Theoretical Seismograms Research Articles

Nature of P-wave signals from Hindukush earthquakes

Several causes for complexity of P-wave signals from earthquakes in the Hindukush focal region and recorded at Gauribidanur seismic array in southern India, have been investigated. Visual inspection of the records of these earthquakes revealed that most of the events occurring at shallow depths had complex signatures as compared to the deeper events. A positive correlation of complexity with magnitude is found. Spectral ratio measurements have demonstrated that complex signals are richer in low frequency energy. A number of theoretical seismograms for short period P-waves were computed and the analysis reveals that within certain constraints, complexity increases with focal fault area and decreases with focal depth. The structure of the fault rock in the source region, the source functions itself, and the ray-scattering in the crust-upper mantle near the source are the main responsibilities for the complexity of the Hindukush earthquake records at GBA since the transmission of the ray-tubes for all events studied is practically identical, with the exception of the very first near source part.

表面波が卓越する周期約2〜20秒のやや長周期地震動の距離減衰特性に関する基礎的研究 : 距離減衰式の整理と理論地震動を用いた検討

We study attenuation characteristics of peak ground motions and relative velocity response spectra of ground motions with predominant surface waves in a period range of about 2 to 20 sec. First, we point out that it is important to know how dispersion of surface waves is in order to understand attenuation relations of surface waves. Then, we calculate attenuation relations of theoretical seismograms due to a shallow point source buried in the velocity structure used in the study by Mamula, et al. (1984) on site amplification factors of many Meteorological observatories in a period range of 3 to 15 sec. As a result, we point out that the idea that attenuation of surface waves is much smaller than that of body waves, which is wide-spreaded in studies on attenuation relations of earthquake ground motions in Japan, is not always appropriate.

The integral operator representation of propagation invariants for elastic waves in irregularly layered media

The reflection and transmission of elastic waves in irregularly layered media can be represented in terms of a set of propagation invariants for elastic wavefields. There are a number of such invariants depending on different integral operators acting on the displacement and traction fields. By exploiting different classes of invariants, representations for reflection and transmission operators at an irregular interface can be derived which are easier to compute than previous forms. In a similar way, a simplified representation for the surface amplification factor for incident waves on a free surface can be constructed. This is particularly useful for calculating theoretical seismograms on the surface of a body.

Lg-Wave Modelling For the North Sea

SUMMARY Theoretical seismograms for inhomogencous 2-D media are computed via summation of surface wave modes and use of transmission coefficient matrices, in an attempt to explain the observed Lg-wave barrier within thc continental structure of the North Sea. Where other scientists have been able to trcat Lg-wave propagation in the North Sea for one frequency, many surface wave modes and a complicated structural model of the North Sea grabens, our method takes into account many frequencies, and is consequentiy limited to a few significant modes. and a relatively simple structural model.

The rupture process of the 1980 Irpinia, Italy, earthquake from the inversion of strong motion waveforms

The distribution of slip and the behaviour of rupture propagation during the 23rd November, 1980, Irpinia earthquake ( M S = 6.9) was investigated by analysing strong motion accelerograms. The rupture was assumed to develop on a two-dimensional, purely normal fault whose geometry was constrained by geologic and geodetic data and by the aftershock space distribution. Theoretical seismograms have been computed using the isochron approach with a spatially variable slip intensity. The asymptotic ray theory is used to evaluate the far-field Green functions. The rupture model was updated following a trial-and-error approach. The fit of observed waveforms with synthetic seismograms allowed several peculiarities in the rupture history to be pointed out. The source model resulting from the solution of the forward waveform modelling was then used as starting model for the inversion of ground velocities. Therefore, we performed a linearized inversion for slip velocity and rupture times on the fault by iteratively perturbing the assumed starting model. The inverse problem is solved by means of a tomographic back-projection technique. The inferred source model shows a bilateral rupture which does not propagate uniformly away from the hypocentre. The rupture velocity and the slip distribution on the fault plane are rather variable. The solution confirms the shallow dislocation gap in the central part of the fault suggested by the behaviour of the surface rupture. The results indicate that the rupture propagated northwestward along a further fault fragment for which no surface evidence is observed. The aftershocks occurred mostly inside of or near to the edges of the source areas of maximum co-seismic slip.

