wavefield jQ+ and j p − at depth level 1 mz − , this extrapolation step yields an estimate of the total wavefield, being denoted by j p < >at intermediate depth level nz ( ) 1 m n m z z z − < < : * 0 0 1 1 0 0 1 1 0 ( , ) ( , ) ( , ) ( , ) ( , ) j n n m j m n m j m p z z Wzz Qz z Wzz pz z + − − − − − < >= + (5) * , WW represent propagation operator and its conjugate complex respectively. Next, a full waveform inversion step is applied: 0 0 0 ( , ) ( , ) ( , ) j n j n j n p z z p z z p z z =< >+Δ (6) 0 0 0 1 ( , ) ( , ) ( , ) ( , ) m j n n l k l l kj l l m k p z z G z z z z p z z χ = − Δ = ∑ ∑ (7) yielding an update of the velocities in each gridpoint of layer( ) 1, m m z z − and an update of the wavefield at mz ,G refers to Green’s function: 0 0 1 1 0 0 ( , ) ( , ) ( , ) ( , ) j m m m j m j m p z z W z z Q z z p z z + + − − = +Δ (8) * 0 0 1 1 0 1 0 ( , ) ( , ) ( , ) ( , ) j m m m j m j m Q z z W z z p z z p z z − − − − − = +Δ (9) After completion, the updated velocities in layer( ) 1, m m z z − as well as the reflectivity and updated wavefield at depth level mz are known, we can apply the following migration and inversion process at deeper depth recursively. 2.2 Contrast source inversion Figure 1．Configuration of the scattering problem
RkJQdWJsaXNoZXIy MjM0NDE=