Phase-matched filters: Application to the study of Love waves

1979 ◽  
Vol 69 (1) ◽  
pp. 27-44
Author(s):  
Tom Goforth ◽  
Eugene Herrin
Keyword(s):  
Rayleigh Waves ◽  
Matched Filter ◽  
Multipath Propagation ◽  
Group Velocity Dispersion ◽  
Wave Train ◽  
Seismic Signal ◽  
Love Waves ◽  
Complex Spectrum ◽  
Matched Filters ◽  
Wave Trains

abstract Seismic surface waves are usually composed of overlapping wave trains representing multipath propagation. A first task in the analysis of such waves is to identify and separate the various component wave trains so that each can be analyzed separately. Phase-matched filters are a class of linear filters in which the Fourier phase of the filter is made equal to that of a given signal. Herrin and Goforth (1977) described an iterative technique which can be used to find a phase-matched filter for a particular component of a seismic signal. Application of the filters to digital records of Rayleigh waves allowed multiple arrivals to be identified and removed, and allowed recovery of the complex spectrum of the primary wave train along with its apparent group-velocity dispersion curve. A comparable analysis of Love waves presents additional complications. Love waves are contaminated by both Love and Rayleigh multipathing and by primary off-axis Rayleigh energy. In the case of explosions, there is much less energy generated as Love waves than as Rayleigh waves. The applicability of phase-matched filtering to Love waves is demonstrated by its use on earthquakes occurring in the Norwegian Sea and near Iceland and on a nuclear explosion in Novaya Zemlya. Despite severe multipathing in two of the three events, the amplitude and phase of each of the primary Love waves were recovered without significant distortion.

Phase-matched filters: Application to the study of Rayleigh waves

1977 ◽  
Vol 67 (5) ◽  
pp. 1259-1275
Author(s):  
Eugene Herrin ◽  
Tom Goforth
Keyword(s):  
Rayleigh Waves ◽  
Matched Filter ◽  
Group Velocity Dispersion ◽  
Wave Train ◽  
Amplitude Spectrum ◽  
Linear Process ◽  
Complex Spectrum ◽  
Greenland Sea ◽  
Matched Filters ◽  
Novaya Zemlya

abstract Phase-matched filters are defined as a class of linear filters in which the Fourier phase of the filter is made equal to that of a given signal. An iterative technique is described which can be used to find a phase-matched filter for a particular seismic signal. The process is then applied to digital records of Rayleigh waves from a synthetic source with propagation across 55° of continental path, an earthquake in the Greenland Sea recorded in Texas, and a nuclear explosion in Novaya Zemlya recorded in New Mexico. Application of the filter allows multiple arrivals to be identified and removed and allows recovery of the complex spectrum of the primary wave train along with its apparent group-velocity dispersion curve. The amplitude spectrum of the primary signal obtained by this linear process is not contaminated by interference from multipath arrivals. The filtering process also provides significant improvement in signal-to-noise ratio, greater than a factor of four for the Greenland Sea and Novaya Zemlya events.

scholarly journals Observations of multiple seismic events

1964 ◽  
Vol 54 (1) ◽  
pp. 19-39
Author(s):  
W. L. Pilant ◽  
L. Knopoff
Keyword(s):  
Amplitude Ratio ◽  
Multipath Propagation ◽  
Wave Train ◽  
Seismic Surface Waves ◽  
Derived Properties ◽  
Beat Phenomenon ◽  
Wave Trains ◽  
The Individual ◽  
Comparable Magnitude ◽  
Resultant Wave

abstract Two or more dispersed wave trains each with constant amplitude will interfere giving a resultant wave train which is amplitude modulated, if the individual waves have their principal energies in a common frequency band and if the trains arrive with time separations small compared to their total length. The dispersive characteristics of the trains need not be the same. If the component trains are of comparable magnitude, the modulation due to interference becomes significant and a “beat” phenomenon occurs. Multiple trains of dispersed seismic surface waves may occur because of a temporal and/or spatial distribution at the source or because of multipath propagation. Each of these causal mechanisms influences the amplitude and phase spectra of the resultant wave train; derived properties such as phase velocities and amplitude ratios are also influenced. In the case of multipath propagation, wavelength dependent time delays may occur. Two cases of twin earthquakes are analyzed, and the significant features of interference are demonstrated. In one case, estimates are obtained for the amplitude ratio and time delay of the second shock with respect to the first. The interpretation of seismograms and spectra influenced by multiple events is discussed.

