Surface Wave Phase Research Articles

New techniques for the determination of surface wave phase velocities

abstract A number of new techniques have been developed for the determination of phase velocities from the digitized seismograms from pairs of stations. One of these techniques is to Fourier analyze the sum (or difference) of the two seismograms after time shifting in steps to correspond to steps in phase velocity. The amplitude of the summed seismogram is a maximum for any particular period when both seismograms are in phase at that period. Another method is to pass both seismograms through a narrow bandpass digital filter centered at various periods and form the cross product of the filtered seismograms, after time shifting. The average of the resultant time series is a maximum when the two signals are in phase. The computer output is a matrix consisting of amplitudes or averages as a function of phase velocity and period. The phase velocity dispersion is determined from the contoured matrix. Using these techniques, interstation phase velocities of Rayleigh waves have been determined for the “World Wide Network Standard Stations” at Pretoria, Bulawayo and Windhoek. The method using cross-products is the most efficient.

Frequency Spectra of Forward Scattered Underwater Sound from a Traveling Sinusoidal Surface

An experiment has been conducted in a model tank to determine the frequency spectrum of an acoustic signal reflected from a traveling sinusoidal surface. An acoustic signal of 1.85 MHz was transmitted continuously and projected toward the surface (beamwidth 3.5°). A vibration generator produced water gravity waves; wavelength and wave-height measurements were made at the point of reflection. The forward scattered signal was envelope detected and analyzed for spectral content. Frequency information regarding the carrier and sidebands was also obtained. A scattering integral developed in the literature was evaluated for a traveling sinusoidal surface to compare the experimental results. Analytical predictions were made, based on the concept that the surface waves phase modulate the acoustic signal. Important observations are: (1) both amplitude and phase modulation are present, (2) the frequency spectrum is symmetrical about the carrier and can contain only sideband frequencies that are multiples of the surface frequency, i.e., f±nf6, (where f = acoustic frequency, n = 0, 1, 2, 3, ⋯, f6 = surface frequency), (3) the amplitudes of the frequency components are dependent on transmitting and receiving geometry and measured surface characteristics.

ELASTIC SURFACE WAVES IN A LAYERED SYSTEM OF CADMIUM SULFIDE ON GERMANIUM

The theoretical behavior of the elastic surface wave phase velocities is presented as a function of direction and layer thickness for a CdS layer on the (001) and (011) faces of a semi-infinite crystal of Ge.

The Crust and Mantle in Finland

The structure of the crust and upper mantle in Finland has been studied by utilizing results of surface wave phase and group velocity determinations and of explosion seismic refraction measurements. The dispersion curves for a set of theoretical models have been calculated by the Thomson-Haskell matrix method. The earth-stretching transformations of Anderson and Toksoz were used in the calculation of Love wave dispersion. The derived layer model has a crustal thickness of 42km and a major crustal discontinuity at the depth of 12km. The existence of a low-velocity layer in the upper mantle with the upper boundary of it at a depth lower than 150km could not be shown with the available data.

Surface wave phase velocities in Finland

Abstract Phase velocities of Rayleigh waves in Finland have been measured by the Fourier analysis method, using records of three stations which are on almost the same great circle as several Greek earthquakes. Phase velocities of Love waves of two of these earthquakes have also been determined. The wave groups were divided by numerical filtering into two frequency channels, which were analyzed separately. The resulting phase velocity curves were then smoothed in order to remove rapid oscillations, and mean values were calculated. The phase velocities were found to be slightly lower than those found for the Canadian Shield (Brune and Dorman, 1963), the maximum deviation for Rayleigh waves being about 0.07 km/sec at a period of 28 seconds and for Love waves about 0.15 km/sec at a period of 32 seconds. At periods shorter than 40 seconds the phase velocities of Rayleigh waves were found to be equal in Northern and Southern Finland within the accuracy of measurement.

Application of the theory of eigenfunctions to the calculations of surface wave velocities

Surface wave phase velocities for an inhomogeneous medium are usually given as eigenvalues of the wave equation. This is a differential equation (Love waves) or pair of differential equations (Rayleigh waves) of the second order. By means of a change of variable the problem is reducible to finding the zeros of a first‐order differential equation or pair of differential equations of first order. The solution can be obtained in any order of surface waves, and the eigenfunctions can be obtained as well by means of this transformation. The solution is thus amenable to computation.

