Time domain waveform inversion—A frequency domain view: How well we need to match waveforms?

1991 ◽  
Vol 81 (6) ◽  
pp. 2351-2370
Author(s):  
Zoltan A. Der ◽  
Robert H. Shumway ◽  
Michael R. Hirano
Keyword(s):  
Time Domain ◽  
High Frequency ◽  
Waveform Inversion ◽  
Quantitative Measure ◽  
Domain Modeling ◽  
Low Frequencies ◽  
Waveform Modeling ◽  
Time Domain Modeling ◽  
Frequency Components ◽  
The Time Domain

Abstract Waveform modeling in the time domain matches the various frequency components of seismic signals unevenly; the agreement is better at low frequencies and becomes progressively worse towards higher frequencies. The net effect of this kind of time-domain modeling is that the resolution in the spatial details of the source is less than optimal since the high-frequency components of the signal with their short wavelengths to resolve finer details do not fit the data. These problems are demonstrated by numerical simulations and by the reanalysis of some aspects of the El Golfo earthquake in using a new seismic imaging technique based on a generalization of an f-k algorithm. This procedure computes a statistic that can be used to derive confidence limits of the parameters sought in the inversion, thus providing a quantitative measure of the uncertainties in the results.

Frequency‐domain elastic wave modeling by finite differences: A tool for crosshole seismic imaging

Geophysics ◽  
1990 ◽  
Vol 55 (5) ◽  
pp. 626-632 ◽  
Author(s):  
R. Gerhard Pratt
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Equations Of Motion ◽  
Domain Modeling ◽  
Multiple Sources ◽  
State Equations ◽  
Migration Imaging ◽  
Time Domain Modeling ◽  
Frequency Components ◽  
The Time Domain

The migration, imaging, or inversion of wide‐aperture cross‐hole data depends on the ability to model wave propagation in complex media for multiple source positions. Computational costs can be considerably reduced in frequency‐domain imaging by modeling the frequency‐domain steady‐state equations, rather than the time‐domain equations of motion. I develop a frequency‐domain approach in this note that is competitive with time‐domain modeling when solutions for multiple sources are required or when only a limited number of frequency components of the solution are required.

3D Laplace-domain waveform inversion using a low-frequency time-domain modeling algorithm

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. R1-R13 ◽  
Author(s):  
Wansoo Ha ◽  
Seung-Goo Kang ◽  
Changsoo Shin
Keyword(s):  
Time Domain ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Domain Modeling ◽  
Laplace Domain ◽  
Long Wavelength ◽  
Velocity Models ◽  
Time Domain Modeling ◽  
The Time Domain ◽  
Domain Inversion

We have developed a Laplace-domain full-waveform inversion technique based on a time-domain finite-difference modeling algorithm for efficient 3D inversions. Theoretically, the Laplace-domain Green’s function multiplied by a constant can be obtained regardless of the frequency content in the time-domain source wavelet. Therefore, we can use low-frequency sources and large grids for efficient modeling in the time domain. We Laplace-transform time-domain seismograms to the Laplace domain and calculate the residuals in the Laplace domain. Then, we back-propagate the Laplace-domain residuals in the time domain using a predefined time-domain source wavelet with the amplitude of the residuals. The back-propagated wavefields are transformed to the Laplace domain again to update the velocity model. The inversion results are long-wavelength velocity models on large grids similar to those obtained by the original approach based on Laplace-domain modeling. Inversion examples with 2D Gulf of Mexico field data revealed that the method yielded long-wavelength velocity models comparable with the results of the original Laplace-domain inversion methods. A 3D SEG/EAGE salt model example revealed that the 3D Laplace-domain inversion based on time-domain modeling method can be more efficient than the inversion based on Laplace-domain modeling using an iterative linear system solver.

A Proposal for the Time Domain Modeling of Split Air Conditioners for Consumer Reimbursement Studies

ENERGYO ◽  
2018 ◽  
Author(s):  
Paulo Henrique Oliveira Rezende ◽  
Afonso Bernardino Almeida Junior ◽  
Isaque Nogueira Gondim ◽  
José Carlos Oliveira
Keyword(s):  
Time Domain ◽  
Domain Modeling ◽  
Air Conditioners ◽  
Time Domain Modeling ◽  
The Time Domain

Modeling and Transient Response of Cable Network

2012 ◽  
Vol 433-440 ◽  
pp. 2868-2873
Author(s):  
Xing Zhou ◽  
Zhen Yu Xiang ◽  
Er Wei Cheng ◽  
Li Si Fan
Keyword(s):  
Transmission Line ◽  
Time Domain ◽  
Modeling Method ◽  
Domain Model ◽  
Domain Modeling ◽  
Cable Network ◽  
Cable Networks ◽  
Time Domain Modeling ◽  
The Time Domain ◽  
Line Network

This paper introduces modeling method for calculating nodes responses of transmission-line network directly in the time domain. Arising from classical telegrapher equations, the time-domain model of transmission line is gained. The transmission-line model, together with transmission-line nodes model, form the network model. Using the time-domain modeling method, transient responses for two given networks are gained. The injection experiments to cable networks are done to validate the calculating results. The consistency of calculating results with measure results indicates the model is feasible.

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.]

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