Numerical study of quarry generated Rg as a discriminant for earthquakes and explosions: Modeling of Rg in southwestern New England

In this study, we modeled 0.5–2.0 s period Rayleigh waves (Rg) generated by quarry and construction blasting for the shallow crustal velocity and intrinsic Q structure in southwestern Connecticut and southeastern New York. In spite of the Rg waves traversing through different geological formations, the Rg dispersion observed along individual paths, namely, the Clinton Point‐BCT, the Clinton Point‐BPT, the North Brandford‐BCT, the New Britain Plainville‐BCT and the Reeds Gap‐BCT paths, are remarkably similar. The dispersion is similar to the Rg dispersion observed in other parts of southern New England. For a representative shallow crustal velocity structure of the region, we therefore inverted the average dispersion curve observed along the Clinton Point‐BPT path. The inverted crustal model, with shear velocity varying between 2.85 and 3.65 km/s down to a depth of 3 km, is similar to the crustal models published earlier for the other parts of southern New England. High‐frequency Rg waves are found to be highly sensitive to anelasticity within the near‐surface crustal layers. The observed Rg waves require Qβ (shear wave quality factor) as low as 15 to produce the best agreement between data and synthetic. A thin till layer affects the Rg waves significantly provided the layer thickness is of the order of Rg wavelength. Theoretical study shows that the delay times between charges caused by the temporal finiteness of arrays of explosions during a quarry blast are found to have produced a significant effect on the high‐frequency Rg waves. We also investigated theoretical seismograms to discriminate between earthquake and quarry explosions. We found that Rg waves are a successful discriminant only for earthquakes at depths greater than 3 km. The shallow earthquakes show strong Rg waves for dip‐slip faults but are preceded by high‐frequency shear arrival, especially in the range of 50–125 km. Beyond 126 km, pSmS and its multibounces become critical with distance and contribute strongly. These waves appear on the explosion seismograms as shear waves. So, this shear wave may provide a diagnostic in the range between 50 and 125 km for discriminating earthquake seismograms from the small quarry explosions.

Modelling of volcanic tremor wave fields

The comparison of the temporal variations of the volcanic tremor for various eruptions shows stable connection between tremor intensity and volcanic activity. We have determined the wave pattern of seismic signals produced by individual explosions in the crater during eruption of the Tolbachik volcano (Kamchatka). Considering an explosion in the crater as the source for formation of the seismic wave field, we determined the relation between the spectrum of the source and volcanic tremor spectra. Theoretical seismograms for the unit source of explosion type in various medium models correlate well with the real volcanic tremor seismograms and explain the formation of the volcanic tremor wave fields in real conditions. Volcanic tremor (frequency range of 0.6–5 Hz) forms as a result of disturbances near the surface in the active crater (explosions, pressure variations at sustained flow, etc.) and consist mostly of surface waves. A comparative estimation of transfer functions for the system “explosion in the crater-volcanic tremor” and for theoretical models with the isolated source of explosion type has been done.

The influence of a crack in a medium on the interference waves

The interference Kr-waves in an elastic half-space with a crack are considered. The processes of dispersion and attenuation of such waves are described and theoretical seismograms are constructed. A number of frequency and velocity characteristics are discussed, which can help to identify the waves in mining investigations.

Nonlinear one‐dimensional seismic waveform inversion using simulated annealing

The seismic inverse problem involves finding a model m that either minimizes the error energy between the data and theoretical seismograms or maximizes the cross‐correlation between the synthetics and the observations. We are, however, faced with two problems: (1) the model space is very large, typically of the order of [Formula: see text]; and, (2) the error energy function is multimodal. Existing calculus‐based methods are local in scope and easily get trapped in local minima of the energy function. Other methods such as “simulated annealing” and “genetic algorithms” can be applied to such global optimization problems and they do not depend on the starting model. Both of these methods bear analogy to natural systems and are robust in nature. For example, simulated annealing is the analog to a physical process in which a solid in a “heat bath” is heated by increasing the temperature, followed by slow cooling until it reaches the global minimum energy state where it forms a crystal. To use simulated annealing efficiently for 1-D seismic waveform inversion, we require a modeling method that rapidly performs the forward modeling calculation and a cooling schedule that will enable us to find the global minimum of the energy function rapidly. With the advent of vector computers, the reflectivity method has proved successful and the time of the calculation can be reduced substantially if only plane‐wave seismograms are required. Thus, the principal problem with simulated annealing is to find the critical temperature, i.e., the temperature at which crystallization occurs. By initiating the simulated annealing process with different starting temperatures for a fixed number of iterations with a very slow cooling, we noticed that by starting very near but just above the critical temperature, we reach very close to the global minimum energy state very rapidly. We have applied this technique successfully to band‐limited synthetic data in the presence of random noise. In most cases we find that we are able to obtain very good solutions using only a few plane wave seismograms.

