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.

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 offset indicator (POI): A study of phase shift versus offset and fluid content

Geophysics ◽  
1986 ◽  
Vol 51 (3) ◽  
pp. 679-688 ◽  
Author(s):  
B. Rafipour ◽  
E. Herrin
Keyword(s):  
Phase Shift ◽  
Theoretical Work ◽  
Linear Process ◽  
Phase Changes ◽  
Study Phase ◽  
Complex Spectrum ◽  
Angle Of Incidence ◽  
Matched Filters ◽  
Fluid Content ◽  
Saturated Medium

There is limited published experimental and theoretical work related to offset‐dependent reflection and phase changes at the interface between porous media. An appropriate relationship between seismic parameters and phase shift has not been well‐established. This investigation measures variations of phase for nonnormal incidence reflection as a function of frequency at the interface of a horizontally layered porous (perforated) medium, using a two‐dimensional Plexiglas model. In both parts of this study, phase‐matched filters (PMF) are used to analyze the data. Phase‐matched filters previously have been applied to digital records of Rayleigh waves and Love waves. The purpose of the first part of the study is to demonstrate application of the PMF process to reflected compressional waves and to use this technique in discriminating multiples from primaries. By using this linear process, the complex spectrum of the primary signal can be recovered from the multiple arrivals. The reduction of reflected compressional pulse wavelets to a zero‐phase wavelet provided a tool to examine the change in phase (and amplitude) as the wave travels through a lossy medium. The second part of the study deals with the relationship of phase shift Δϕ at an interface of a horizontally layered porous medium, as a function of fluid content, angle of incidence (offset), and frequency. The result indicates that, at midband frequency of 60 kHz, an air‐ (gas‐) saturated medium would cause a large increase in Δϕ with offset, whereas a water‐saturated medium would show less change in Δϕ with offset. The phase shift‐versus‐offset response for oil is assumed to be intermediate between the responses for gas and water.

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.

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.

Precursors to PKKP

1978 ◽  
Vol 68 (4) ◽  
pp. 1059-1079
Author(s):  
Andre C. Chang ◽  
John R. Cleary
Keyword(s):  
Regional Variation ◽  
Wave Train ◽  
Seismic Array ◽  
Qualitative Explanation ◽  
Similar Investigation ◽  
Mantle Boundary ◽  
Core Mantle Boundary ◽  
Novaya Zemlya ◽  
The Core

abstract Consistent precursors to PKKP from Novaya Zemlya explosions have been detected at the LASA seismic array in Montana. The precursory wave train is at least 65 sec long, and up to seven distinct and correlatable arrivals can be observed in the train. A similar investigation of E. Kazakh explosions, however, showed no evidence of precursors. A hypothesis of scattering on reflection at the core-mantle boundary provides a qualitative explanation of the observed precursors. The source of the scattered waves cannot be established with certainty, but the simplest interpretation is that they are generated by irregularities (“bumps”) on the boundary itself. The absence of precursors from E. Kazakh explosions is at least partly explicable in terms of the lower magnitudes of these events, but could be a result also of regional variation in the scattering properties of the core-mantle boundary.

scholarly journals Synthesis of matched filters.

2021 ◽  
Author(s):  
A.N. Degtyaryov ◽  
◽  
I.L. Afonin ◽  
A.L. Polyakov ◽  
A.S. Kozhemyakin ◽  
...  
Keyword(s):  
Fourier Series ◽  
Impulse Response ◽  
Correlation Functions ◽  
Matched Filter ◽  
Matched Filters ◽  
Low Pass ◽  
Pulse Characteristics ◽  
Low Pass Filters ◽  
Direct Use ◽  
Complex Transmission

Methods for approximating the impulse response of a matched, physically realizable filter with the minimum required number of functional nodes are in thei focus of the paper. Methods for approximating the pulse characteristics of a matched filter are proposed, namely: approximation by causal physically realizable functions, which are the correlation functions of the pulse characteristics of low-pass filters (LPF) Butterworth; using the Fourier series to describe the complex transmission coefficient of the filter; direct use of the Fourier series to approximate the impulse response of a matched filter. As a result, the number of elements of the matched filter is significantly reduced.

Forecast of Critical Wave Groups From Surface Elevation Snapshots

2007 ◽  
Author(s):  
Gu¨nther F. Clauss ◽  
Daniel Testa ◽  
Sascha Kosleck ◽  
Robert Stu¨ck
Keyword(s):  
Wave Train ◽  
Wave Length ◽  
Wave Spectrum ◽  
Amplitude Spectrum ◽  
Response Spectra ◽  
Phase Spectrum ◽  
Surface Elevation ◽  
Fast Fourier Transformation ◽  
Wave Groups ◽  
The Impact

Reports on damages of ships, cargo and structures during heavy seas have been increasing within the last years. The impact of single extreme waves or wave groups on marine structures and ships causes enormous forces often leading to critical situations or even loss of crew, ship and cargo. Dangerous situations can be predicted by a forecast of encountering wave trains and the identification of critical wave groups. The paper presents a method to calculate the wave train a ship will encounter from surface elevation snapshots of the surrounding sea, taken by the ship radar. The time-dependent surface elevation snapshot far ahead of the ship is transferred into frequency domain by the use of Fast Fourier Transformation (FFT). The resulting complex Fourier spectrum given over the inverse wave length 1/L is converted into an amplitude spectrum and a phase spectrum. By shifting the phase spectrum to the position of the cruising ship the encountering waves can in turn be calculated in advance — depending on speed. The permanent processing of incoming snapshots delivers a continuous prediction of the water surface elevation at the position of the cruising ship. Based on these data the expected ship motion behaviour can be calculated continuously in time domain. In addition the response spectra, resulting from the wave spectrum and the relevant RAOs, are also evaluated. As wave data far ahead of the ship are used, it allows a forward glance, and dangerous situations, particularly resonance and parametric resonance are detectable before the ship is encountering this wave train. Consequently, the procedure can be used by the master as an assistance support system.

Rayleigh waves in southern New Guinea

1969 ◽  
Vol 59 (2) ◽  
pp. 945-958 ◽  
Author(s):  
J. A. Brooks
Keyword(s):  
Rayleigh Waves ◽  
Velocity Structure ◽  
Group Velocity Dispersion ◽  
Focal Depth ◽  
New Guinea ◽  
Shear Velocity ◽  
Stationary Wave ◽  
Period Range ◽  
Mode Group ◽  
Path Lengths

abstract A shear velocity structure having features similar to the Gutenberg model for the upper 200 km of the mantle is consistent with features of higher mode Rayleighwave group-velocity dispersion curves in the period range 4 to 30 seconds, for paths across southern New Guinea. Pronounced discontinuities appear to be absent within the crust where shear velocities are expected to gradually increase with depth. Clearly dispersive second mode (M21) Rayleigh waves, well separated in time from the fundamental mode, are shown for path lengths less than 2000 km. Frequencies excited show some dependence on focal depth. Stationary wave groups of period 10-20 seconds, very like the Sa phase, and generated by earthquakes of focal depth between 100 and 160 km coincide with expected normal mode group arrivals.

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