Seismic Modeling And Inversion Methods Based On Meshfree Wave Equation

Seismic modelling bridges the seismic wave with earth medium by wave propagation,promoting seismic inversion of the earth parameters.According to dynamics theory,we researched into seismic modelling base on wave equation with meshfree method,and discussed wave propagation in an inhomogeneous medium.Sequence,full waveform inversion using meshfree method is performed,giving more reliable inversion parameters and benefiting for seismic data processing and interpretation.Seismic modeling for complex medium using meshfree method is achieved by the discrete of the wave equation and the model with meshfree nodes.According to energy conservation,we derived the elastic wave equations based on weak-form meshfree method.As the radial point interpolation method(RPIM)behavior as Kronecker delta and also avoid dealing with the essential boundary which should be considered for moved least-square method,we get the acoustic wave equation according to the decouple principle of wave equation and its discrete equation based on MFree weak-form methods using radial point interpolation method shape functions.In order to improve the computational efficiency for full waveform inversion,we further derived the Local weak-form method and collocation method based on radial point interpolation.It is easy to get the multiscale-node internal for the medium with low-velocity body by meshfree method.And time-domain full waveform inversion is developed by truncated Newton method and the linear step length controlled by nonlinear theory,providing a more reliable geophysical information.A velocity-adaption node-created method is suggested to determine the interval and coordinates of the nodes according to the velocity and wave length.And then the model with low-velocity body is discrete by meshfree method,which reduces the calculation increasing of full waveform inversion.For the time-domain truncated Newton method,the number of forward modeling is a function of the number of shots and independent of the geophone array.At the same time,it is not needed to get the explicit Hessian,and therefore the requirement for storage decreases.The non-geological artifices were also depressed by the time-domain truncated Newton method.Starting from the Backtracking method,the linear step length optimal with nonlinear method was developed to ensure the inversion convergent.As the real earth performs non-elastic,seismic data modeling by meshfree method in viscoelastic medium match the real data perfectly,while basising for the multi-parameter inversion.We derived meshfree seismic wave equation for viscoelastic medium.To ensure the accuracy of the constant Q model within seismic frequency band,we studied an independent represention method based on generalized rheological body.Full waveform inversion gradient is constructed for viscoacoustic medium based on generalized rheological body.The analysis of seismic wave amplitude versus frequency for backpropagation in viscoacoustic medium is done.The optimal checkpointing method is introduced to obtain the gradient of full waveform inversion in viscous medium,which adapts the unstable of the viscous system.A double optimal checkpointing method is proposed to balance the efficiency,storage and computing wave field stability of full waveform inversion by viscoacoustic wave equation.Bad field data and computation efficiency constraints full waveform inversion in the actual application data.Incomplete data caused by irregular seismic acquisition geometry in complex surface and subsurface geological zone,bring noise to the gradient of full waveform inversion.The gradient interfere with noise is analyzed in the wave number domain,and the suppression of noise in wave number domain is used for the gentle geological structure.For steep dip geological formations,we investigated the ability of an approximate Hessian of total model and sub-models,and built the full waveform inversion with blocked model based on meshfree method,which improves the reliability of full waveform inversion.