A variational method for love waves in nonhorizontally layered structures

1973 ◽  
Vol 63 (3) ◽  
pp. 1013-1023
Author(s):  
B. Gjevik
Keyword(s):  
Travel Time ◽  
Wave Train ◽  
Love Waves ◽  
Wave Number ◽  
Transient Wave ◽  
Varying Thickness ◽  
Wave Trains ◽  
The Mean ◽  
Gradual Variation ◽  
Impulsive Source

abstract A variational principle for Love waves propagating in a layer with varying thickness overlying a half-space is formulated. By an averaging procedure, the wave modulation due to gradual variation of the thickness of the upper layer is found. The case of long-period Love waves is particularly examined and the wave number and amplitude modulation both for a monochromatic wave and for a transient wave train due to an impulsive source are determined. Moreover, the travel time for a certain phase in the wave train is determined. It is found that for well-dispersed wave trains the travel time is given by the phase velocity corresponding to the mean depth of the upper layer.

Rayleigh waves from high-gain long-period stations: Signal extraction, amplitude determination, and separation of overlapping wave trains

1975 ◽  
Vol 65 (6) ◽  
pp. 1761-1778 ◽  
Author(s):  
Eduard Berg
Keyword(s):  
Rayleigh Waves ◽  
Signal To Noise Ratio ◽  
High Gain ◽  
Clear Separation ◽  
Novaya Zemlya ◽  
Oceanic Surface ◽  
Single Station ◽  
Wave Trains ◽  
Short Time

abstract For a signal-to-noise ratio between 0.2 and 0.1 on the original single-component records, amplitudes for Rayleigh waves over oceanic paths of 155° at station MAT and 98° at station KIP have been determined as 12 mμ and 24 mμ peak-to-peak, respectively, with a standard error of less than 11 per cent. In each case the processed correlation signal is the highest in a half-hour record. The method makes use of preliminary high-pass filtering and normalized reference earthquake-matched filtering, and takes full advantage of the well-dispersed oceanic surface wave. The method also provides high resolution of co-located events with short time separation, or of widely spaced events with Rayleigh waves arriving nearly simultaneously at a single station, when the summed vertical and radial matched filtered components are used. Examples include: (1) clear separation and amplitude determination at stations KIP and MAT of two MS = 6.5 earthquakes located 0.7° and 145 sec apart off the coast of central Chile; (2) clear separation at station KIP of a Novaya Zemlya mb = 4.8 event from interfering Rayleigh waves of an mb = 5.0 Kermadec Island earthquake arriving 120 to 140 sec prior to the searched event, with almost complete elimination of interference on the summed vertical and radial processed components; and (3) clear separation at station KIP of two co-located mb = 4.4 and 4.5 earthquakes 6 min apart off the coast of Chile, with determination of their amplitudes in the presence of interfering Rayleigh waves from two central Alaska earthquakes, the first (mb = 4.1) arriving 15 min prior to the first Chile Rayleigh wave and the second between the two Chile arrivals. The single-station threshold reached (10 and 25 digital units, p-p) for stations MAT and KIP at 155° and 98°, respectively, corresponds to an MS = 3.3 and probably can be improved further.

