共查询到20条相似文献，搜索用时 15 毫秒
1.
Y. Y. Kagan 《Geophysical Journal International》1987,91(3):891-912
We construct a catalogue of all the possible elementary point sources of seismic waves. There are three general classes of sources, two spheroidal and one toroidal. We consider excitation functions for these point-like sources as well as for sources of finite size in far-, intermediate- and near-field for an infinite homogeneous isotropic medium. The sources corresponding to seismic-moment tensors for the second-, third- and fourth-ranks are considered in more detail; we identify 10 different seismic sources in this range: one monopole, two or three dipoles, three quadrupoles, etc. For the step-function of the scalar seismic-moment release, the amplitude spectrum for the third-rank sources is proportional to the angular frequency ω in the region below the corner frequency ω cr . The fourth-rank sources have an ω 2 spectrum in the same range. The possibility of separate and simultaneous inversion of seismic body-wave data and static deformation data for sources of different order is discussed. Some equivalent-force moment higher-rank sources are 'shielded' by lower-rank sources of the same order; the former sources cannot be inverted from seismic data without additional assumptions. Because of their simple radiation pattern, the lower order multipoles, i.e. the monopole and dipoles, are the first sources other than the double-couple which should be considered for inversion. 相似文献
2.
D. J. Doornbos 《Geophysical Journal International》1982,69(1):235-251
Summary. Parameters pertaining to the kinematics of a finite source are usually estimated by fitting specific fault models to the data. On the other hand, these parameters, including source location, are also contained in the moment tensors of higher degree. In this paper, the seismic response is represented in terms of 20 source parameters which are related to components of the moment tensors; they are also related to the parameters of fault models, as will be demonstrated for a number of 'classical' models. A linearized inversion for the moment tensor shows that with real data, or with realistic synthetic data, the results are not necessarily physically meaningful, unless constraints are imposed. The constraints are precisely those appearing as a priori assumptions in the conventional methods of source analysis; it is thus possible to investigate the impact of these assumptions. We will discuss in particular the assumption of a general deviatoric point source (not necessarily a double couple) versus that of a plane fault in finite sources. Although at this stage experience with practical performance of the new method is limited, it is suggested that in the appropriate circumstances constrained inversion for the seismic moment tensors offers a viable alternative to estimate kinematic source parameters. 相似文献
3.
Stable inversions for complete moment tensors 总被引：5，自引：0，他引：5
The seismic moment tensors for certain types of sources, such as volcanic earthquakes and nuclear explosions are expected to contain an isotropic component. Some earlier efforts to calculate the isotropic component of these sources are flawed due to an error in the method of Jost & Herrmann. We corrected the method after Herrmann & Hutchensen and found great improvement in the recovery of non-double-couple moment tensors that include an isotropic component. Tests with synthetic data demonstrate the stability of the corrected linear inversion method, and we recalculate the moment tensor solutions reported in Dreger et al. for Long Valley caldera events and Dreger & Woods for Nevada Test Site nuclear explosions. We confirm the findings of Dreger et al. that the Long Valley volcanic sources contain large statistically significant isotropic components. The nuclear explosions have strikingly anomalous source mechanisms, which contain very large isotropic components, making it evident that these events are not tectonic in origin. This indicates that moment tensor inversions could be an important tool for nuclear monitoring. 相似文献
4.
5.
Summary. We investigate the effects of various sources of error on the estimation of the seismic moment tensor using a linear least squares inversion on surface wave complex spectra. A series of numerical experiments involving synthetic data subjected to controlled error contamination are used to demonstrate the effects. Random errors are seen to enter additively or multiplicitively into the complex spectra. We show that random additive errors due to background recording noise do not pose difficulties for recovering reliable estimates of the moment tensor. On the other hand, multiplicative errors from a variety of sources, such as focusing, multipathing, or epicentre mislocation, may lead to significant overestimation or underestimation of the tensor elements and in general cause the estimates to be less reliable. 相似文献
6.
7.
Cluster analysis of seismic moment tensor orientations 总被引：1，自引：0，他引：1
Raymond J. Willemann 《Geophysical Journal International》1993,115(3):617-634
This paper demonstrates that well-known methods of cluster analysis and multivariate data analysis are useful for geodynamic interpretation of seismic moment tensors. To use these methods, moment tensors are expressed as vectors in a 6-D space. These are vectors in a rigorous sense, rather than an arbitrary set of ordered numbers, because a dot product can be defined that is independent of the coordinate system. In this vector space, non-isotropic moment tensors are a 5-D linear subspace and normalized moment tensors are unit vectors, or points on a unit sphere. Distance along a great circle of the unit sphere satisfies reasonable requirements for any measure of the difference between normalized moment tensors. In regions with a few isolated sets of orientations, cluster analysis based on the great circle distance identifies the same groups of earthquakes that a seismologist would. Figures based on principal component analysis and discriminant analysis illustrate orientation clustering better than equal area projections of moment tensor principal axes. In one case where clusters have been claimed to exist, orientations appear to be continuously distributed and no evidence is found for separate populations of moment tensors. 相似文献
8.
