PULSE DISTORTION IN CAUSTIC REGIONS1

It is well known that there is a phase shift of π associated with the propagation of a seismic pulse through a focus. But this simple behaviour is true only if the two points at which the pulse is observed lie sufficiently far from the focus, one on either side. Near the focus matters are more complicated and the shape of the pulse may be severely distorted because of diffraction. To examine this problem we consider a pulse generated by a point source and focused by a spherical reflector. Using a general combined method of ray tracing and diffraction, we compute seismograms for receivers lying both inside and outside the focal region, and determine how the shape of the pulse changes on propagation through the focus. To assist the physical interpretation of the numerical results, we also present relevant exact and asymptotic results for comparison.     

Calculation of magnetic anomalies caused by 2D bodies of arbitrary shape with consideration of demagnetization

Forward calculations of magnetic anomalies caused by two-dimensional bodies of any shape and magnetic properties may be performed either without considering demagnetization as in the equivalent source technique or taking demagnetization into account as in the volume integral equation (VIE) approach, in which, for this purpose, magnetized bodies are divided into a set of rectangular prismatic cells. Ignoring demagnetization may result in distortion of the shape and the amplitude of an anomaly, whereas rectangular cells may not be an optimal representation of the source. Moreover, an inaccurate form approximation in the VIE technique may lead to inconsistent results in the near-body region. In this paper, a method is proposed, based on the VIE approach but differing by applying triangular elementary cells. The method largely overcomes the above-mentioned limitations of the VIE technique. It allows us to delineate large and complex structures exactly and only requires the source to be divided into a few elementary cells to take demagnetization into account satisfactorily. These improvements have been attained through analytical calculation of the Green's function in the complex plane, using the theory of the Cauchy-type integral. Comparing numerical solutions with analytical solutions for homogeneous elliptic cylinders without remanence, the method is found to be consistent with the theory in the range of relative magnetic permeability of 2–20, not only far from but also at subcell distances from the body. The method is appropriate for modelling highly and inhomogeneously magnetized 2D bodies of any shape. It may be of value in interpreting underground measurements or topographic effects, as well as in modelling regional geomagnetic profiles, and it is also a convenient tool for testing questionable geological hypotheses. In the framework of the method, the gravitational anomaly for the same causative bodies can be easily calculated. However, at higher and geologically uncommon values of relative magnetic permeability, the algorithm may become unstable but may be stabilized with SVD regularization. The fact that discrepancies were found with the method employed is a basis for further research.     

Quantitative Interpretation of Self-Potential Anomalies of Some Simple Geometric Bodies

We have developed a new numerical method to determine the shape (shape factor), depth, polarization angle, and electric dipole moment of a buried structure from residual self-potential (SP) anomalies. The method is based on defining the anomaly value at the origin and four characteristic points and their corresponding distances on the anomaly profile. The problem of shape determination from residual SP anomaly has been transformed into the problem of finding a solution to a nonlinear equation of the form q = f (q). Knowing the shape, the depth, polarization angle and the electric dipole moment are determined individually using three linear equations. Formulas have been derived for spheres and cylinders. By using all possible combinations of the four characteristic points and their corresponding distances, a procedure is developed for automated determination of the best-fit-model parameters of the buried structure from SP anomalies. The method was applied to synthetic data with 5% random errors and tested on a field example from Colorado. In both cases, the model parameters obtained by the present method, particularly the shape and depth of the buried structures are found in good agreement with the actual ones. The present method has the capability of avoiding highly noisy data points and enforcing the incorporation of points of the least random errors to enhance the interpretation results.     

Nomograms for rapid evaluation of magnetic anomalies over long tabular bodies

The magnetic anomaly due to a long tabular body usually consists of a maximum and a minimum. The distances and the amplitudes of the maximum and the minimum, when defined in dimensionless quantities, may be used as characteristics of the source. In this paper, a method based on the positions of the maximum and the minimum on the magnetic anomaly due to a long tabular body has been presented. Characteristic ratios,D andA involving the distances and amplitudes of the maximum and the minimum points on the anomaly curve are defined. Nomograms showing the variations ofD andA with the parameters of (1) the dike and (2) the vertical fault models are presented. The parameters of the causative source are evaluated from the two ratiosD andA and the nomograms, using some simple analytical relations presented here. From the nomograms, it is observed that (a) for a thick dike,A is always greater thanD, (b)A=D for a thin sheet and (c) for a vertical fault,A is always less thanD. Thus from the characteristic ratiosD andA it is possible to evaluate the source parameters and also to distinguish whether the source is a dike, sheet or a vertical fault. The method is fast and is applicable for the magnetic anomalies either in total, vertical or horizontal component. The method has been applied on two field examples and the results are found to be in close agreement with those obtained by using other methods. A simple method of locating the origin on the anomaly curve is included. The limitations of the method are also discussed.     

