Spectra of S-waves radiated from bilateral fracture

1967 ◽  
Vol 57 (1) ◽  
pp. 39-54
Author(s):  
J. C. Savage
Keyword(s):  
Amplitude Spectrum ◽  
Regular Sequence ◽  
Time Function ◽  
Source Time Function ◽  
S Waves ◽  
Amplitude Spectra ◽  
Bilateral Fracture ◽  
Tensile Fractures ◽  
Wave Trains ◽  
Phase Spectra

abstract The phase and amplitude spectra of the S waves radiated from five different bilateral, tensile fractures in two-dimensional models are discussed. Two S waves, radiated in approximately opposite directions, were recorded for each fracture. The amplitude spectra display the regular sequence of holes first explained by Ben-Menahem. The phase spectra display a phase jump of π radians associated with each hole in the corresponding amplitude spectrum. The phase of the source-time function was extracted from the phase spectra; it is consistent with a representation of the source-time function by a ramp function of 14 μsec duration. An explanation of the observed spectra is given in terms of interference between the initial and stopping phases of the radiated signal. From this viewpoint Ben-Menahem's directivity method is seen as a procedure for detecting the stopping phase in dispersed wave trains. Finally, it is suggested that the analyses by Ben-Menahem and Toksöz of the phase spectra of the Kamchatka 1952 and Alaska 1958 earthquakes have not properly taken account of the phase jumps in the spectra.

Determination of crustal thickness from spectral behavior of SH waves

1969 ◽  
Vol 59 (3) ◽  
pp. 1247-1258
Author(s):  
Abou-Bakr K. Ibrahim
Keyword(s):  
Amplitude Spectrum ◽  
Body Waves ◽  
Multiple Reflections ◽  
Matrix Formulation ◽  
Sh Waves ◽  
Crustal Model ◽  
Amplitude Spectra ◽  
Phase Spectra ◽  
Zero Phase

abstract The amplitude spectrum obtained from Haskell's matrix formulation for body waves travelling through a horizontally layered crustal model shows a sequence of minima and maxima. It is known that multiple reflections within the crustal layers produce constructive and destructive interferences, which are shown as maxima and minima in the amplitude spectrum. Analysis of the minima in the amplitude spectra, which correspond to zero phase in the phase spectra, enables us to determine the thickness of the crust, provided the ratio of wave velocity in the crust to velocity under the Moho is known.

scholarly journals Object Clusters or Spectral Energy? Assessing the Relative Contributions of Image Phase and Amplitude Spectra to Trypophobia

2019 ◽  
Author(s):  
R. Nathan Pipitone ◽  
Chris DiMattina
Keyword(s):  
Amplitude Spectrum ◽  
Spectral Energy ◽  
Visual Comfort ◽  
Visual Discomfort ◽  
Comfort Levels ◽  
Spatial Frequencies ◽  
Amplitude Spectra ◽  
Small Clusters ◽  
Full Factorial ◽  
Phase Spectra

Trypophobia refers to the visual discomfort experienced by some people when viewing clustered patterns (e.g., clusters of holes). Trypophobic images deviate from the 1/f amplitude spectra typically characterizing natural images by containing excess energy at mid-range spatial frequencies. While recent work provides partial support for the idea of excess mid-range spatial frequency energy causing visual discomfort when viewing trypophobic images, a full factorial manipulation of image phase and amplitude spectra has yet to be conducted. Here, we independently manipulated the phase and amplitude spectra of 31 Trypophobic images using a standard Fast Fourier Transform (FFT). Participants rated the four different versions of each image for levels of visual comfort, and completed the Trypophobia Questionnaire (TQ). Images having the original phase spectra intact (with either original or 1/f amplitude) explained the most variance in comfort ratings and were rated lowest in comfort. However, images with the original amplitude spectra but scrambled phase spectra were rated higher in comfort, with a smaller amount of variance in comfort attributed to the amplitude spectrum. Participant TQ scores correlated with comfort ratings only for images having the original phase spectra intact. There was no correlation between TQ scores and comfort levels when participants viewed the original amplitude / phase-scrambled images. Taken together, the present findings show that the phase spectrum of trypophobic images, which determines the pattern of small clusters of objects, plays a much larger role than the amplitude spectrum in determining visual comfort.