The two-point correlation function of the seismic moment tensor 总被引：2，自引：0，他引：2
Summary. We use the invariants of the two-point correlation function of the seismic moment to investigate the degree of irregularity of an earthquake fault, i.e. to study the rapidity with which a complex fault changes its direction of orientation. The two-point correlation function is a fourth-order tensor which has three scalar invariants in the isotropic case. Although the accuracy of present-day catalogues of fault plane solutions is rather low for our purpose, nevertheless the invariants of these correlation tensors confirm the generally 相似文献
9.
J. &#;ílený 《Geophysical Journal International》1997,131(3):767-769
When discussing error estimates of the point-source mechanism and the source time function obtained by the two-step procedure by Šílený, Panza & Campus (1992), the authors insist that in the first step—inversion of seismograms (after Sipkin 1982) to get the moment tensor rate functions (MTRFs)—a homogeneous variance for all the data is needed to keep the advantageous symmetry of the normal equations. We show that this is too strong a requirement and can be dropped. 相似文献
10.
The first-order statistical moment of the seismic moment tensor 总被引：2，自引：0，他引：2
Summary. If a complex earthquake is assumed to be a set of individual, randomly oriented elementary pure double couple sources, the solution for the seismic moment of the complex event projected on the mean trend of the fault will perforce be comprised of sources of both double couple and compensated linear vector dipole (CLVD) types. We investigate the statistical properties of these two components of seismic sources in terms of the invariants of the seismic moment tensor of a realistic set of synthetic earthquakes. It is very likely that the size of the CLVD component is two to three orders of magnitude smaller than that of the double couple component. 相似文献
11.
We investigate the effect of laterally varying earth structure on centroid moment tensor inversions using fundamental mode mantle waves. Theoretical seismograms are calculated using a full formulation of surface wave ray theory. Calculations are made using a variety of global tomographic earth models. Results are compared with those obtained using the so-called great-circle approximation, which assumes that phase corrections are given in terms of mean phase slowness along the great circle, and which neglects amplitude effects of heterogeneity. Synthetic tests suggest that even source parameters which fit the data very well may have large errors due to incomplete knowledge of lateral heterogeneity. The method is applied to 31 shallow, large earthquakes. For a given earthquake, the focal mechanisms calculated using different earth models and different forward modelling techniques can significantly vary. We provide a range of selected solutions based on the fit to the data, rather than one single solution. Difficulties in constraining the dip-slip components of the seismic moment tensor often produce overestimates of seismic moment, leading to near vertical dip-slip mechanisms. This happens more commonly for earth models not fitting the data well, confirming that more accurate modelling of lateral heterogeneity can help to constrain the dip-slip components of the seismic moment tensor. 相似文献
12.
Peiliang Xu 《Geophysical Journal International》1999,138(1):1-24
The random principal eigenvalues and random eigenvector parameters have been routinely estimated from second-rank symmetric (SRS) random tensors and geophysically interpreted in the Earth Sciences. Statistical inference of random eigen-values and random eigenvector parameters has almost always been made as if they were normally distributed. The practical validity and applicability of the assumption of normal distributions for random eigenvalues and random eigenvector parameters has not yet been checked, however. Statistical inference of random eigenvalues and random eigenvector parameters should be based on their joint probability density function (pdf) derived from that of the original random tensor. We shall extend the work of Xu & Grafarend (1996a , b ) to the case of constrained SRS random tensors in this paper. All the relevant Jacobians for n -D unconstrained and 3-D constrained SRS tensors have been obtained. We then propose three pdf models for original SRS random tensors, which cover the commonly used Gaussian and Laplace pdfs and include pdf models for positive definite random material tensors. The pdfs of the random eigenvalues and random eigenvector parameters have been worked out. It is shown that the pdfs of the random eigenvalues and random eigenvector parameters are significantly different from the commonly used Gaussian pdf model. Deviatoric stress tensors and double-couple seismic moment tensors have been simulated to show the applications of the developed theory. The simulations have additionally indicated that Fisher's pdf model for directional data is not representative of the random rotations of constrained SRS random tensors. 相似文献
13.
We have collected and re-examined macroseismic information for large Central American earthquakes since the beginning of the period of instrumental recording about one hundred years ago, and combined this with a reassessment of early instrumental information to produce a catalogue of 51 events that, we believe includes ail those with magnitudes ( Ms ) greater than 7.0. We have reassessed surface-wave magnitudes by consulting station bulletins and we have derived a correction that gives an equivalent Ms for events of intermediate depth. We have also developed a regional relationship between Ms and seismic moment, which enables us to estimate the seismic slip rate across the Middle American Trench. Our best estimates give an average slip rate several times smaller than suggested convergence rates, but with the seismic slip in the central segment of the trench almost an order of magnitude smaller than that in the segments on either side. The low seismic slip rate may indicate aseismic crustal deformation 相似文献
14.