Inelastic displacement ratio of near‐source pulse‐like ground motions

Near‐source pulse‐like records resulting from rupture's directivity have been found to depart from so‐called ordinary ground motions in terms of both elastic and inelastic structural seismic demands. In fact, response spectra may be strong if compared with what is expected from common ground motion prediction equations. Moreover, because not all spectral ordinates are affected uniformly, a peculiar spectral shape, with an especially amplified region depending on the pulse period, may follow. Consequently, inelastic seismic demand may show trends different to records not identified as pulse‐like (i.e., ordinary). This latter aspect is addressed in the study reported in this short communication, where a relatively large dataset of identified impulsive near‐source records is used to derive an analytical‐form relationship for the inelastic displacement ratio. It is found that, similar to what was proposed in literature for soft soil sites, a double‐opposite‐bumps form is required to match the empirical data as a function of the structural period over the pulse period ratio. The relationship builds consistently on previous studies on the topic, yet displays different shape with respect to the most common equations for static structural assessment procedures. Copyright © 2012 John Wiley & Sons, Ltd.     

Sources of microseismicP waves

Summary Origin ofP waves detected earlier in microseisms of very quiet locations in the USSR is discussed in detail. It appears that the most pronounced sources ofP waves are tropical cyclones over the Pacific. The amplitude of the force in the source for a medium power typhoon is found to be of the order of 10¹⁶ dynes. The effective source area is estimated as 10⁴–10⁵ km² approximately. The shape of the amplitude spectrum ofP wave corrected for the absorption in the mantle does not contradict with the standing wave theory of microseisms generation. Results of observations at various epicentral distances give strong evidences of the predominant attenuation of the fundamental Rayleigh mode as compared with higher Rayleigh modes andP waves in the frequency band of 0.3–0.15 cps.     

A new least-squares minimization approach to depth and shape determination from magnetic data

We have developed a least‐squares minimization approach to depth determination using numerical second horizontal derivative anomalies obtained from magnetic data with filters of successive window lengths (graticule spacings). The problem of depth determination from second‐derivative magnetic anomalies has been transformed into finding a solution to a non‐linear equation of the form, f(z) = 0. Formulae have been derived for a sphere, a horizontal cylinder, a dike and a geological contact. Procedures are also formulated to estimate the magnetic angle and the amplitude coefficient. We have also developed a simple method to define simultaneously the shape (shape factor) and the depth of a buried structure from magnetic data. The method is based on computing the variance of depths determined from all second‐derivative anomaly profiles using the above method. The variance is considered a criterion for determining the correct shape and depth of the buried structure. When the correct shape factor is used, the variance of depths is less than the variances computed using incorrect shape factors. The method is applied to synthetic data with and without random errors, complicated regionals, and interference from neighbouring magnetic rocks. Finally, the method is tested on a field example from India. In all the cases examined, the depth and the shape parameters are found to be in good agreement with the actual parameters.     

A heat pulse technique for the determination of small‐scale flow directions and flow velocities in the streambed of sand‐bed streams

The hyporheic zone (HZ) has the capability to eliminate and attenuate nutrients and contaminants in riverine systems. Biogeochemical reactions and the potential elimination of contaminants are strongly controlled by the flow paths and dynamics in the HZ. Nevertheless, an easily applicable method for the field determination of flow patterns in the HZ is still lacking. Therefore, a heat pulse technique, which traces the movement of a short heat pulse in the upper part of the HZ and other sand beds, was developed. Five rods are vertically driven into the sediment of the streambed; one rod with a heater as point source located in about 10‐cm sediment depth and four rods with four temperature sensors in 3 cm distance, arranged concentrically with 7 cm diameter around the heating rod. Subsequently, a heat pulse is applied and the resulting breakthrough curves are indicative of flow velocities and flow directions in the streambed. A rough data analysis procedure is also suggested. In addition, laboratory experiments were performed to test the heat pulse technique. These experiments were validated based on coupled numerical modelling of flow and heat transport. First field tests of the method prove that the method is easily applicable under field conditions. These first field tests showed highly complex flow patterns with flow velocities from 1·8 to 4·9 cm min^?1 and flow directions from parallel to surface flow to opposite to surface flow. This suggests the need for a robust method to quantify hyporheic flow patterns in situ. Copyright © 2011 John Wiley & Sons, Ltd.     

