scholarly journals Wave-equation traveltime inversion with multifrequency bands: Synthetic and land data examples

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. B305-B315 ◽  
Author(s):  
Han Yu ◽  
Sherif M. Hanafy ◽  
Gerard T. Schuster
Keyword(s):  
Wave Equation ◽  
Velocity Model ◽  
Inversion Method ◽  
Data Sets ◽  
Traveltime Inversion ◽  
Numerical Tests ◽  
Classical Wave ◽  
Classical Wave Equation ◽  
Zero Offset ◽  
Starting Model

We have developed a wave-equation traveltime inversion method with multifrequency bands to invert for the shallow or intermediate subsurface velocity distribution. Similar to the classical wave-equation traveltime inversion, this method searches for the velocity model that minimizes the squared sum of the traveltime residuals using source wavelets with progressively higher peak frequencies. Wave-equation traveltime inversion can partially avoid the cycle-skipping problem by recovering the low-wavenumber parts of the velocity model. However, we also use the frequency information hidden in the traveltimes to obtain a more highly resolved tomogram. Therefore, we use different frequency bands when calculating the Fréchet derivatives so that tomograms with better resolution can be reconstructed. Results are validated by the zero-offset gathers from the raw data associated with moderate geometric irregularities. The improved wave-equation traveltime method is robust and merely needs a rough estimate of the starting model. Numerical tests on the synthetic and field data sets validate the above claims.

scholarly journals 3D wave-equation dispersion inversion of Rayleigh waves

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. R673-R691 ◽  
Author(s):  
Zhaolun Liu ◽  
Jing Li ◽  
Sherif M. Hanafy ◽  
Gerard Schuster
Keyword(s):  
Wave Equation ◽  
Wave Velocity ◽  
Rayleigh Waves ◽  
Waveform Inversion ◽  
Shear Velocity ◽  
Velocity Model ◽  
Azimuth Angle ◽  
Inversion Method ◽  
S Wave ◽  
Starting Model

The 2D wave-equation dispersion (WD) inversion method is extended to 3D wave-equation dispersion inversion of surface waves for the shear-velocity distribution. The objective function of 3D WD is the frequency summation of the squared wavenumber [Formula: see text] differences along each azimuth angle of the fundamental or higher modes of Rayleigh waves in each shot gather. The S-wave velocity model is updated by the weighted zero-lag crosscorrelation between the weighted source-side wavefield and the back-projected receiver-side wavefield for each azimuth angle. A multiscale 3D WD strategy is provided, which starts from the pseudo-1D S-velocity model, which is then used to get the 2D WD tomogram, which in turn is used as the starting model for 3D WD. The synthetic and field data examples demonstrate that 3D WD can accurately reconstruct the 3D S-wave velocity model of a laterally heterogeneous medium and has much less of a tendency to getting stuck in a local minimum compared with full-waveform inversion.

Wave‐equation traveltime inversion

Geophysics ◽  
1991 ◽  
Vol 56 (5) ◽  
pp. 645-653 ◽  
Author(s):  
Y. Luo ◽  
G. T. Schuster
Keyword(s):  
Wave Equation ◽  
Ray Tracing ◽  
High Frequency ◽  
Velocity Model ◽  
Head Wave ◽  
Inversion Method ◽  
Diffraction Reflection ◽  
Traveltime Inversion ◽  
Wave Inversion ◽  
Full Wave

This paper presents a new traveltime inversion method based on the wave equation. In this new method, designated as wave‐equation traveltime inversion (WT), seismograms are computed by any full‐wave forward modeling method (we use a finite‐difference method). The velocity model is perturbed until the traveltimes from the synthetic seismograms are best fitted to the observed traveltimes in a least squares sense. A gradient optimization method is used and the formula for the Frechét derivative (perturbation of traveltimes with respect to velocity) is derived directly from the wave equation. No traveltime picking or ray tracing is necessary, and there are no high frequency assumptions about the data. Body wave, diffraction, reflection and head wave traveltimes can be incorporated into the inversion. In the high‐frequency limit, WT inversion reduces to ray‐based traveltime tomography. It can also be shown that WT inversion is approximately equivalent to full‐wave inversion when the starting velocity model is “close” to the actual model. Numerical simulations show that WT inversion succeeds for models with up to 80 percent velocity contrasts compared to the failure of full‐wave inversion for some models with no more than 10 percent velocity contrast. We also show that the WT method succeeds in inverting a layered velocity model where a shooting ray‐tracing method fails to compute the correct first arrival times. The disadvantage of the WT method is that it appears to provide less model resolution compared to full‐wave inversion, but this problem can be remedied by a hybrid traveltime + full‐wave inversion method (Luo and Schuster, 1989).

