disadvantage of this approach based on integral equation formulation is that the background medium is usually a simple homogeneous medium. Finite-difference based contrast source inversion(FDSCI) method is adaptive to the arbitrary inhomogeneous background medium[2,3,5,12], similar to the IE contrast source inversion method, the unknown contrast source and the unknown contrast function are updated alternately to reconstruct the scatters without requiring the solution of forward problem at each iteration step. An attractive feature of FDCSI approach is that the impendence matrix is only dependent on the background medium, which is invariant throughout the inversion process, Hence, the FD operator needs to be inverted only once and the results can be reused for multiple source positions. 2. THEORY 2.1 Joint migration and inversion In the joint migration and inversion process, first extrapolate the receiver wavefield from depth level 1 mz − to mz , then inversion process is applied at depth mz , and we will use the wavefield from all depth level which represents the internal and surface-related multiples. In full wavefield inversion process, the difference between the known background properties and the unknown real medium properties is inverted. Each gridpoint act as a point scatterer in the background medium, called as contrast source. The total wavefield in the true medium equals the sum of the wavefield of the primary sources in the background and the wavefield of all point scatterers in the background. The contrasts and the total wavefield are alternately updated until the total simulated wavefield matches the recorded wavefield at the detector positions. After that the full wavefield migration is applied to yield the angle-dependent reflectivity, which is solved as a constrained least-squares minimization problem. The two minimization process is in the same mathematic form[1]: 0 0 0 ( , ) (, ) (,) (, ) (,) min m m m m m m m Q z z UzzPzz VzzPzz − + − ⎡ ⎤ − + = ⎣ ⎦ (1) In which P represents the incident wavefield and Q refers to response of depth mz In the migration process, the matrices U and V represent reflectivity: 1 2 ( , ) ( , , , ) m m k U z z R R R = U U U L L (2) 1 2 ( , ) ( , , , ) m m k V z z R R R = I I I L L (3) In the inversion process, the matrices U and V are same and represent contrast: 1 2 ( , ) ( , ) ( , , , ) m m m m k U z z V z z χ χ χ = = L L (4) In the JMI process full wavefield extrapolation is applied from 1 mz − to mz , using the
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