Shifted first arrival point travel time NMO inversion

Serious stretch appears in shallow long offsset signals after NMO correction. In this article we study the generation mechanism of NMO stretch, demonstrate that the conventional travel time equation cannot accurately describe the travel time of the samples within the same reflection wavelet. As a result, conventional NMO inversion based on the travel time of the wavelet＇s central point occurs with errors. In this article, a travel time equation for the samples within the same wavelet is reconstructed through our theoretical derivation （the shifted first arrival point travel time equation）, a new NMO inversion method based on the wavelet＇s first arrival point is proposed. While dealing with synthetic data, the semblance coefficient algorithm equation is modified so that wavelet first arrival points can be extracted. After that, NMO inversion based on the new velocity analysis is adopted on shot offset records. The precision of the results is significantly improved compared with the traditional method. Finally, the block move NMO correction based on the first arrival points travel times is adopted on long offset records and non-stretched results are achieved, which verify the proposed new equation.

Arrival time measurements of first arrival phases P and PKIKP using the method of fixed scale wavelet transformation ratio

The arrival times of first teleseismic phases are difficult to be measured precisely because of slowly and gradually changed onsets and weak amplitudes. The arrival times measured manually are usually behind the real ones. In this paper, using the ratio method of fixed scale wavelet transformations improved by us, the arrival times for the first arrival phases (such as P and PKIKP) at the teleseismic and far-teleseismic distances were measured. The results are reasonable and reliable based on the analysis and discussion of the reliabilities and errors.

Wavefield reconstruction inversion with weaktotal-variation constraint based on first arrival traveltime tomography

The objective function of full waveform inversion is a strong nonlinear function,the inversion process is not unique,and it is easy to fall into local minimum.Firstly,in the process of wavefield reconstruction,the wave equation is introduced into the construction of objective function as a penalty term to broaden the search space of solution and reduce the risk of falling into local minimum.In addition,there is no need to calculate the adjoint wavefield in the inversion process,which can significantly improve the calculation efficiency;Secondly,considering that the total variation constraint can effectively reconstruct the discontinuous interface in the velocity model,this paper introduces the weak total variation constraint to avoid the excessive smooth estimation of the model under the strong total variation constraint.The disadvantage of this strategy is that it is highly dependent on the initial model.In view of this,this paper takes the long wavelength initial model obtained by first arrival traveltime tomography as a prior model constraint,and proposes a weak total variation constrained wavefield reconstruction inversion method based on first arrival traveltime tomography.Numerical experimental results show that the new method reduces the dependence on the initial model,the interface description is more accurate,the error is reduced,and the iterative convergence efficiency is significantly improved.

OPTIMAL MODELS FOR THE FIRST ARRIVAL TIME DISTRIBUTION FUNCTION IN CONTINUOUS TIME－WITH A SPECIAL CASE

Optimal Models for first arrival time (rH) and first arrival target total return (WH) distribution functions on MDP in continuous time are presented. Asymptotic expansions of rH and WH are derived and expressed in simple, explicit forms, and some of their properties are discussed. Two methods to find an optimal policy for distribution function of rH are given. Several necessary and sufficient conditions for the existence of the optimal policy are obtained. This result leads to that the scope of finding the optimal policy is greatly reduced. A special case is also discussed and some deep results are given.

The Doppler effect induced by earthquakes:A case study of the Wenchuan MS8.0 earthquake

Seismologists have found that the first arrival frequencies of P waves at different seismic stations have different widths,that is,different periods or frequencies,and they think that this phenomenon can be used to identify whether a Doppler effect is induced by earthquakes.However,the fault rupture process of a real earthquake is so complex that it is difficult to identify a frequency shift similar to the Doppler effect.A method to identify whether a Doppler effect is induced by an earthquake is proposed here.If a seismic station is in the direction of fault rupture propagation,this station could observe a Doppler effect induced by the earthquake.The Doppler effect causes the frequency of the seismic wave to shift from low frequency to high frequency,and the high frequency amplitudes become mutually superimposed.Under the combined influences of the absorption effect,geometric spreading effect and Doppler effect,the high frequency amplitude of the seismic wave will gradually become higher than the low frequency amplitude with increasing epicentral distance.If we find that the high frequency amplitude is higher than the low frequency amplitude with increasing epicentral distance in the direction of fault rupture propagation,then there is a Doppler effect.The fault that generated the Wenchuan earthquake is a reverse fault,and its horizontal rupture propagation velocity was low.To link fault rupture propagation velocity with the Doppler effect and identify the Doppler effect more easily,we decompose three-component records into two directions:the direction of fault rupture propagation and the direction perpendicular to the fault rupture propagation along the fault plane.The initial components of the two directions are processed by wavelet transform.Several seismic stations in the direction of fault rupture propagation of the Wenchuan earthquake were selected,and it was found that with increasing epicentral distance,the high frequency amplitudes of the wavelet spectra become obviously higher than the low frequency amplitudes.It can be concluded that due to the existence of the Doppler effect,high frequency amplitudes can overcome the influences of the absorption and geometric spreading effects on seismic waves in the fault rupture propagation process.