A note on tsunami amplitudes above submarine slides and slumps

Tsunami generated by submarine slumps and slides are investigated in the near-field, using simple source models, which consider the effects of source finiteness and directivity. Five simple two-dimensional kinematic models of submarine slumps and slides are described mathematically as combinations of spreading constant or slopping uplift functions. Tsunami waveforms for these models are computed using linearized shallow water theory for constant water depth and transform method of solution (Laplace in time and Fourier in space). Results for tsunami waveforms and tsunami peak amplitudes are presented for selected model parameters, for a time window of the order of the source duration.The results show that, at the time when the source process is completed, for slides that spread rapidly (c_R/c_T≥20, where c_R is the velocity of predominant spreading), the displacement of the free water surface above the source resembles the displacement of the ocean floor. As the velocity of spreading approaches the long wavelength tsunami velocity the tsunami waveform has progressively larger amplitude, and higher frequency content, in the direction of slide spreading. These large amplitudes are caused by wave focusing. For velocities of spreading smaller than the tsunami long wavelength velocity, the tsunami amplitudes in the direction of source propagation become small, but the high frequency (short) waves continue to be present. The large amplification for c_R/c_T1 is a near-field phenomenon, and at distances greater than several times the source dimension, the large amplitude and short wavelength pulse becomes dispersed.A comparison of peak tsunami amplitudes for five models plotted versus L/h (where L is characteristic length of the slide and h is the water depth) shows that for similar slide dimensions the peak tsunami amplitude is essentially model independent.     

P波和S波接收函数的贝叶斯联合反演

S波接收函数对于研究岩石圈速度结构具有重要价值. 本文利用合成地震图技术研究了S波接收函数的动力学特征. 在接收函数非线性复谱比反演方法的基础上,发展了基于贝叶斯理论的P波和S波接收函数的非线性联合反演方法. 结果表明:(1)适用于S波接收函数反演的震中距范围约为55°~80°,S波接收函数反演要求所用远震事件的震级大于5级; (2)与陡变的岩石圈底部界面(LAB)相比,梯度带类型LAB上生成的S_LP转换波相对较弱,台站下方的沉积盖层有助于相对增强S_LP震相; (3)由于S波接收函数径向分量不符合δ脉冲,不依赖于等效震源假定的三分量接收函数多道最大或然性反褶积方法更适合S波接收函数的估计;(4)数值检验的结果表明,在初始模型速度参数偏离真实模型20%的情况下,本文的方法能够预测300 km深度范围内的P波和S波速度结构;(5)观测数据的反演结果表明,由于P波接收函数低频分量相对不足,本文的联合反演方法对于大于100 km深度上地幔的S波速度结构约束相对较弱.     

Earthquake ground motion modeling of induced seismicity in the Groningen gas field

A physics‐based numerical approach is used to characterize earthquake ground motion due to induced seismicity in the Groningen gas field and to improve empirical ground motion models for seismic hazard and risk assessment. To this end, a large‐scale (20 km × 20 km) heterogeneous 3D seismic wave propagation model for the Groningen area is constructed, based on the significant bulk of available geological, geophysical, geotechnical, and seismological data. Results of physics‐based numerical simulations are validated against the ground motion recordings of the January 8, 2018, M_L 3.4 Zeerijp earthquake. Taking advantage of suitable models of slip time functions at the seismic source and of the detailed geophysical model, the numerical simulations are found to reproduce accurately the observed features of ground motions at epicentral distances less than 10 km, in a broad frequency range, up to about 8 Hz. A sensitivity analysis is also addressed to discuss the impact of 3D underground geological features, the stochastic variability of seismic velocities and the frequency dependence of the quality factor. Amongst others, results point out some key features related to 3D seismic wave propagation, such as the magnitude and distance dependence of site amplification functions, that may be relevant to the improvement of the empirical models for earthquake ground motion prediction.     