We evaluate the seismic moment–frequency relation for the Harvard catalogue in the period 1977–1994. This catalogue is composed of about 12 000 earthquakes. After selection of events in terms of depth and energy, we retain about 8000 data points. We estimate two parameters of the seismic moment distribution: the power exponent β and the cut-off value M m . The method used is a least-squares linear fit on a log–log scale performed over a range selected on the basis of the standard deviation from the histogram. The analysis is carried out for different subdivisions of the Earth in square grids of different sizes. Neither parameter exhibits a dependence on cell size, suggesting the universality of their values and the interpretation of the existence of a cut-off as a finite size effect linked to a finite catalogue length. The variations of the parameters are investigated as a function of time (duration of the catalogue) and versus the number of events used for building up the distribution. Again, β and M m do not depend on time, but M m depends on the number of events, reaching a stable value for N ≈ 1000. The only significant change in the parameters is observed for different values of M 0upper in the catalogue, revealing the existence of universality classes. 相似文献
15.
Finite difference (FD) simulation of elastic wave propagation is an important tool in geophysical research. As large-scale 3-D simulations are only feasible on supercomputers or clusters, and even then the simulations are limited to long periods compared to the model size, 2-D FD simulations are widespread. Whereas in generally 3-D heterogeneous structures it is not possible to infer the correct amplitude and waveform from 2-D simulations, in 2.5-D heterogeneous structures some inferences are possible. In particular, Vidale & Helmberger developed an approach that simulates 3-D waveforms using 2-D FD experiments only. However, their method requires a special FD source implementation technique that is based on a source definition which is not any longer used in nowadays FD codes. In this paper, we derive a conversion between 2-D and 3-D Green tensors that allows us to simulate 3-D displacement seismograms using 2-D FD simulations and the actual ray path determined in the geometrical optic limit. We give the conversion for a source of a certain seismic moment that is implemented by incrementing the components of the stress tensor.
Therefore, we present a hybrid modelling procedure involving 2-D FD and kinematic ray-tracing techniques. The applicability is demonstrated by numerical experiments of elastic wave propagation for models of different complexity. 相似文献
Therefore, we present a hybrid modelling procedure involving 2-D FD and kinematic ray-tracing techniques. The applicability is demonstrated by numerical experiments of elastic wave propagation for models of different complexity. 相似文献
16.
Our objectives are as follows. First, we wish to develop a methodology to recover the long-term component of deformation from any set of distributed, time-averaged geodetic strain measurements that were subject to seismic disturbance, given a catalogue of local seismicity that occurred during the measurement period. Second, using seismic and geodetic data sets that span approximately 100 years, we apply this technique in the western Aegean to assess the role of local seismicity in regional deformation. The methodology is developed using a model for crustal deformation constructed from a long-term, smooth regional strain field combined with instantaneous, local perturbations from upper-crustal earthquakes approximated by static elastic dislocations. By inverting geodetic displacements for the smooth field while simultaneously floating influential but uncertain earthquake source parameters, an estimate of the regional component of deformation that is approximately independent of the seismicity can be made. In the western Aegean we find that the horizontal component of regional deformation can be described with minor inaccuracy by a quadratic relative displacement field. The principal horizontal extensional axes calculated from the regionally smooth displacement field agree in orientation with the T-axes of earthquakes in the region. These observations indicate that the instantaneous elastic strain of the 10 km thick seismogenic layer is driven by a stress field that is smooth on the scale of the geodetic network as a whole, 200-300 km. 相似文献
17.
George E. Backus 《Geophysical Journal International》1977,51(1):27-45
Let ζΛ and r Λ . be the hypocentral position and time of an extended indigenous seismic source. Backus showed that the force moment tensors of the source, Γ( m +1, n ) (ζΛ , r Λ ), determine and are determined by the motion which the source produces. For small m + n , only the long-period motion is relevant. The glut moment tensor Λ( m,n ) (ζΛ , r Λ .) can be calculated uniquely from γ( m +1, n ) (ζΛ r Λ ) only if m = 0 or m = 1. The tensor G =Λ(2,0) (ζΛ ) gives the spatial variance tensor WΛ of the source, and WΛ . roughly describes the size, shape and orientation of the source region. Therefore the failure of the observed F =Γ(3,0) (ζΛ ) to determine G uniquely is of seismological interest. In the present paper we show that F determines G uniquely if we assume the source to be a simple straight line source (SSLS) or an ideal fault in an isotropic medium with isotropic prestress (IFIMIP). We give tests on F which determine whether it can come from a SSLS, from an IFIMIP or from a simple plane surface source (SPSS). If we assume the source to be a SPSS then knowing F and the fault plane determines G to within an unknown scalar multiple of a certain tensor tangent to the fault plane. Moreover F determines the fault plane uniquely unless F can come from a SSLS. If it can, then F determines this virtual source line uniquely, and F permits the fault plane to be any plane containing the virtual source line. 相似文献
18.