Inversion of seismograms to determine simultaneously the moment tensor components and source time function for a point source buried in a horizontally layered medium

A method of determining simultaneously the moment tensor and source time function in the point source approximation is presented. For trial values of the moment tensor components and of the source time function, parametrized by the sum of overlapping triangles delayed in time, theoretical seismograms can be synthetized and compared with the recorded ones. The iterative procedure determines the adjustment of source parameters until a good correlation of both synthetic and observed records is reached. The Green functions in a horizontally stratified medium are constructed with the use of a modal summation method. The limits of applicability of the algorithm are illustrated by the inversion of four synthetic seismograms constructed for two horizontally stratified models of the structure in Friuli area, Italy. The records constructed for the same structural model as for which the Green functions were computed can be inverted even in the high-frequency range. In the opposite case, when the records and Green functions used corresponded to different structural models, a good correlation of the input records with the final synthetics was obtained for low - pass filtered data only. Additional tests performed with input seismograms contaminated with random noise yielded good resolution of the moment tensor and the duration of the source time function even for a high noise to signal ratio.

The reflectivity method with polar sampling

AbstractA modification to the reflectivity method that results in more accurate and efficiently computed theoretical seismograms is introduced. The reflectivity method involves an explosive point source and a radially symmetric earth, and in the temporal frequency domain the displacement field and the complex plane wave reflectivity are, to within a phase factor, Hankel transform pairs in the polar coordinate variables radial offset and wavenumber. This motivates formulation of the time-transformed displacement field into a Fourier-Bessel series over the reflectivity function, and replacement of the traditional method for sampling the plane-wave reflectivity with the proper polar sampling scheme, based on the finite Fourier transform representation for a band-limited signal. Several numerical examples are discussed.

Inversion of source parameters for subcrustal earthquakes in the Hellenic Arc

SUMMARY A one-station method was developed to invert simultaneously for seismic moment, focal depth, and the orientations of the nodal planes. This method was tested on seismograms recorded at the broadband Grefenberg array (GRF) for earthquakes in the central to eastern Hellenic arc and southern Turkey. The complete P and S body-wave responses, including all near source surface reflections, were synthesized using the reflectivity method. The minimum misfit between the observed and theoretical seismograms in the WWSSN-LP band was determined by cross-correlation, searching the whole parameter space of strike, dip and rake of a pair of orthogonal nodal planes, and adjusting the source depth and seismic moment. The initial searching step of 20° was reduced to 5° in the vicinity of the minimum misfit position, for a final search. The best fitting solution was then compared to the Harvard (HRVD) moment tensor solution best double couple which was derived using long-period data and to the P-wave first motion polarities reported by the ISC. Most solutions based on GRF data agree well with those found by HRVD, but in some cases some features of the observed GRF signals cannot be matched by the HRVD solution or solutions similar to it. The nine earthquakes we analysed in detail had magnitudes between 5.2 and 5.8. Our depth determinations ranged from 35 to 155 km. The deepest events (80–155 km) were located near Rhodes and to the east of it. One earthquake located in southern Turkey was confirmed to have a focus at about 125 km depth. The focal mechanisms of the intermediate depth earthquakes in the eastern Hellenic arc show P-axes approximately parallel to the strike of the deep slab.

Computation of complete waveforms in general anisotropic media-results from an explosion source in an anisotropic medium

SUMMARY An algorithm of generating complete waveforms in general anisotropic media (21 constants) is presented. Complete waveforms have been computed including a point-source in the anisotropic medium and the reflection and transmission properties of individual interfaces. A recursive scheme of scatterer operators and the numerical wavenumber integration technique are used. The 6 X 6 system matrix A of each layer is derived. Each element of A is expressed in such a manner that the wavenumber could be used as an inner loop (vectorizing loop). A numerical algorithm is used to compute simultaneously the eigenvalues and eigenvectors of A. The upgoing and downgoing eigenvalues are separated according to a radiation condition and the properties of the z-component Poynting vector. Filon integration is applied to evaluate the integrals over horizontal wavenumbers. Since wave propagation in an anisotropic medium is a 3-D problem, it requires an enormous number of computations. To reduce the computation time, the wavenumber is used as the deepest loop. An efficient computer code has been developed for vectorization in the super computer. Both source and receivers can be placed at arbitrary depths. Three-component synthetic seismograms are computed from an explosion in the anisotropic medium. Examples are calculated for half-space multilayered anisotropic media. Theoretical seismograms show that radiation patterns are strongly affected by the anisotropy. For example, an explosion in an anisotropic medium with horizontal axes of symmetry generates P-, SV-, and Rayleigh waves, all whose amplitudes are varying with azimuth, and significant transverse (SH) waves at certain azimuths. These effects could be explained by the non-spherical behaviour of the source due to the directional dependence of elastic moduli. The waveforms are further complicated by the reflection and conversion phenomena of waves propagating in anisotropic media.