Partial derivatives of surface wave phase velocity with respect to physical parameter changes within the Earth

By using energy equations, which are equivalent to fundamental equations and boundary conditions in surface wave problems, we can get analytical expressions for partial derivatives of phase velocity with respect to changes of physical parameters within the earth. These derivatives can be calculated by knowing only the eigenfunction corresponding to the phase velocity. Numerical examples are worked out for CANSD (a model proposed by Brune and Dorman for the Canadian shield), the Jeffreys model, and the Gutenberg model for crustmantle structure. An application of the present result to numerical inversion of surface wave data is demonstrated by an example.

Surface wave radiation patterns for underground nuclear explosions and small-magnitude earthquakes

The surface wave radiation patterns (amplitude and initial phase) were determined for several of the larger underground nuclear explosions in Nevada. Initial phases of surface waves from explosions and earthquakes were obtained by performing a Fourier analysis of the record and equalizing the phase to the source, using long-period records from the temporary long-range seismic measurement stations installed by the Geotechnical Corporation. Rayleigh waves from explosions in tuff and alluvium appear to have nearly the same initial phase at all azimuths, indicating an explosive force acting as a step function in time as the probable approximate source mechanism. However, the presence of Love waves, along with some asymmetry in Rayleigh wave amplitudes, indicates that some asymmetrical forces are also acting at the origin. The collapses following these explosions generate Rayleigh waves with polarities apparently reversed from those of the explosions. The collapses generate much weaker Love waves relative to Rayleigh waves than the explosions, and therefore the Love waves must be generated at or very near the source. The one explosion in granite (Hardhat) gave a surface wave radiation pattern with double-couple symmetry in both phase and amplitude, a symmetry very different from that found for the explosions in tuff and alluvium. Such a radiation pattern cannot be explained by a simple, symmetric explosive force. Several explanations of this double-couple symmetry are considered, including the possibilities that the surface waves were generated by cracking or forced motion along pre-existing cracks, tectonic strain release resulting from cavity formation, or, more probably, triggering of tectonic motion. The latter hypothesis would explain the radiation pattern, and it is supported by the occurrence of an aftershock sequence, outside the cavity zone, similar to that common for earthquakes. Analysis of surface waves from earthquakes indicates that, in many cases, the earthquake sources are more complicated than the explosion sources. The information about source mechanisms obtained in this study is of fundamental importance to the problem of the identification of explosions and earthquakes.

Crustal structure in the California-Nevada region

A case is made for the combined use of three methods for the study of the earth's crust in a given region: seismic refractions, surface wave phase velocity, and gravity. Only by this approach can the fine details of crustal structure be revealed. The standard phase-velocity curves are revised to take into account recent refraction results in South Africa and the Gutenberg low-velocity zone of the upper mantle. Restrictions on the use of the phase-velocity method alone are discussed. In the California-Nevada region seismic refractions reveal the following structure below the sediments: 23 km of granitic rock with velocities of 6.11 km/sec and 3.49 km/sec for compressional and shear waves; 26 km of gabbroic-ultramafic rock with a compressional velocity of 7.66 km/sec underlain by a zone of ultramafic rock with a compressional velocity of 8.11 km/sec. When this structure is used in computing theoretical Rayleigh wave phase velocities and gravity anomaly, discrepancies are found with the observed values which can be resolved by reducing the mean shear velocity and the density in the crust. It is probable that this reduction is limited to the intermediate crustal layer, and several modifications consistent with all three exploration methods are discussed.

Higher modes of continental Rayleigh waves

ABSTRACT A long dispersive train of waves corresponding to higher modes of the Rayleigh-wave equation (including Sezawa's M2 wave) for the continental crust-mantle system is positively identified, apparently for the first time. Observed particle motion is elliptical and retrograde, in agreement with theory. Although several theoretical studies have been published in which progressive elliptical particle motion was found, all of these involved values of the elastic constants unsuitable for the present problem. The beginnings of the short-period branches of the higher modes can account for the high-frequency longitudinal and vertical components of the continental surface-wave phase Lg. The large amplitudes and the peculiar appearance of Rg appear to depend on the broad flat minimum of the group velocity curve of the lowest or Rayleigh mode.

