ASYMPTOTIC APPROXIMATION OF OCEAN-ACOUSTIC PULSE PROPAGATION IN THE TIME DOMAIN

2004 ◽  
Vol 12 (02) ◽  
pp. 197-215 ◽  
Author(s):  
G. N. MAKRAKIS ◽  
E. K. SKARSOULIS
Keyword(s):  
Time Domain ◽  
Pulse Propagation ◽  
Acoustic Pulse ◽  
Normal Modes ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Fourier Synthesis ◽  
The Time Domain

Broadband and narrowband time-domain asymptotics are proposed for pulse propagation in range-independent ocean environments. The broadband approximation results by applying the stationary-phase method to the Fourier transform of the Green's function, expressed in terms of normal modes. The narrowband approximation is obtained by incorporating the shape function of the emitted signal — assumed Gaussian — into the phase term and applying the steepest-descent method. The roots of the frequency-derivative of the phase are located in the complex plane by using a second-order expansion of the eigenvalues. The performance of the two approximations is studied numerically. While the broadband approximation improves with increasing bandwidth, the narrowband approximation improves when the bandwidth decreases. Both approximations improve with increasing range, and they can be used for delivering time-domain results more efficiently than with standard Fourier synthesis.

Second-Order Fourier Synthesis of Broadband Acoustic Signals Using Normal Modes

1997 ◽  
Vol 05 (04) ◽  
pp. 355-370 ◽  
Author(s):  
E. K. Skarsoulis
Keyword(s):  
Time Domain ◽  
Normal Modes ◽  
Acoustic Signals ◽  
Second Order ◽  
Single Frequency ◽  
Closed Form Expression ◽  
Fourier Synthesis ◽  
Eigenvalues And Eigenfunctions ◽  
Intermediate Order ◽  
The Time Domain

A scheme for approximate normal-mode calculation of broadband acoustic signals in the time domain is proposed based on a second-order Taylor expansion of eigenvalues and eigenfunctions with respect to frequency. For the case of a Gaussian impulse source a closed-form expression is derived for the pressure in the time domain. Using perturbation theory, analytical expressions are obtained for the involved first and second frequency-derivatives of eigenvalues and eigenfunctions. The proposed approximation significantly accelerates arrival-pattern calculations, since the eigenvalues, the eigenfunctions and their frequency-derivatives need to be calculated at a single frequency, the central frequency of the source. Furthermore, it offers a satisfactory degree of accuracy for the lower and intermediate order modes. This is due to the fact that essential wave-theoretic mechanisms such as dispersion and frequency dependence of mode amplitudes are contained in the representation up to a sufficient order. Numerical results demonstrate the efficiency of the method.

INCLUDING DISPERSION AND ATTENUATION IN TIME DOMAIN MODELING OF PULSE PROPAGATION IN SPATIALLY-VARYING MEDIA

2004 ◽  
Vol 12 (04) ◽  
pp. 501-519 ◽  
Author(s):  
GUY V. NORTON ◽  
JORGE C. NOVARINI
Keyword(s):  
Wave Equation ◽  
Time Domain ◽  
Pulse Propagation ◽  
Acoustic Pulse ◽  
Dispersive Media ◽  
Linear Wave ◽  
Domain Modeling ◽  
Time Domain Modeling ◽  
Media Work ◽  
The Time Domain

Modeling of acoustic pulse propagation in nonideal fluids requires the inclusion of attenuation and its causal companion, dispersion. For the case of propagation in a linear, unbounded medium Szabo developed a convolutional propagation operator which, when introduced into the linear wave equation, accounts for attenuation and causal dispersion for any medium whose attenuation possesses a generalized Fourier transform. Utilizing a one dimensional Finite Difference Time Domain (FDTD) model Norton and Novarini showed that for an unbounded isotropic medium, the inclusion of this unique form of the convolutional propagation operator into the wave equation correctly carries the information of attenuation and dispersion into the time domain. This paper addresses the question whether or not the operator can be used as a basic building block for pulse propagation in a spatially dependent dispersive environment. The operator is therefore used to model 2-D pulse propagation in the presence of an interface separating two dispersive media. This represents the simplest description of a spatially dependent dispersive media. It was found that the transmitted and backscattered fields are in excellent agreement with theoretical expectations demonstrating the effectiveness of the local operator to model the field in spatially dependent dispersive media. [Work supported by ONR/NRL.]

Thermoacoustic interplay between intrinsic thermoacoustic and acoustic modes: non-normality and high sensitivities

2019 ◽  
Vol 878 ◽  
pp. 190-220 ◽  
Author(s):  
Francesca M. Sogaro ◽  
Peter J. Schmid ◽  
Aimee S. Morgans
Keyword(s):  
Time Domain ◽  
Time Scale ◽  
Initial Conditions ◽  
Normal Modes ◽  
Time Domain Analysis ◽  
Normal Behaviour ◽  
Optimal Perturbation ◽  
Acoustic Modes ◽  
Energy Growth ◽  
The Time Domain

