FLUCTUATIONS OF THE MODAL ARRIVAL TIMES DUE TO LINEAR INTERNAL WAVES: APPLICATION TO INVERSION

2006 ◽  
Vol 14 (04) ◽  
pp. 469-487 ◽  
Author(s):  
GERALDINE BOUCHAGE ◽  
MICHAEL I. TAROUDAKIS
Keyword(s):  
Travel Time ◽  
Internal Waves ◽  
Acoustic Field ◽  
Sound Speed ◽  
Inversion Method ◽  
Perturbation Approach ◽  
Arrival Times ◽  
Inversion Procedure ◽  
Time Information ◽  
A Current

It is well known that internal waves in the ocean are an important source of environmental variability which has serious effects in the structure of an acoustic field due to a known source. When measurements of the acoustic field form the input data for an inversion procedure aiming at the recovery of the environmental parameters, the information they carry on includes the internal wave effects. It is therefore natural to assume that neglecting the effects of the internal waves in an inversion procedure based on acoustic field measurements, errors are induced in the inversion. The paper deals with this problem and addresses the case of inversion schemes using travel time information of an acoustic signal. Using a statistical 2D model of the internal waves, based on the Garrett and Munk spectrum, the spatial and temporal evolution of the internal waves field as well as the fluctuations of the sound speed profile is estimated for a characteristic shallow-water environment. Considering a sound speed anomaly in the water column as the oceanographic feature to be recovered, the paper studies the influence of the internal waves field on the modal travel time information obtained through the propagation of a tomographic signal through this environment. The sound speed anomaly denoted as "current" is described by a suitable Gaussian function. Using an analytical expression based on a perturbation approach, the difference in the modal arrival times calculated for a background environment and a perturbed one (considering that the sound speed perturbations are due either to a current or to the summation of a current and of the internal waves field) was calculated for each propagating mode of the waveguide. These calculations led to the conclusion that the internal waves have a non-negligible impact on the arrival times and that the maximum amplitude of a current can be under- or overestimated of several meters per second when these waves are not taken into account in the inversion method, whereas they are present in the oceanic medium.

Tomography without rays

1993 ◽  
Vol 83 (2) ◽  
pp. 509-528 ◽  
Author(s):  
Charles J. Ammon ◽  
John E. Vidale
Keyword(s):  
Simulated Annealing ◽  
Travel Time ◽  
Velocity Structure ◽  
Random Noise ◽  
Time Inversion ◽  
Arrival Times ◽  
Inversion Technique ◽  
Travel Time Inversion ◽  
First Arrival ◽  
Inversion Procedure

Abstract We present two new techniques for the inversion of first-arrival times to estimate velocity structure. These travel-time inversion techniques are unique in that they do not require the calculation of ray paths. First-arrival times are calculated using a finite-difference scheme that iteratively solves the eikonal equations for the position of the wavefront. The first inversion technique is a direct extension of linearized waveform inversion schemes. The nonlinear relationship between the observed first-arrival times and the model slowness is linearized using a Taylor series expansion and a solution is found by iteration. For a series of two-dimensional numerical tests, with and without random noise, this travel-time inversion procedure accurately reconstructed the synthetic test models. This iterative inversion procedure converges quite rapidly and remains stable with further iteration. The second inversion technique is an application of simulated annealing to travel-time topography. The annealing algorithm is a randomized search through model space that can be shown to converge to a global minimum in well-posed problems. Our tests of simulated annealing travel-time topography indicate that, in the presence of less than ideal ray coverage, significant artifacts may be introduced into the solution. The linearized inversion scheme outperforms the nonlinear simulated annealing approach and is our choice for travel-time inversion problems. Both techniques are applicable to a variety of seismic problems including earthquake travel-time tomography, reflection, refraction/wide-angle reflection, borehole, and surface-wave phase-velocity tomography.

scholarly journals Plasma flows and sound-speed perturbations in the average supergranule

2021 ◽  
Vol 646 ◽  
pp. A184
Author(s):  
David Korda ◽  
Michal Švanda
Keyword(s):  
Travel Time ◽  
Sound Speed ◽  
Deep Structure ◽  
Solar Rotation ◽  
Vertical Component ◽  
Inversion Method ◽  
Time Averaging ◽  
Vertical Flow ◽  
Near Surface ◽  
Time Distance

Context. Supergranules create a peak in the spatial spectrum of photospheric velocity features. Even though they have some properties of convection cells, their origin is still being debated in the literature. The time–distance helioseismology constitutes a method that is suitable for investigating the deep structure of supergranules. Aims. Our aim is to construct the model of the flows in the average supergranular cell using fully consistent time–distance inverse methodology. Methods. We used the Multi-Channel Subtractive Optimally Localised Averaging inversion method with regularisation of the cross-talk. We combined the difference and the mean travel-time averaging geometries. We applied this methodology to travel-time maps averaged over more than 104 individual supergranular cells. These cells were detected automatically in travel-time maps computed for 64 quiet days around the disc centre. The ensemble averaging method allows us to significantly improve the signal-to-noise ratio and to obtain a clear picture of the flows in the average supergranule. Results. We found near-surface divergent horizontal flows which quickly and monotonously weakened with depth; they became particularly weak at the depth of about 7 Mm, where they even apparently switched sign. The amplitude of the ‘reversed’ flow was comparable to the background flows. The inverted vertical flows and sound-speed perturbations were spoiled by unknown systematic errors. To learn about the vertical component, we integrated the continuity equation from the surface. The derived estimates of the vertical flow depicted a sub-surface increase from about 5 m s−1 at the surface to about 35 m s−1 at the depth of about 3 Mm followed by a monotonous decrease to greater depths. The vertical flow remained positive (an upflow) and became indistinguishable from the background at the depth of about 15 Mm. We further detected a systematic flow in the longitudinal direction. The course of this systematic flow with depth agrees well with the model of the solar rotation in the sub-surface layers.

PREDICTION OF THE TRANSPORT PROPERTIES OF SF6 WITH O2, CO2, CF4, N2 AND CH4 MIXTURES AT LOW DENSITY BY THE INVERSION METHOD (PART II)

2004 ◽  
Vol 03 (01) ◽  
pp. 69-90 ◽  
Author(s):  
BEHZAD HAGHIGHI ◽  
ALIREZA HASSANI DJAVANMARDI ◽  
MOHAMAD MEHDI PAPARI ◽  
MOHSEN NAJAFI
Keyword(s):  
Potential Energy ◽  
Diffusion Coefficients ◽  
Potential Energy Function ◽  
Model Potential ◽  
Inversion Method ◽  
Low Density ◽  
Initial Model ◽  
Lennard Jones ◽  
Inversion Procedure ◽  
And Diffusion

Viscosity and diffusion coefficients for five equimolar binary gas mixtures of SF 6 with O 2, CO 2, CF 4, N 2 and CH 4 gases are determined from the extended principle of corresponding states of viscosity by the inversion technique. The Lennard–Jones 12-6 (LJ 12-6) potential energy function is used as the initial model potential required by the technique. The obtained interaction potential energies from the inversion procedure reproduce viscosity within 1% and diffusion coefficients within 5%.

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