Application of Boundary Element Method for Determination of the Wavemaker Driving Signal

2018 ◽  
Author(s):  
Anatoliy Khait ◽  
Lev Shemer
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Wave Train ◽  
Amplitude Spectrum ◽  
Surface Elevation ◽  
Wave Tank ◽  
Amplitude Spectra ◽  
Wave Trains ◽  
Driving Signal ◽  
Element Method

Excitation of steep unidirectional broad-banded wave trains is studied numerically and experimentally. Iterative method is developed to adjust the driving signal of a paddle-type wavemaker to generate wave train with a prescribed free waves’ spectrum. Analytical post-processing procedure based on the Zakharov equation is applied to separate complex amplitude spectrum of the surface elevation into free and bound components, as required for the proposed method of the adjustment of the wavemaker driving signal. Numerical wave tank in the simulations was based on application of the Boundary Element Method. The results of numerical simulations were supported by measurements in a wave tank. The measured and the designed shapes of the surface elevation variation with time, as well as of the corresponding amplitude spectra were found to be in a good agreement.

scholarly journals Fully probabilistic seismic source inversion – Part 1: Efficient parameterisation

2013 ◽  
Vol 5 (2) ◽  
pp. 1125-1162 ◽  
Author(s):  
S. C. Stähler ◽  
K. Sigloch
Keyword(s):  
Moment Tensor ◽  
Source Parameters ◽  
Practical Importance ◽  
Principal Component ◽  
Seismic Source ◽  
Empirical Orthogonal Functions ◽  
Time Function ◽  
Source Inversion ◽  
Source Time Function ◽  
Earthquake Parameters

Abstract. Seismic source inversion is a non-linear problem in seismology where not just the earthquake parameters themselves, but also estimates of their uncertainties are of great practical importance. Probabilistic source inversion (Bayesian inference) is very adapted to this challenge, provided that the parameter space can be chosen small enough to make Bayesian sampling computationally feasible. We propose a framework for PRobabilistic Inference of Source Mechanisms (PRISM) that parameterises and samples earthquake depth, moment tensor, and source time function efficiently by using information from previous non-Bayesian inversions. The source time function is expressed as a weighted sum of a small number of empirical orthogonal functions, which were derived from a catalogue of >1000 STFs by a principal component analysis. We use a likelihood model based on the cross-correlation misfit between observed and predicted waveforms. The resulting ensemble of solutions provides full uncertainty and covariance information for the source parameters, and permits to propagate these source uncertainties into travel time estimates used for seismic tomography. The computational effort is such that routine, global estimation of earthquake mechanisms and source time functions from teleseismic broadband waveforms is feasible.

On: “Mineral discrimination and removal of inductive coupling with multifrequency IP” by W. H. Pelton, S. H. Ward, P. G. Hallof, W. R. Sill, and P. H. Nelson (GEOPHYSICS, 43, 588–609).

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1556-1557
Author(s):  
Heikki Soininen
Keyword(s):  
Apparent Resistivity ◽  
Dispersion Model ◽  
Constant Factor ◽  
Constant Independent ◽  
Real Constant ◽  
Frequency Range ◽  
Dilution Factor ◽  
Amplitude Spectra ◽  
Polarizable Body ◽  
Phase Spectra

The authors discussed the behavior of the resistivity spectra by means of the Cole‐Cole dispersion model. They also discussed the corrections with which the petrophysical resistivity spectrum can be reduced into an apparent resistivity spectrum caused by a polarizable body embedded in an unpolarizable environment. The application of the Cole‐Cole dispersion model is a marked step forward in spectral IP analysis. However, closer attention must be paid to the assumptions and approaches on which the authors base the relations between the petrophysical and apparent spectra. The authors based their relations between the true and apparent spectra on the use of the dilution factor [Formula: see text]. In accordance with the definition by Seigel (1959), they assumed that [Formula: see text] is a real constant (independent of frequency) over the whole frequency range under consideration. First consider the justification for the assumption of the existence of a constant factor [Formula: see text] in the light of an example calculated for phase spectra. Similar considerations could also be made with the aid of amplitude spectra.

