High-order Staggered-Grid Finite Difference VSP Simulation And Data Processing

Vertical Seismic Profile(VSP)is a ground-induced,well-received seismic exploration technology.The technology has been widely used in seismic exploration because of the advantages of less interference,high precision,rich geological information,as well as obvious kinematic and dynamic characteristics.High-precision VSP data are obtained based on the numerical simulation of wave equation.And then the numerical VSP data are processed by various data processing methods.The whole process includes the main steps of theoretical study and formula derivation,program preparation,numerical VSP data acquisition,VSP data processing,interpretation and application,which basically completes all steps of the VSP theory,and provides an intuitive and profound understanding of this method.Firstly,the high-order finite difference scheme based on the staggered grid is deduced from the first-order velocity-stress acoustic wave equation,and the perfectly matched layer(PML)is added as the boundary condition for absorbing the artificial reflection.Then numerical acoustic wave propagation is carried out by programming and the influence of grid spacing,time step,differential precision,frequency of wavelet and velocity on the stability and accuracy of numerical wavefields is discussed in detail.Based on the results of high-precision wavefields simulation,numerical VSP records are obtained by arranging the detectors inside the model to detect seismic waves with the source placed on the surface of the model.VSP records must be processed using a variety of data processing methods before it can be used.VSP data processing is a systematic project,and has no fixed process,for different data and purposes,the process can be different,but generally inseparable from a few core steps.This paper mainly studies the role of the core algorithms in VSP processing,including first-arrival extraction,up-and down-going wave alignment,wavefields separation,corridor superposition and so on.The first arrival extraction is a very important step in VSP processing,and its accuracy has a decisive effect on the final outcome.The article uses the cross-correlation method to obtain an ideal first arrival.The use of this method requires high similarity in shape between different traces,besides the first arrival of the standard trace selected to cross correlate other traces must be as accurate as possible.After that,the down-going wavefields can be rearranged along the depth direction simply by subtracting its first arrival time from each trace,and plus 2 times of its first arrival time to rearrange the up-going wavefields in the depth direction.Wavefields separation is another indispensable step in VSP data processing.In this work,the wavefields separation is performed by singular value decomposition(SVD),frequency-wavenumber domain method(f-k)and median filter(m-f),respectively,and both the advantages and disadvantages of the three methods are analyzed in detail.In general,the three methods can.achieve wavefields separation,however the processing results are dependent on data characteristics and the impact of the methods.The SVD method requires strict alignment of the up-and down-going wavefields,which needs high-accuracy first arrival.Due to the use of Fourier transform,the f-k method is easy to introduce extra noise.To properly use the median m-f method,the input data should be the aligned up-or down-going wavefeilds,otherwise the results will be bad,besides,the length of window also has a great impact on the results.In dealing with actual data,the most appropriate wavefields separation method should be selected in consideration of the characteristics of the data.The article finally describes the interpretations and applications of VSP data,and part of the applications are illustrated in detail by figures.