Abstract: For desert seismic data with low signal-to-noise ratio，random noise is mainly non-stationary and non-Gaussian low-frequency colored noise． It is difficult to effectively identify and characterize seismic signals by using conventional noise suppression methods，resulting in the loss of signals with weak textural structure． The fractional order gradient operator is introduced，and a spatial fractional complex diffusion based seismic random noise suppression algorithm is proposed． The spatial fractional order gradient is used to enhance the weak texture and details of seismic signals，and the diffusion intensity is controlled according to the structures of seismic events under the complex diffusion framework． The synthetic seismic data and field desert seismic data are used to evaluate the performance of the proposed algorithm． The experimental results show that the spatial fractional complex diffusion filtering algorithm can suppress random noise and retain the effective signal structure in desert seismic data．

Key words: complex diffusion, fractional order gradient, nonlinear, desert random noise, seismic exploration