Application of the method of summation of Gaussian beams to the calculation of theoretical seismograms

A new method of calculation of theoretical seismograms is proposed, which is based on space-time Gaussian beams. The method permits one to overcome the difficulties of calculation of the wave field near caustics and does not contain any calculations of Fourier transforms. Numerical experiments confirm the efficiency of the method for the calculation of theoretical seismograms.

The interaction of the S-wavefield with upper mantle heterogeneity

SUMMARY Many methods for the analysis of long-period and broad-band S-waveforms depend on a representation of the seismic wavefield in terms of a sum of modes of a reference structure. In addition it is frequently assumed that the propagation of the modal contributions from source to receiver may be regarded as independent. This assumption may not be warranted if there is significant heterogeneity in seismic properties along the propagation path. The interaction between modal components in different styles of heterogeneity model for the upper mantle is examined using a coupled mode propagation technique (Kennett 1984) which allows direct construction of reflection and transmission matrices with full allowance for intermode interactions for 2-D heterogeneity structures. The first type of structure considered has been proposed to explain amplitude and traveltime anomalies in body wave studies of upper mantle phases. This heterogeneity has an amplitude of about 1 per cent and is distributed with a horizontal scale of around 300-400km and a vertical scale which increases from 70km in the uppermost mantle to 200 km at 900 km depth. Horizontally travelling S-waves are hardly affected by this class of heterogeneity for frequencies less than 0.07 Hz. The second heterogeneity model was based on the WEPL3 model proposed by Nolet (1990) from waveform inversion for the structure under the NARS array in western Europe. The heterogeneity reaches 5 per cent deviation from the reference model PREMC in organized regions 700 km or more in length. For this structure surface wave modes with group velocity below 4.2kms-’ can be regarded as propagating independently up to 0.020Hz. The body wave group of modes with higher group velocity succumbs to significant interaction above 0.040 Hz. The frequency limit for largely independent propagation for the body wave group of modes can be extended to about 0.05 Hz for a velocity model with up to 1 per cent additional variability superimposed on WEPL3. Such a composite heterogeneity model would be consistent with both body wave and surface wave behaviour. The errors introduced into the analysis methods by ignoring mode interactions above these frequency limits will depend on the distribution of energy across the modes imposed by the source, and the criterion used for waveform matching between observed and theoretical seismograms. Theoretical seismograms for the heterogeneity structures based on WEPL3 including full allowance for intermode coupling show a distinct phase shift for the fundamental mode when compared with the corresponding calculations for the reference model PREMC: as is indeed observed at the NARS stations. The parts of the seismograms which show the largest influence from the presence of lateral heterogeneity are those which depend on interference phenomena, such as Su. The disruption of the phase patterns can have a profound influence on the appearance of the waveforms. The presence of small-scale heterogeneity has very little influence on the seismograms below 0.035 Hz but becomes more important as the frequency increases, especially for the body wave phases.

Optimum strong‐motion array geometry for source inversion—II

AbstractOptimum strong‐motion array geometry for source inversions is again determined for each of three types of earthquake faults: strike‐slip, dip‐slip and offshore subduction thrust. The method is the same as employed in a previous study;1 however, use of a complete Green's function in an elastic half‐space provides better results for engineering practice. It is found that the complete Green's function is capable of stabilizing the accuracy of an inversion solution obtained using theoretical seismograms, regardless of the differences in array configuration. The optimum strong‐motion array for a strike‐slip fault is characterized by stations well distributed in azimuth, while the optimum array for a dip‐slip event has stations arranged in a grid‐shaped form. The array geometries obtained here are grossly similar to those in the previous study,1 which were derived using only the far‐field S waves, and are more consistent with those proposed at the 1978 International Workshop on Strong‐Motion Earthquake Instrument Arrays.2.

