Determination of the seismograph phase response from the amplitude response

1972 ◽  
Vol 62 (6) ◽  
pp. 1665-1672 ◽  
Author(s):  
P. M. Bolduc ◽  
R. M. Ellis ◽  
R. D. Russell
Keyword(s):  
Hilbert Transform ◽  
Rapid Determination ◽  
Phase Response ◽  
Minimum Phase ◽  
Amplitude Response ◽  
Amplitude Data ◽  
The Hilbert Transform ◽  
Seismic System

abstract Determination of the phase response of a minimum-phase seismic system directly from the amplitude response by the Hilbert transform is investigated. The error by this technique is found to be less than 2° with the major source of inaccuracy being the uncertainties in the amplitude data. This technique is useful for rapid determination of the phase response if the amplitude response is known.

scholarly journals Amplitude response of a telemetered seismic system from seismometers to digital acquisition system

1995 ◽  
Vol 38 (1) ◽  
Author(s):  
R. Di Giovambattista ◽  
S. Barba ◽  
A. Marchetti
Keyword(s):  
Digital Signals ◽  
Amplitude Response ◽  
Automatic Mode ◽  
Steady State Method ◽  
Sinusoidal Current ◽  
Fully Automatic ◽  
The Difference ◽  
High Degree ◽  
Seismic System

Automated amplitude response of the complete seismometer, telemetry and recording system js obtaiued trom sinusoidal inputs to the calibration coil. Custom-built software was designed to perform fully automatic cali- bration analyses of the digital signals. In this paper we describe the signals used for calibration and interactive and batch procedures designed to obtain calibration functions in automatic mode. By using a steady-state method we reach a high degree of accuracy in the determination of both the frequency and amplitude of the \ignal. The only parameters required by this procedure are the seismometer mass, the calibration-coil constant and the intensity of the current injected into the calibration coil. This procedure is applicable to telemetered seismic systems and represents an optimization of the processing time. The software was designed to requjre no modification" jf the device used to generate the sinusoidal current should change. In particular, it is possi- ble to changc the number of monotrequcncy packages transmitted to the calibration coil with the on]y restric- tion that the difference between the frequency of two consecutjve packages be greater than 5%; for these rea- sons the procedure is expected to be usefu] for the seismological community. The paper inc]udes a generaI de- scription of thc designing criteria, and of the hardware and software architecture, as well as an account of thc system's performancc during a two year period of operation.

A scheme for expressing instrumental responses parametrically

1977 ◽  
Vol 67 (3) ◽  
pp. 957-969 ◽  
Author(s):  
Peter C. Luh
Keyword(s):  
Transfer Function ◽  
Linear Systems ◽  
Hilbert Transform ◽  
Transfer Functions ◽  
Poor Quality ◽  
Phase Response ◽  
Seismic Instrument ◽  
Amplitude Response ◽  
Response Range

abstract This study shows that, provided a seismic instrument as a whole behaves linearly over its response range, and provided its phase response is known accurately, the instrumental responses can be parametrically expressed in terms of transfer functions of linear systems. The scheme is based on the observation that knowing accurately the detailed overall amplitude and phase responses of a linear instrument is tantamount to knowing all the pertinent constants for the construction of its overall transfer function. Because of generally poor quality of empirical phase calibrations, empirical phases are substituted by minimum phases, calculated via a Hilbert transform of amplitude response. Application of the scheme to actual SRO (LP) and USGS (SP) instruments resulted in sufficiently close agreements between parametric and actual responses to warrant the utility of the scheme.

CEPSTRUM ALIASING AND THE CALCULATION OF THE HILBERT TRANSFORM

Geophysics ◽  
1974 ◽  
Vol 39 (4) ◽  
pp. 543-544 ◽  
Author(s):  
Paul L. Stoffa ◽  
Peter Buhl ◽  
George M. Bryan
Keyword(s):  
Hilbert Transform ◽  
Phase Function ◽  
Amplitude Spectrum ◽  
Magnetic Data ◽  
Minimum Phase ◽  
Original Function ◽  
Cepstrum Analysis ◽  
Complex Cepstrum ◽  
The Hilbert Transform ◽  
Special Case

Schafer (1969) has pointed out that the Hilbert transform approach used in computing the minimum‐phase spectrum of a given amplitude spectrum corresponds to a special case of complex‐cepstrum analysis in which the phase information of the original function is ignored. The resulting complex cepstrum is an even function. Since a minimum‐phase function has no complex‐cepstrum contributions for T<0, its even part must exactly cancel the odd part for T<0. Thus, by setting all complex‐cepstrum contributions for T<0 equal to zero and doubling all contributions for T>0, we obtain the complex cepstrum of the minimum‐phase function corresponding to the original function. However, the DFT-calculated complex cepstrum is an aliased function (Stoffa et al., 1974). Thus some negative periods will appear at positive locations and vice versa. Appending the original function with zeros will reduce the aliasing. Shuey (1972), in computing the Hilbert transform for magnetic data, indicates that the computation breaks down near the end of the profile, or at long cepstrum periods. This is precisely the point in the even cepstrum where aliasing will have its greatest effect.

scholarly journals Determination of fundamental asteroseismic parameters using the Hilbert transform

2015 ◽  
Vol 578 ◽  
pp. A56 ◽  
Author(s):  
René Kiefer ◽  
Ariane Schad ◽  
Wiebke Herzberg ◽  
Markus Roth
Keyword(s):  
Hilbert Transform ◽  
The Hilbert Transform

A Dispersive Model for the Propagation of Ultrasound in Soft Tissue

1982 ◽  
Vol 4 (4) ◽  
pp. 355-377 ◽  
Author(s):  
K. V. Gurumurthy ◽  
R. Martin Arthur
Keyword(s):  
Soft Tissue ◽  
Phase Velocity ◽  
Hilbert Transform ◽  
Phase Function ◽  
Path Length ◽  
Minimum Phase ◽  
Velocity Measurements ◽  
Tissue Model ◽  
Dispersive Model ◽  
The Hilbert Transform

Although the dispersion of tissue is small and difficult to measure, it can be calculated from a knowledge of the tissue's attenuation. A minimum-phase function, which characterizes tissue dispersion was derived using the Hilbert transform. This function was incorporated into a tissue model which has a causal impulse response and from which accurate estimates of the slope of attenuation times path length can be extracted. Predictions of phase velocity closely match available dispersion measurements. The model suggests that phase velocity measurements must be much more accurate than attenuation measurements for a comparable description of tissue.

Weak Beam Imaging and Diffraction Studies of Stacking Faults in Silicon

1976 ◽  
Vol 34 ◽  
pp. 590-591
Author(s):  
T. Y. Tan ◽  
W. K. Tice
Keyword(s):  
Fast Neutron ◽  
Rapid Determination ◽  
Stacking Faults ◽  
Imaging Method ◽  
Large Reduction ◽  
Dislocation Loops ◽  
Fringe Spacing ◽  
Weak Beam ◽  
Kinematical Theory

In studying ion implanted semiconductors and fast neutron irradiated metals, the need for characterizing small dislocation loops having diameters of a few hundred angstrom units usually arises. The weak beam imaging method is a powerful technique for analyzing these loops. Because of the large reduction in stacking fault (SF) fringe spacing at large sg, this method allows for a rapid determination of whether the loop is faulted, and, hence, whether it is a perfect or a Frank partial loop. This method was first used by Bicknell to image small faulted loops in boron implanted silicon. He explained the fringe spacing by kinematical theory, i.e., ≃l/(Sg) in the fault fringe in depth oscillation. The fault image contrast formation mechanism is, however, really more complicated.

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