Full-wave-equation True-amplitude Migration Based On Surface Wavefield Derivative Reconstruction

True amplitude migration is the development trend of seismic migration technology and an important technology in seismic exploration.The migration results can be used to analyze lithology and hydrocarbon.Solving the wave equation is the basis of seismic migration.To accurately solve the full wave equation,two initial conditions are required: one is the surface wave field value,and the other is the vertical partial derivative of the wavefield at the surface.Because conventional seismic acquisition system only receives the surface wavefield value and cannot provide the vertical partial derivative,traditional migration methods have to approximate the full wave equation,and this approximation can affect the amplitude-preserving performance.Aiming at this problem,two key scientific issues were studied:(1)derivation of theoretical calculation formula for the vertical partial derivative of the wavefield at the surface;(2)implementation of a full-wave-equation depth extrapolation for true amplitude migration based on the reconstruction of the surface wavefield derivative.Under the assumption that the free interface is horizontal,I derived the formula for calculating the vertical partial derivative of surface wavefield.The spatial derivative value of the wavefield can be calculated from the surface wavefield value without assuming that the velocity near the surface is laterally uniform.I use the spectral projection method to remove evanescent waves during depth extrapolation,and test the imaging performance of my proposed method through some experiments.In these experiments,I studied the amplitude preservation performance of migration methods through comparison of the calculated reflection coefficients obtained from the migration results with the theoretical reflection coefficients.Experimental results shown that our proposed method can provide true amplitudes while imaging the accurate structure position and have a better amplitude-preserving performance than that of the reverse time migration algorithm.I compared my proposed method with a dual-sensor depth migration method in synthetic examples and a real seismic data test.Experimental results demonstrated that my proposed method has similar imaging performance to the dual-sensor depth migration method in synthetic examples.In real seismic data experiment,my method had better image quality.I proposed a new method for calculating the vertical partial derivative from the surface wavefield without making any assumptions about the surface conditions.Based on the calculated derivative,I implemented a depth-extrapolation-based full-wave-equation migration from topography using the direct downward continuation.I tested the imaging performance of my proposed method with several experiments.The results of the Marmousi model experiment shown that my proposed method is superior to the conventional reverse time migration algorithm in terms of imaging accuracy and amplitude-preserving performance at medium and deep depths.In the Canadian Foothills model experiment,I proved that my method can still accurately image complex structures and maintain amplitude under topographic scenario.