Non-Gaussian probability distributions of solar wind fluctuations

The probability distributions of field differences x()=x(t+)-x(t), where the variable x(t) may denote any solar wind scalar field or vector field component at time t, have been calculated from time series of Helios data obtained in 1976 at heliocentric distances near 0.3 AU. It is found that for comparatively long time lag , ranging from a few hours to 1 day, the differences are normally distributed according to a Gaussian. For shorter time lags, of less than ten minutes, significant changes in shape are observed. The distributions are often spikier and narrower than the equivalent Gaussian distribution with the same standard deviation, and they are enhanced for large, reduced for intermediate and enhanced for very small values of x. This result is in accordance with fluid observations and numerical simulations. Hence statistical properties are dominated at small scale by large fluctuation amplitudes that are sparsely distributed, which is direct evidence for spatial intermittency of the fluctuations. This is in agreement with results from earlier analyses of the structure functions of x. The non-Gaussian features are differently developed for the various types of fluctuations. The relevance of these observations to the interpretation and understanding of the nature of solar wind magnetohydrodynamic (MHD) turbulence is pointed out, and contact is made with existing theoretical concepts of intermittency in fluid turbulence.     

RAPID DETERMINATION OF CUBE'S GRAVITY FIELD *

Gravity modeling involves the evaluation of gravity field due to bodies of irregular shape. This is commonly accomplished by dividing the body into smaller units of regular shape whose field can be determined analytically. Cubes are ideal building blocks for constructing bodies of irregular shape. However, the exact expression defining the gravity field of a cube-shaped body is very long and requires tedious numerical work. Approximation formulas for rapid evaluation of the cube's gravity field are presented and discussed in detail. Their use for computing the field for small distances leads to large errors in the results; on the other hand, using the exact formula for large distances where approximation formulas yield practically identical results, is waste of time. After a detailed analysis about the nature of the cube's gravity field, certain criteria are established for suitably combining the two alternatives. This results in tremendous reduction in the task of computations without affecting the accuracy of data.     

Stochastic modeling of solute transport in 3-D heterogeneous porous media with random source condition

During probabilistic analysis of flow and transport in porous media, the uncertainty due to spatial heterogeneity of governing parameters are often taken into account. The randomness in the source conditions also play a major role on the stochastic behavior in distribution of the dependent variable. The present paper is focused on studying the effect of both uncertainty in the governing system parameters as well as the input source conditions. Under such circumstances, a method is proposed which combines with stochastic finite element method (SFEM) and is illustrated for probabilistic analysis of concentration distribution in a 3-D heterogeneous porous media under the influence of random source condition. In the first step SFEM used for probabilistic solution due to spatial heterogeneity of governing parameters for a unit source pulse. Further, the results from the unit source pulse case have been used for the analysis of multiple pulse case using the numerical convolution when the source condition is a random process. The source condition is modeled as a discrete release of random amount of masses at fixed intervals of time. The mean and standard deviation of concentration is compared for the deterministic and the stochastic system scenarios as well as for different values of system parameters. The effect of uncertainty of source condition is also demonstrated in terms of mean and standard deviation of concentration at various locations in the domain.     

Comparison of alternative upscaled model formulations for simulating DNAPL source dissolution and biodecay

This paper compares the performance of analytical and numerical approaches for modeling DNAPL dissolution with biodecay. A solution derived from a 1-D advective transport formulation (“Parker” model) is shown to agree very closely with high resolution numerical solutions. A simple lumped source mass balance solution in which with decay is assumed proportional to DNAPL mass (“Falta1” model) over- or underpredicts aqueous phase biodecay depending on the magnitude of the exponential factor governing the relationship between dissolution rate and DNAPL mass. A modification of the Falta model that assumes decay proportional to the source exit concentration is capable of accurately simulating source behavior with strong aqueous phase biodecay if model parameters are appropriately selected or calibrated (“Falta2” model). However, parameters in the lumped models exhibit complex interdependencies that cannot be quantified without consideration of transport processes within the source zone. Combining the Falta2 solution with relationships derived from the Parker model was found to resolve these limitations and track the numerical model results. A method is presented to generalize the analytical solutions to enable simulation of partial mass removal with changes in source parameters over time due to various remedial actions. The algorithm is verified by comparison with numerical simulation results. An example application is presented that demonstrates the interactions of partial mass removal, enhanced biodecay, enhanced mass transfer and source zone flow reduction applied at various time periods on contaminant flux reduction. Increasing errors that arise in numerical solutions with coarse discretization and high decay rates are shown to be controlled by using an adjusted decay coefficient derived from the Parker analytical solution.     