The 14 September 1995 (M = 7.3) Copala, Mexico, earthquake: A source study using teleseismic, regional, and local data

1997 ◽  
Vol 87 (4) ◽  
pp. 999-1010
Author(s):  
F. Courboulex ◽  
M. A. Santoyo ◽  
J. F. Pacheco ◽  
S. K. Singh
Keyword(s):  
Time Window ◽  
Time Function ◽  
Source Process ◽  
Source Time Function ◽  
Nonlinear Method ◽  
Local Data ◽  
Plate Interface ◽  
Linear Inversion ◽  
Field Source ◽  
Mexico Earthquake

Abstract We analyze source characteristics of the 14 September 1995, Copala, Mexico, earthquake (M = 7.3) using teleseismic, regional, and local seismograms. In the analysis of the teleseismic and the regional seismic waves, we apply the empirical Green's function (EGF) technique. The recording of an appropriate aftershock is taken as the EGF and is used to deconvolve the mainshock seismogram, thus obtaining an apparent far-field source-time function at each station. The deconvolution has been done using surface waves. For teleseismic data, we apply a spectral deconvolution method that enables us to obtain 37 apparent source-time functions (ASTFs) at 29 stations. In the analysis of the regional broadband seismograms, we use two different aftershocks as EGF, and the deconvolution is performed in the time domain with a nonlinear method, imposing a positivity constraint, and the best azimuth for the directivity vector is obtained through a grid-search approach. We also analyze two near-source accelerograms. The traces are inverted for the slip distribution over the fault plane by applying a linear inversion technique. With the aid of a time-window analysis, we obtain an independent estimation of the source-time function and a more detailed description of the source process. The analysis of the three datasets permits us to deduce the main characteristics of the source process. The rupture initiated at a depth of 16 km and propagated in two directions: updip along the plate interface toward 165° N and toward 70° N. The source duration was between 12 and 14 sec, with the maximum of energy release occurring 8 sec after the initiation of the rupture. The estimated rupture dimension of 35 × 45 km is about one-fourth of the aftershock area. The average dislocation over the fault was 1.4 m (with a maximum dislocation of 4.1 m located 10 km south of the hypocenter), which gives roughly 1 MPa as the average static stress drop.

The Effect of Directional Spreading on Interaction of Focused Wave Groups With a Cylinder

2004 ◽  
Author(s):  
Eugeny V. Buldakov ◽  
Rodney Eatock Taylor ◽  
Paul H. Taylor
Keyword(s):  
Numerical Solutions ◽  
Amplitude Spectrum ◽  
Wave Group ◽  
Helmholtz Equations ◽  
Incoming Wave ◽  
Wave Groups ◽  
Practical Applications ◽  
Amplitude Spectra ◽  
Focused Wave ◽  
Focused Wave Group

The problem of diffraction of a directionally spread focused wave group by a bottom-seated circular cylinder is considered from the view point of second-order perturbation theory. After applying the time Fourier transform and separation of vertical variable the resulting two-dimensional non-homogeneous Helmholtz equations are solved numerically using finite differences. Numerical solutions of the problem are obtained for JONSWAP amplitude spectra for the incoming wave group with various types of directional spreading. The results are compared with the corresponding results for a unidirectional wave group of the same amplitude spectrum. Finally we discuss the applicability of the averaged spreading angle concept for practical applications.

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