Research On The Application Of Shearlet Transform In Seismic Data Processing

Seismic exploration is affected by the field environment,and the collected seismic data often contains random noise and surface waves,which seriously affect the identification of effective seismic data;on the other hand,limited by the sampling cost and the actual sampling environment,the seismic data is prone to bad or dead channels.Therefore,it is necessary to perform interpolation and reconstruction processing on the collected seismic data to improve the quality of seismic data.This paper mainly studies the application effects of Shearlet transform in suppressing the random noise of seismic data,removing surface wave interference and interpolating and reconstructing missing seismic data.Shearlet transformation has a good application advantage in seismic data processing.Compared with other sparse transformation methods,Shearlet transformation has a better tightly supported structure,which can finely represent the distribution characteristics of seismic data in different frequency bands;at the same time,it can provide a unified transformation form for seismic data in discrete and continuous systems.Close to the optimal sparse representation effect;Shearlet transformation also has multi-scale and multi-directional characteristics,which can analyze the distribution characteristics of seismic data in the Shearlet domain from multiple angles.Random noise is a widespread interference in seismic data.The conventional method based.on sparse transformation suppresses the random seismic noise by setting a single threshold.This method will lose part of the effective seismic information in the process of removing the random noise.Based on the multi-scale and multi-directional decomposition characteristics of the Shearlet transform,this paper proposes to use the maximum noise distributed in each direction within a specific scale of the Shearlet domain as the noise of the scale layer distribution,and set a threshold that adaptively changes with the scale and direction to suppress random noise.The method in this paper can separate effective waves and random noises well,suppress random noises to the greatest extent,and retain more effective seismic information.Surface wave is a representative linear interference in seismic data.Conventional methods for removing surface wave interference include FK transformation and KL transformation.The FK transformation method will lose effective seismic information when removing seismic surface waves.The KL transformation method is based on the energy difference between the surface wave and the effective wave and recovers the surface waves and filter out,this method cannot completely remove surface waves.This paper combines the Shearlet transformation with the conventional surface wave removal method to propose a more reasonable and effective method for removing surface wave interference.First,the FK transformation filter is used to initially separate the part of the effective seismic data that does not contain surface waves.The area is converted to the Shearlet domain,and the KL transformation is used to accurately separate the surface wave and the effective wave in each scale and direction,and finally the effective seismic data is merged to obtain the surface wave removal result.The method is divided into two steps,which not only overcomes the shortcomings of FK transform losing effective signals,but also makes full use of the principal component analysis characteristics of KL transform in Shearlet domain,and has a better effect of removing surface wave interference from seismic data.Seismic data interpolation reconstruction is a very important part of seismic data processing.Based on the sparse transformation seismic data interpolation method,the interpolation reconstruction problem is converted into the corresponding minimization mathematical model for solution.This paper describes two conventional interpolation methods for missing seismic data:the minimum weighted norm method based on Fourier transform and the iterative weighted least square method based on Curvelet transform.Both methods have their own application limitations.The Fourier-based interpolation method is prone to aliasing,while the Curvelet-based interpolation method has limited reconstruction effects.Since Shearlet transform has multi-scale and multi-directional decomposition characteristics and excellent sparse representation characteristics compared with Fourier transform and Curvelet transform,this paper proposes an iterative weighted least square method based on Shearlet transform to reconstruct seismic data by interpolation.This method overcomes false frequency and reconstruction of missing seismic data have limited effects,which can better restore missing seismic data,achieve better interpolation reconstruction effects,obtain more complete seismic data,and improve seismic data quality.