A LAYER-STRIPPING TECHNIQUE FOR THE SUPPRESSION OF WATER-BOTTOM MULTIPLE REFLECTIONS*

A new method to suppress water-bottom multiples (water-bottom reverberations) uses the fact that in the domain of intercept time and ray parameter (τ–p domain) the water-bottom reverberations are strictly periodical for a horizontal flat sea bottom. Using this property a comb filter can be designed. The window of the filter should be approximately equal to the duration of a source pulse. The algorithm finds the maximum of the periodical energy throughout the τ–p domain and then designs the comb filter which eliminates the water bottom reverberations from each trace in the τ– p domain. This process can be repeated for higher order reverberations. Finally the τ–p domain with attenuated multiples is transformed back to the conventional x -- t space. The method is illustrated on a variety of synthetic data and on a set of real marine CMP data acquired in the North Sea near the Norwegian shore.     

Estimation of crustal structure in central and west Japan from waveform modeling of regionalPL waves

An inverse method of modeling the regionalPL waveform with the predominant period of about 20 s was developed to estimate the averageS-velocity structure of the upper crust. Applicability of the waveform modeling was confirmed by the results of the numerical experiments: thePL waveform is most sensitive to theS velocity in the upper crust, whereas it is not affected significantly by errors involved in the focal mechanism solution and focal depth determination when thePL wave is well developed. The method was applied to the observed seismograms recorded in central Japan from the earthquakes with epicentral distances 300–500 km. As a result, distinct regional differences were found in the upper crustalS velocity; in particular, between the southern Shikoku district, west Japan, and the southern Chubu district, central Japan, and between the mountainous and the coastal areas in the southern Chubu district. These differences are in agreement with the general features ofP-velocity structures obtained by explosion experiments and by analyses of natural earthquakes. Our method is effective to the extent that the crustal structure along the propagation path can be assumed a horizontally layered structure; it is not applicable when the sensitivity of thePL waveform to the error in the focal mechanism solution is exceptionally high.     

Interpretation of magnetic data using analytic signal derivatives

This paper develops an automatic method for interpretation of magnetic data using derivatives of the analytic signal. A linear equation is derived to provide source location parameters of a 2D magnetic body without a priori information about the nature of the source. Then using the source location parameters, the nature of the source can be ascertained. The method has been tested using theoretical simulations with random noise for two 2D magnetic models placed at different depths with respect to the observation height. In both cases, the method gave a good estimate for the location and shape of the sources. Good results were obtained on two field data sets.     

SOURCE ARRAY SCALING FOR WAVELET DECONVOLUTION*

A seismic source array is normally composed of elements spaced at distances less than a wavelength while the overall dimensions of the array are normally of the order of a wavelength. Consequently, unpredictable interaction effects occur between element and the shape of the far field wavelet, which is azimuth-dependent, can only be determined by measurements in the far field. Since such measurements are very often impossible to make, the shape of the wavelet—particularly its phase spectrum—is unknown. A theoretical design method for overcoming this problem is presented using two scaled arrays. The far field source wavelets from the source arrays have the same azimuth dependence at scaled frequencies, and the far field wavelets along any azimuth are related by a simple scaling law. Two independent seismograms are generated by the two scaled arrays for each pair of source-receiver locations, the source wavelets being related by the scaling law. The technique thus permits the far field waveform of an array to be determined in situations where it is impossible to measure it. Furthermore it permits the array design criteria to be changed: instead of sacrificing useful signal energy for the sake of the phase spectrum, the array may be designed to produce a wavelet with desired amplitude characteristics, without much regard for phase.     

A compact representation of spatio-temporal slip distribution on a rupturing fault

We propose a mathematical representation to qualitatively describe the spatio-temporal slip evolution during earthquake rupture in an efficient and easy-to-use manner for numerical simulations of strong ground motion. It is based on three basis functions and associated expansion coefficients. It is an extension of the approach of Ide and Takeo, (J Geophys Res, 102:27379–27391, 1997). We compare our approach and theirs using simple kinematic source models to illustrate differences between the two approaches, and show that our approach more accurately represents the spatio-temporal slip evolution. We also propose a technique based on our representation for extracting a spatio-temporal slip velocity function from a kinematic source model obtained by the conventional source inversion. We then demonstrate the feasibility of our procedure with application to an inverted source model of the 26 March 1997 Northwestern Kagoshima, Japan, earthquake (M _W6.1). In the simulations for actual earthquakes, source models obtained from kinematic source inversions are commonly employed. Our scheme could be used as an interpolation method of slip time functions from relatively coarse finite-source models obtained by conventional kinematic source inversions.