First-arrival traveltime inversion of seismic diving waves observed on undulant surface

2021 ◽  
Vol 225 (2) ◽  
pp. 1020-1031
Author(s):  
Huachen Yang ◽  
Jianzhong Zhang ◽  
Kai Ren ◽  
Changbo Wang
Keyword(s):  
Turning Points ◽  
Analytical Formula ◽  
Velocity Model ◽  
Western China ◽  
Inversion Method ◽  
Mountain Area ◽  
Traveltime Inversion ◽  
Static Correction ◽  
Velocity Models ◽  
First Arrival

SUMMARY A non-iterative first-arrival traveltime inversion method (NFTI) is proposed for building smooth velocity models using seismic diving waves observed on irregular surface. The new ray and traveltime equations of diving waves propagating in smooth media with undulant observation surface are deduced. According to the proposed ray and traveltime equations, an analytical formula for determining the location of the diving-wave turning points is then derived. Taking the influence of rough topography on first-arrival traveltimes into account, the new equations for calculating the velocities at turning points are established. Based on these equations, a method is proposed to construct subsurface velocity models from the observation surface downward to the bottom using the first-arrival traveltimes in common offset gathers. Tests on smooth velocity models with rugged topography verify the validity of the established equations, and the superiority of the proposed NFTI. The limitation of the proposed method is shown by an abruptly-varying velocity model example. Finally, the NFTI is applied to solve the static correction problem of the field seismic data acquired in a mountain area in the western China. The results confirm the effectivity of the proposed NFTI.

Traveltime information-based wave-equation inversion

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCC27-WCC36 ◽  
Author(s):  
Yu Zhang ◽  
Daoliu Wang
Keyword(s):  
Wave Equation ◽  
Conventional Method ◽  
Seismic Data ◽  
Waveform Inversion ◽  
Back Propagation ◽  
Velocity Model ◽  
Data Fitting ◽  
Inversion Method ◽  
New Wave ◽  
Seismic Record

We propose a new wave-equation inversion method that mainly depends on the traveltime information of the recorded seismic data. Unlike the conventional method, we first apply a [Formula: see text] transform to the seismic data to form the delayed-shot seismic record, back propagate the transformed data, and then invert the velocity model by maximizing the wavefield energy around the shooting time at the source locations. Data fitting is not enforced during the inversion, so the optimized velocity model is obtained by best focusing the source energy after a back propagation. Therefore, inversion accuracy depends only on the traveltime information embedded in the seismic data. This method may overcome some practical issues of waveform inversion; in particular, it relaxes the dependency of the seismic data amplitudes and the source wavelet.

Radiation and Response of Cylindrical Beams Excited by Sound

1972 ◽  
Vol 94 (1) ◽  
pp. 139-147 ◽  
Author(s):  
J. R. Bailey ◽  
F. J. Fahy
Keyword(s):  
Wave Equation ◽  
Pure Tone ◽  
Experimental Program ◽  
Acoustic Excitation ◽  
Resonant Response ◽  
Reverberation Chamber ◽  
At Resonance ◽  
Classical Wave ◽  
Theoretical Predictions ◽  
Classical Wave Equation

The sound radiated from an unbaffled cylindrical beam vibrating transversely at resonance is calculated by solution of the classical wave equation subject to the boundary conditions imposed by the motion of the beam. The interaction of sound and vibration is then demonstrated by using a theory based on the principle of reciprocity to predict the resonant response of a cylindrical beam to acoustic excitation. The results show that radiation and resonant response are highly frequency dependent. An experimental program is also reported. The power radiated from three cylindrical beams vibrating at resonance and the resonant response of the beams to pure-tone acoustic excitation are measured in a reverberation chamber. The experimental results agree well with the theoretical predictions.

Classical wave equation in fluid filament stretching

1988 ◽  
Vol 27 (5) ◽  
pp. 466-476 ◽  
Author(s):  
S. Kase ◽  
T. Nishimura
Keyword(s):  
Wave Equation ◽  
Filament Stretching ◽  
Classical Wave ◽  
Fluid Filament ◽  
Classical Wave Equation

Generalization of traveltime inversion

Geophysics ◽  
1992 ◽  
Vol 57 (1) ◽  
pp. 9-14 ◽  
Author(s):  
Gérard C. Herman
Keyword(s):  
Time Windows ◽  
Velocity Model ◽  
Inversion Method ◽  
Nonlinear Inversion ◽  
Error Norm ◽  
Arrival Times ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
Use Of Data

A nonlinear inversion method is presented, especially suited for the determination of global velocity models. In a certain sense, it can be considered as a generalization of methods based on traveltimes of reflections, with the requirement of accurately having to determine traveltimes replaced by the (less stringent and less subjective) requirement of having to define time windows around main reflections (or composite reflections) of interest. It is based on an error norm, related to the phase of the wavefield, which is directly computed from wavefield measurements. Therefore, the cumbersome step of interpreting arrivals and measuring arrival times is avoided. The method is applied to the reconstruction of a depth‐dependent global velocity model from a set of plane‐wave responses and is compared to other methods. Despite the fact that the new error norm only makes use of data having a temporal bandwidth of a few Hz, its behavior is very similar to the behavior of the error norm used in traveltime inversion.

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