c_{0} \) ) of background media up to 10 %, and its inversion errors are unacceptable for the perturbation beyond 10 %. In contrast, the quadratic inversion can give more accurate amplitude-preserved recovery for the perturbation up to 40 %. Our inversion scheme is able to manage double scattering effects by estimating a transmission factor from an integral over a small area, and therefore, only a small portion of computational time is added to the original linear migration/inversion process.