Seismic phases and scaling associated with small high-explosive surface shots

1981 ◽  
Vol 71 (6) ◽  
pp. 1731-1741
Author(s):  
I. N. Gupta ◽  
R. A. Hartenberger
Keyword(s):  
Blast Wave ◽  
Rayleigh Waves ◽  
Wave Train ◽  
Simple Wave ◽  
P Wave ◽  
Peak Ground Velocity ◽  
Air Blast ◽  
Geological Conditions ◽  
Wide Range ◽  
First Arrival

Abstract An analysis of seismic field data from surface shots in two radically different geologic environments shows significantly different seismic phases at the two sites. At the first site, which has a layered sedimentary section, five distinct phases are observed: the P-wave first arrival; a complex wave train consisting of higher mode Rayleigh waves; a precursor to air-blast wave; the air blast wave; and the air-coupled Rayleigh waves. Records from the second site, overlying an unlayered mass of igneous rocks, show only three distinct seismic phases: the P-wave first arrival; a simple wave train of fundamental-mode Rayleigh and Love waves; and an air blast wave. Peak ground velocity, based on the average of the three largest amplitudes in the surface waves preceding the air blast wave, scales well with yield for both sites. Measurements of peak ground velocity may be used to estimate yields of explosive charges at either site within a factor of about 2 if the source distance is known. The scaling relationship appears to be valid over a wide range of yields and site geological conditions.

Stability of periodic waves in shallow water

1974 ◽  
Vol 66 (1) ◽  
pp. 81-96 ◽  
Author(s):  
P. J. Bryant
Keyword(s):  
Shallow Water ◽  
Wave Train ◽  
Periodic Wave ◽  
Fundamental Wave ◽  
Cnoidal Waves ◽  
Margin Of Stability ◽  
Fundamental Wavelength ◽  
Stokes Waves ◽  
Wave Trains ◽  
Permanent Shape

Waves of small but finite amplitude in shallow water can occur as periodic wave trains of permanent shape in two known forms, either as Stokes waves for the shorter wavelengths or as cnoidal waves for the longer wavelengths. Calculations are made here of the periodic wave trains of permanent shape which span uniformly the range of increasing wavelength from Stokes waves to cnoidal waves and beyond. The present investigation is concerned with the stability of such permanent waves to periodic disturbances of greater or equal wavelength travelling in the same direction. The waves are found to be stable to infinitesimal and to small but finite disturbances of wavelength greater than the fundamental, the margin of stability decreasing either as the fundamental wave becomes more nonlinear (i.e. contains more harmonics), or as the wavelength of the periodic disturbance becomes large compared with the fundamental wavelength. The decreasing margin of stability is associated with an increasing loss of spatial periodicity of the wave train, to the extent that small but finite disturbances can cause a form of interaction between consecutive crests of the disturbed wave train. In such a case, a small but finite disturbance of wavelength n times the fundamental wavelength converts the wave train into n interacting wave trains. The amplitude of the disturbance subharmonic is then nearly periodic, the time scale being the time taken for repetitions of the pattern of interactions. When the disturbance is of the same wavelength as the permanent wave, the wave is found to be neutrally stable both to infinitesimal and to small but finite disturbances.

On a uniformly valid model for surface wave interaction

1993 ◽  
Vol 247 ◽  
pp. 589-601 ◽  
Author(s):  
Yehuda Agnon
Keyword(s):  
Surface Wave ◽  
Water Waves ◽  
Wave Train ◽  
Wave Interaction ◽  
Shallow Water Waves ◽  
First Order ◽  
Near Resonance ◽  
Wave Trains ◽  
Velocity Changes ◽  
Forced Waves

Nonlinear interaction of surface wave trains is studied. Zakharov's kernel is extended to include the vicinity of trio resonance. The forced wave amplitude and the wave velocity changes are then first order rather than second order. The model is applied to remove near-resonance singularities in expressions for the change of speed of one wave train in the presence of another. New results for Wilton ripples and the drift current and setdown in shallow water waves are readily derived. The ideas are applied to the derivation of forced waves in the vicinity of quartet and quintet resonance in an evolving wave field.