CRUSTAL STRUCTURE OF THE ARCTIC REGIONS FROM THE Lg PHASE

Research Article| September 01, 1955 CRUSTAL STRUCTURE OF THE ARCTIC REGIONS FROM THE Lg PHASE JACK OLIVER; JACK OLIVER LAMONT GEOLOGICAL OBSERVATORY (COLUMBIA UNIVERSITY), PALISADES, NEW YORK Search for other works by this author on: GSW Google Scholar MAURICE EWING; MAURICE EWING LAMONT GEOLOGICAL OBSERVATORY (COLUMBIA UNIVERSITY), PALISADES, NEW YORK Search for other works by this author on: GSW Google Scholar FRANK PRESS FRANK PRESS LAMONT GEOLOGICAL OBSERVATORY (COLUMBIA UNIVERSITY), PALISADES, NEW YORK Search for other works by this author on: GSW Google Scholar GSA Bulletin (1955) 66 (9): 1063–1074. https://doi.org/10.1130/0016-7606(1955)66[1063:CSOTAR]2.0.CO;2 Article history received: 23 Aug 1954 first online: 02 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation JACK OLIVER, MAURICE EWING, FRANK PRESS; CRUSTAL STRUCTURE OF THE ARCTIC REGIONS FROM THE Lg PHASE. GSA Bulletin 1955;; 66 (9): 1063–1074. doi: https://doi.org/10.1130/0016-7606(1955)66[1063:CSOTAR]2.0.CO;2 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGSA Bulletin Search Advanced Search Abstract The presence of the Lg earthquake surface-wave phase, which is indicative of continental structure between the epicenter and recording station, is used in the exploration of Arctic regions. Water-covered areas of continental structure include the Canadian archipelago, parts of Baffin Bay and Davis Strait, the Barents Sea, Bering Strait, and the shallow parts of the Bering and Greenland seas. Areas of noncontinental structure include the Arctic Ocean, Beaufort Sea, Norwegian Sea, and the deep parts of the Bering and Greenland seas. This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

The instrumental phase-difference of seismograph records; an illustration of the properties of damped oscillatory systems

A discussion is given of the method of interpretation of the maxima shown on the records of earthquakes during the surface-wave phase. The usual procedure is to treat the waves (which actually appear as beats) as being truly simple-harmonic and to apply the formulae which are derived on this assumption. It is shown that, in general, this procedure does not necessarily lead to the correct interpretation. In the case of direct registration the true earth-maximum may have occurred one half-period later than the time obtained by the usual correction. With galvanometric registration the maximum may have occurred either one, two, or three half-periods earlier than the time indicated by the usual formula due to Galitzin. Some curves are included to illustrate these points, and an attempt is made to obtain a mathematical explanation. It is shown that there is no easy method of eliminating an ambiguity of one half-period. For direct registration, therefore, the phase-correction at present in use appears to be as good as the one alternative. In the case of galvanometric registration, although there are altogether four forms of phase-correction, the number of alternatives for any particular period cannot exceed two. The final recommendation in this case is that the correction suggested by Somville and which is one half-period less than Galitzin's, be adopted for general use.

Societies and Academies

LONDON. Physical Society, Feb. 6.E. B. Moss: A ballistic recorder for small electric currents. The standard thread recorder is so modified that it records ballistic throws in instead of the usual steady deflection. By this means, the current-sensitivity may be increased at least twenty-five times.F. J. Scrase: The instrumental phase-difference of seismograph records: an illustration of the properties of damped oscillatory systems. A discussion is given of the method of interpretation of the maxima shown on the records of earthquakes during the surface-wave phase. The usual procedure is to treat the waves (which actually appear as beats) as being truly simple harmonic. In genera], this procedure does not necessarily lead to the correct interpretation. In direct registration, the true earth maximum may have occurred one half-period later than the time obtained by the usual correction. With galvanometric registration, the maximum may have occurred either one, two, or three half-periods earlier than the time indicated by the usual formula due to Galitzin. For direct registration, the phase correction at present in use appears to be as good as one of the alternatives. For galvanometric registration, the correction suggested by Somville, which is one half-period less than Galitzin's, should be adopted.H. E. Beckett: The reflecting powers of rough surfaces at solar wave-lengths. A hemispherical mirror was used for integrating diffusely-reflected energy upon a thermopile receiver. The paper deals at length with the errors inherent in the method and with the adjustment of the apparatus. The theory of the method is simplified by the introduction of an auxiliary specimen which, in particular, renders the observations independent of the degree of blackness of the thermopile receiver.