From PM equation we derive muhi-dimensionay diffusion filtering equation discrete formula and its stable condition. We construct multi-scale decomposition and reconstruction method based on diffusion filtering, and provide two specific implementation plans. Application in practical seismic data shows that the method is reasonable and reliable. In the first plan 2D Fourier wave-number spectrum main energy is away from spectrum center with increase of scale, and residual signal acts at high wave numbers, which shows perfect application in random noise suppression. In the second plan 2D Fourier wave-number spectrum energy is close to spectrum center with increase of scale, and residual signal acts at low wave numbers, which shows perfect application in low-frequency reverse time migration noise suppression. The method computation is simple and easy to implement. It provides a multi-scale decomposition and reconstruction method for signal processing. It may has great application in seismic signal processing.

We present an equivalent dual elastic wave separation equation, which simulates particle-velocity, pressure, divergence and curl fields in pure P- and S- modes. The method is used in full elastic wave numerical simulations. We give complete derivations of explicit high-order staggered-grid finite difference discrete equations, together with stability condition, dispersion relation and perfectly matched layer (PML) absorbing boundary condition. Theoretical analysis and numerical simulations show that pare P-waves and S-waves in final numerical results are completely separated in the method. Effect of absorbing boundary is perfect. Storage and computing time requirements are greatly reduced compared with previous works.