This study analyses the interplay between classical acoustic modes and intrinsic thermoacoustic (ITA) modes in a simple thermoacoustic system. The analysis is performed using a frequency-domain low-order network model as well as a time-domain spatially discretised model. Anti-correlated modal sensitivities are found to arise due to a pairwise interplay between acoustic and ITA modes. The magnitude of the sensitivities increases as the interplay between the modes grows stronger. The results show a global behaviour of the modes linked to the presence of exceptional points in the spectrum. The time-domain analysis results in a delay-differential equation and allows the investigation of non-normal behaviour and its consequences. Pseudospectral analysis reveals that energy amplification is crucially linked to an interplay between acoustic and ITA modes. While higher non-orthogonality between two modes is correlated with peaks in modal sensitivity, transient energy growth does not necessarily involve the most sensitive modes. In particular, growth estimates based on the Kreiss constant demonstrate that transient amplification relies critically on the proximity of the non-normal modes to the imaginary axis. The time scale for transient amplification is identified as the flame time delay, which is further corroborated by determining the optimal initial conditions responsible for the bulk of the non-modal energy growth. The flame is identified as an active and dominant contributor to energy gain. The frequency of the optimal perturbation matches the acoustic time scale, once more confirming an interplay between acoustic and ITA structures. Flame-based amplification factors of two to five are found, which are significant when feeding into the acoustic dynamics and eventually triggering nonlinear limit-cycle behaviour.

scholarly journals Time-domain observation and synthesis of split spheroidal and torsional free oscillations of the 1960 chilean earthquake: Preliminary results

1978 ◽  
Vol 68 (2) ◽  
pp. 325-332 ◽  
Author(s):  
Seth Stein ◽  
Robert J. Geller
Keyword(s):  
Time Domain ◽  
Normal Modes ◽  
Wave Form ◽  
Central Frequency ◽  
Complex Wave ◽  
Location Depth ◽  
The Time Domain ◽  
Theoretical Results ◽  
Good Agreement ◽  
Chilean Earthquake

Abstract The rotationally and elliptically split normal modes of the earth are observed for the 1960 Chilean earthquake by analysis in the time domain. One hundred and fifty hours of the Isabella, California, strain record are narrow band filtered about the central frequency of each split multiplet to isolate the complex wave form resulting from the interference of the different singlets. We compute synthetic seismograms using our previous theoretical results, which show the dependence of the amplitude and phase of the singlets on source location, depth, mechanism, and the position of the receiver. By comparing these synthetics to the filtered record, we conclusively demonstrate the splitting of modes whose splitting had not been definitely resolved: torsional modes (0T3, 0T4) and spheroidal modes (0S4, 0S5). The splitting of 0S2 and 0S3 is reconfirmed. We obtain good agreement between the synthetics and the filtered data for a source mechanism (previously determined from long-period surface waves) of thrust motion on a shallow dipping fault.

Green function method for the time domain simulation of pulse propagation

2014 ◽  
Vol 53 (16) ◽  
pp. 3533 ◽  
Author(s):  
Jing Huang ◽  
Jianquan Yao ◽  
Degang Xu ◽  
Runhua Li
Keyword(s):  
Green Function ◽  
Time Domain ◽  
Function Method ◽  
Pulse Propagation ◽  
Time Domain Simulation ◽  
Green Function Method ◽  
The Time Domain

scholarly journals Earth’s free oscillations excited by the 2011 Tohoku earthquake recorded in multiple GPS networks

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Cheng-Yin Chu ◽  
Benjamin F. Chao ◽  
Hao Ding ◽  
Linguo Yuan
Keyword(s):  
Time Domain ◽  
Near Field ◽  
Sampling Rate ◽  
Normal Modes ◽  
Tohoku Earthquake ◽  
High Sensitivity ◽  
The 2011 Tohoku Earthquake ◽  
Optimal Sequence ◽  
Spectral Peaks ◽  
The Time Domain

AbstractWe search in the continuous GPS 3-D displacement data for the signals of the normal modes of Earth’s free oscillation that were excited by the 2011 Mw 9.0 Tohoku earthquake. A previous study has reported such a detection; we here conduct a more comprehensive and detailed study. We use GPS data from three separate networks: (i) about 1000 stations from the Japan GEONET; (ii) about 600 stations from the western USA PBO; and (iii) about 140 stations of the global IGS, and solve and form records of 21 h length at 30-s sampling rate. We conduct various multiple-record stacking methods: the frequency-domain power spectrum stacking that reduces the variance of the noises, and the time-domain stackings that boost the SNR of target modes while suppressing the non-target modes. We find the time-domain stacking method of optimal sequence estimation (OSE) to be the most effective, which show clearly high sensitivity and detectability of the modes in the spectrum. For the near-field GEONET where all excited modes have anti-nodes, all the spheroidal fundamental modes 0S9–0S43 below 5 MHz and some of the lower-degree overtones as well as most of the low-degree toroidal fundamental modes show up as prominent spectral peaks against the PREM model eigenfrequencies. The PBO sees less strong (being far-field and generally off-antinodes), but still clearly identifiable spectral peaks of the fundamental modes. The global IGS network data detect barely a handful of these modes because of its sparsity and small numbers of stations. We thus demonstrate that GPS does actually record the tiny seismic signals that can be revealed by means of multiple-record stacking methods, potentially useful for studying earthquake source mechanisms exciting the normal modes.

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