Noise models by selection of transform coefficients

Abstract

A data set representing features of a geologic formation is formed from two or more signal acquisition data set representing independent aspects of the same wavefield. A wavelet transform is performed on the two or more signal acquisition data sets, and the data sets are further transformed to equalize signal portions of the data sets. Remaining differences in the data sets are interpreted as excess noise and are removed by different methods to improve the signal-to-noise ratio of any resulting data set.

1 .- 15 . (canceled) 
     
     
         16 . A method of reducing noise in a geophysical acquisition record, comprising:
 identifying a first data set representing a first aspect of a wavefield;   identifying a second data set representing a second aspect of the physical wavefield;   transforming the first data set and the second data set to a frequency-wavenumber domain;   applying a first filter to the transformed first data set to form a first equalized data set and a second filter to the transformed second data set to form a second equalized data set, wherein a signal part of the first equalized data set is equal to a signal part of the second equalized data set;   forming a noise model from the first equalized data set and the second equalized data set by subtracting each data point of the first equalized data set from a corresponding data point of the second equalized data set and retaining the value of the result;   linearly combining the first equalized data set and the second equalized data set to form a combined data set; and   using the noise model to remove noise from the combined data set.   
     
     
         17 . The method of  claim 16 , wherein at least the transforming the first data set and the second data set, the applying the first filter and the second filter, the forming the noise model, and the linearly combining are performed using a computer with a computer-readable medium containing instructions to perform the transforming the first data set and the second data set, the applying the first filter and the second filter, the forming the noise model, and the linearly combining. 
     
     
         18 . The method of  claim 16 , wherein the first aspect and the second aspect are independent. 
     
     
         19 . The method of  claim 18 , wherein using the noise model to remove noise from the combined data set comprises adaptively subtracting the noise model from the combined data set. 
     
     
         20 . The method of  claim 18 , wherein using the noise model to remove noise from the combined data set comprises transforming the combined data set and the noise model to a domain of distance and time to form a combined data set and a noise model, and adaptively subtracting the noise model from the combined data set. 
     
     
         21 . A method of reducing noise in a geophysical acquisition record, comprising:
 obtaining a first data set representing a first aspect of a physical wavefield;   obtaining a second data set representing a second aspect of the physical wavefield;   transforming the first data set and the second data set to a frequency-wavenumber domain;   applying a first filter to the transformed first data set to form a first equalized data set and a second filter to the transformed second data set to form a second equalized data set, wherein a signal part of the first equalized data set is equal to a signal part of the second equalized data set;   transforming the first equalized data set and the second equalized data set to a wavelet domain to form a first wavelet coefficient set and a second wavelet coefficient set;   forming a noise model from the first wavelet coefficient set and the second wavelet coefficient set by subtracting each wavelet coefficient of the first wavelet coefficient set from a corresponding wavelet coefficient of the second wavelet coefficient set and retaining the value of the result;   linearly combining the first equalized data set and the second equalized data set to form a combined data set; and   using the noise model to remove noise from the combined data set.   
     
     
         22 . 34 . (canceled) 
     
     
         35 . The method of  claim 21 , wherein the first aspect and the second aspect are independent. 
     
     
         36 . The method of  claim 21 , wherein using the noise model to remove noise from the combined data set comprises adaptively subtracting the noise model from the combined data set. 
     
     
         37 . The method of  claim 21 , wherein using the noise model to remove noise from the combined data set comprises transforming the combined data set and the noise model to a domain of distance and time to form a combined data set and a noise model, and adaptively subtracting the noise model from the combined data set. 
     
     
         38 . A computer-readable medium that stores instructions, wherein the instructions are executable to implement operations comprising:
 identifying a first data set representing a first aspect of a wavefield;   identifying a second data set representing a second aspect of the physical wavefield;   transforming the first data set and the second data set to a frequency-wavenumber domain;   applying a first filter to the transformed first data set to form a first equalized data set and a second filter to the transformed second data set to form a second equalized data set, wherein a signal part of the first equalized data set is equal to a signal part of the second equalized data set;   forming a noise model from the first equalized data set and the second equalized data set by subtracting each data point of the first equalized data set from a corresponding data point of the second equalized data set and retaining the value of the result;   linearly combining the first equalized data set and the second equalized data set to form a combined data set; and   using the noise model to remove noise from the combined data set.   
     
     
         39 . The computer-readable medium of  claim 38 , wherein the first aspect and the second aspect are independent. 
     
     
         40 . The computer-readable medium of  claim 38 , wherein using the noise model to remove noise from the combined data set comprises adaptively subtracting the noise model from the combined data set. 
     
     
         41 . The computer-readable medium of  claim 38 , wherein using the noise model to remove noise from the combined data set comprises transforming the combined data set and the noise model to a domain of distance and time to form a combined data set and a noise model, and adaptively subtracting the noise model from the combined data set. 
     
     
         42 . A computer-readable medium that stores instructions, wherein the instructions are executable to implement operations comprising:
 obtaining a first data set representing a first aspect of a physical wavefield;   obtaining a second data set representing a second aspect of the physical wavefield;   transforming the first data set and the second data set to a frequency-wavenumber domain;   applying a first filter to the transformed first data set to form a first equalized data set and a second filter to the transformed second data set to form a second equalized data set, wherein a signal part of the first equalized data set is equal to a signal part of the second equalized data set;   transforming the first equalized data set and the second equalized data set to a wavelet domain to form a first wavelet coefficient set and a second wavelet coefficient set;   forming a noise model from the first wavelet coefficient set and the second wavelet coefficient set by subtracting each wavelet coefficient of the first wavelet coefficient set from a corresponding wavelet coefficient of the second wavelet coefficient set and retaining the value of the result;   linearly combining the first equalized data set and the second equalized data set to form a combined data set; and   using the noise model to remove noise from the combined data set.   
     
     
         43 . The computer-readable medium of  claim 42 , wherein the first aspect and the second aspect are independent. 
     
     
         44 . The computer-readable medium of  claim 42 , wherein using the noise model to remove noise from the combined data set comprises adaptively subtracting the noise model from the combined data set. 
     
     
         45 . The computer-readable medium of  claim 42 , wherein using the noise model to remove noise from the combined data set comprises transforming the combined data set and the noise model to a domain of distance and time to form a combined data set and a noise model, and adaptively subtracting the noise model from the combined data set.