Preliminary analysis of resolving power of existing strong-motion arrays for source inversion.

The effectiveness of existing strong-motion arrays for source inversion analysis is investigated by estimating the accuracy of the inversion solution using simplified theoretical seismograms. The resolving power is examined for different subfault sizes and for different array configurations for four existing array networks. They are for the 1979 Imperial Valley and the anticipated Parkfield, California earthquakes, and the 1968 Tokachi-Oki and the anticipated Tokai, Japan earthquakes. We use the method previously developed by Miyatake, Iida, and Shimazaki in 1986 based on the Wolberg's prediction analysis. The main results are: (1) The array used for an analysis of the 1979 Imperial Valley earthquake is not suitable for source inversion; especially the El Centro array, a linear array crossing perpendicularly the fault trace, is ineffective. (2) The array installed for the anticipated Parkfield earthquake by the end of 1985 seems to be satisfactory because of the intensive installation of many stations. However, the resolving power of the whole array will further increase by adding a few stations in the northwestern part of the fault or in distant areas for a better azimuthal coverage in the northwest of the fault. (3) Detailed source inversion analysis cannot be expected for the 1968 Tokachi-Oki, Japan, earthquake because of both the large fault area and lack of offshore stations. Strong-motion, ocean bottom instruments within the fault area are required for a further improvement of the inversion analysis for this type of earthquake. (4) An addition of several land stations on the west and north sides of the fault area is desirable to the present network for the anticipated Tokai, Japan earthquake. The resolving power of the whole array for this earthquake is strongly dependent on a rupturing direction because station coverage of the southern oceanic part of the fault tends to be poor.

Stick-slip unstable shear failure as a source of high frequency elastic radiation

The results of laboratory measurements on square perspex models with a stress concentrator under uniaxial compression are presented. An attempt was made to interpret these results in order to determine the mutual relations between the mechanical parameters characterizing the treated models, including their focal zones, parameters of model loading, parameters of seismogenic displacement and parameters of radiated elastic pulses. Particular attention was given to the study of slip displacement, slip velocity, rupture velocity, nucleation points of rupture propagation, nucleation points of elastic radiation and to the frequency analysis of radiated pulses. Measurements of the displacement in the focal zone enabled us to determine the source function, to construct theoretical seismograms in a far field and to compare them with the real pulses from ultrasonic transducers located there. This allowed testing theoretical and experimental approaches to the study of how slip displacement, slip velocity and rupture velocity are related to the parameters of radiated pulses.

Cluster and spectral characteristics of the aftershock activity of the Kalamata, September 13, 1986 earthquake, South Greece

The spatial and temporal evolution of the aftershock sequence of the Kalamata (South Greece), 1986 earthquake is examined by the method of principal parameters (Ebbling and Michelini, 1986). The application of the method to 515 aftershocks of known location reveals a variety of orientations and dips for the subfaults which were activated during the aftershock sequence. Events which occurred in the northern area indicate the existence of two types of orientation which dip at four different angles, while the southern area is characterized by almost uniform behavior, activated later in the sequence. Displacement spectra obtained from hand digitized seismograms have been interpreted as evidence for a possible regional variation in the source parameters. Visual techniques were replaced by a numerical generalized inversion method which was applied to the spectra to evaluate spectral source parameters. Initial pulse widths, measured on the seismograms, were also used for the evaluation of source dimensions and average path attenuation. Theoretical seismograms were computed, according to the model of Sato and Hirasawa (1973) and were then compared to the obtained initial pulses. The results revealed that both regions are characterized by similar spectral properties typified by ω-square or higher high-frequency decay. Statistical methods showed no significant difference in the source parameters of the earthquakes between the two regions.

Propagation of transient SH-waves in a dipping structure by finite- and boundary element methods

The boundary and the finite element formulations for the equations of elasticity are presented and applied to the problem of propagation of transient SH-waves in dipping layers overlying a half-space. When the finite element formulation is used, appropriate boundary conditions are imposed on the additional boundary dividing the half-space into a finite and an infinite region. These conditions ensure the transmission of waves across this boundary. When the boundary element method is applied, it is necessary to satisfy the radiation conditions. Theoretical seismograms for the displacement on the surface of the half-space are presented. They show that, for a specific case, the agreement between the two methods is satisfactory. The results can be compared with those found by the exact method of generalized rays in order to check the validity of the finite and the boundary element methods for the specific problem studied in this paper.