scholarly journals SIMULATION MODELING OF THE INTERFERENCE IMMUNITY OF THE RADARS OPERATING WITH COMPRESSED SIGNAL

2020 ◽  
Vol 8 (12) ◽  
pp. 799-804
Author(s):  
Sevdalin Ivanov Spassov ◽  
Keyword(s):  
Simulation Modeling ◽  
Pulse Compression ◽  
Matched Filter ◽  
Chirp Signal ◽  
Interference Immunity ◽  
Matched Filters ◽  
Matlab Software ◽  
Interference Signals

The immunity to the interference of a radar operating with a pulse compression signal is an important feature. The matched filter is one of the elements of the radar, providing resistance to interference. A model of a matched filter to chirp signal has synthesized using the Simulink tool of the Matlab software. Two types of interference signals have fed to the matched filter input, and the output signals are measured. The matched filters degree of suppression against these two interference signals has been assessed. Inferences about the interference immunity of the radars operating with compressed signals have been made.

scholarly journals Surface waves in multilayered elastic media I. Rayleigh and Love waves from buried sources in a multilayered elastic half-space

1964 ◽  
Vol 54 (2) ◽  
pp. 627-679
Author(s):  
David G. Harkrider
Keyword(s):  
Surface Waves ◽  
Frequency Domain ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Half Space ◽  
Love Waves ◽  
Displacement Fields ◽  
Matrix Formulation ◽  
Total Displacement ◽  
Rayleigh And Love Waves

ABSTRACT A matrix formulation is used to derive integral expressions for the time transformed displacement fields produced by simple sources at any depth in a multilayered elastic isotropic solid half-space. The integrals are evaluated for their residue contribution to obtain surface wave displacements in the frequency domain. The solutions are then generalized to include the effect of a surface liquid layer. The theory includes the effect of layering and source depth for the following: (1) Rayleigh waves from an explosive source, (2) Rayleigh waves from a vertical point force, (3) Rayleigh and Love waves from a vertical strike slip fault model. The latter source also includes the effect of fault dimensions and rupture velocity. From these results we are able to show certain reciprocity relations for surface waves which had been previously proved for the total displacement field. The theory presented here lays the ground work for later papers in which theoretical seismograms are compared with observations in both the time and frequency domain.

A survey of the microseisms recorded at Aberdeen in 1955, together with a review of the meteorological conditions under which they may have arisen

1958 ◽  
Vol 48 (1) ◽  
pp. 65-76
Author(s):  
A. E. M. Geddes
Keyword(s):  
Fast Moving ◽  
Rayleigh Waves ◽  
Standing Waves ◽  
Meteorological Conditions ◽  
Love Waves ◽  
Norwegian Coast ◽  
Pressure Distributions ◽  
Moving Storm ◽  
Set Up ◽  
Rocky Coast

Abstract As observations of microseisms at Aberdeen appeared to indicate that microseisms may arise from a cause or causes other than from standing waves set up by reflection from a steep rocky coast or by a mixture of waves in a fast-moving storm, a survey of Aberdeen records for 1955 has been carried out and a comparison made with the meteorological conditions prevailing at the time. A noticeable feature on the weather charts was the frequent occurrence of pressure distributions with two centres, while the occasions on which fast-moving storms occurred, or reflection from rocky coasts, were rare. Consequently there seemed to be grounds for supposing that the standing waves arose from the interference of two sets of wave systems generated by double low-pressure centres. Further, single low centres off either the Norwegian coast or that of America produced very little effect at Aberdeen. The survey suggests that the principal regions where such microseisms were produced appeared to be in the Atlantic north of 50° N and off the rocky coast of northwest Scotland. From a comparison of the displacements on the E-W and N-S records there is some support for the hypothesis that microseisms are due to a mixture of Rayleigh waves and Love waves.

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