Long-offset transient electromagnetic (LOTEM) data have traditionally been represented as early- and late-time apparent resistivities. Time-varying electric field data recorded in a LOTEM survey made with multiple sources can be represented by an 'instantaneous apparent resistivity tensor'. Three independent, coordinate-invariant, time-varying apparent resistivities can be derived from this tensor. For dipolar sources, the invariants are also independent of source orientation. In a uniform-resistivity half-space, the invariant given by the square root of the tensor determinant remains almost constant with time, deviating from the half-space resistivity by a maximum of 6 per cent. For a layered half-space, a distance–time pseudo-section of the determinant apparent resistivity produces an image of the layering beneath the measurement profile. As time increases, the instantaneous apparent resistivity tensor approaches the direct current apparent resistivity tensor. An approximate time-to-depth conversion can be achieved by integrating the diffusion depth formula with time, using the determinant apparent resistivity at each instant to represent the resistivity of the conductive medium. Localized near-surface inhomogeneities produce shifts in the time-domain apparent resistivity sounding curves that preserve the gradient, analogous to static shifts seen in magnetotelluric soundings. Instantaneous apparent resistivity tensors calculated for 3-D resistivity models suggest that profiles of LOTEM measurements across a simple 3-D structure can be used to create an image that reproduces the main features of the subsurface resistivity. Where measurements are distributed over an area, maps of the tensor invariants can be made into a sequence of images, which provides a way of 'time slicing' down through the target structure. 相似文献
19.
Summary. There is evidence that the equivalent seismic sources of the Amchitka Island explosions — Longshot, Milrow and Cannikin — depart significantly from the simple model of a point compressional-source in a layered elastic-medium. Consequently modelling the observed seismograms using standard source-models may not be the most efficient method of determining source properties. Here an alternative to modelling is used to obtain information on the seismic sources due to the explosions. Broad-band (BB) estimates of the P signals are obtained from the short-period (SP) seismograms, corrected for attenuation, and interpreted in terms of P, pP and radiation from secondary sources. the main conclusions are:
(i) BB estimates of the radiated displacement from the explosions can be obtained with only a small reduction in the signal-to-noise ratio seen on SP seismograms;
(ii) observations of differences in pulse amplitudes and spectra are not necessarily due to differences in anelastic attenuation;
(iii) P and pP at a given station may differ in shape so that notches in the signal spectrum may not be related to source depth;
(iv) there is evidence of arrivals that others have identified as due to slap-down but which could be interpreted as an overshoot to pP;
(v) direct interpretation of the estimated ground displacement is a better procedure for determining the seismic source properties of explosions than modelling SP seismograms using idealised models as a starting point. 相似文献
(i) BB estimates of the radiated displacement from the explosions can be obtained with only a small reduction in the signal-to-noise ratio seen on SP seismograms;
(ii) observations of differences in pulse amplitudes and spectra are not necessarily due to differences in anelastic attenuation;
(iii) P and pP at a given station may differ in shape so that notches in the signal spectrum may not be related to source depth;
(iv) there is evidence of arrivals that others have identified as due to slap-down but which could be interpreted as an overshoot to pP;
(v) direct interpretation of the estimated ground displacement is a better procedure for determining the seismic source properties of explosions than modelling SP seismograms using idealised models as a starting point. 相似文献
20.
Bruce R. Julian 《Geophysical Journal International》1986,84(2):431-443
Summary. Linear-programming methods are powerful and efficient tools for objectively analysing seismic focal mechanisms and are applicable to a wide range of problems, including tsunami warning and nuclear explosion identification. The source mechanism is represented as a point in the six-dimensional space of moment-tensor components. Each observed polarity provides an inequality constraint, linear with respect to the moment tensor components, that restricts the solution to a half-space bounded by a hyperplane passing through the origin. The intersection of these half-spaces is the convex set of all acceptable solutions. Using linear programming, a solution consistent with the polarity constraints can be obtained that maximizes or minimizes any desired linear function of the moment tensor components; the dilatation, the thrust-like nature, and the strike-slip-like nature of an event are examples of such functions. The present method can easily be extended to fit observed seismic-wave amplitudes (either signed or absolute) subject to polarity constraints, and to assess the range of mechanisms consistent with a set of measured amplitudes. 相似文献