Device and method for deghosting variable depth streamer data

Abstract

Computing device, computer instructions and method for deghosting seismic data related to a subsurface of a body of water. The method may include receiving input seismic data recorded by seismic receivers that located at different depths (z r ), generating migration data (du) and mirror migration data (dd) from the input seismic data, deriving a ghost free model (m) based on simultaneously using the migration data (du) and mirror migration data (dd), generating primary (p) and ghost (g) datasets based on the ghost free model (m), simultaneously adaptively subtracting the primary (p) and ghost (g) datasets from the migration data (du) to provide adapted primary (p′ 1 and p′ 2 ) and adapted residual (r′ 1 and r′ 2 ) datasets and generating a final image (f) of the subsurface based on the adapted primary (p′ 1 and p′ 2 ) and the adapted residual (r′ 1 and r′ 2 ) datasets.

1 . A method for de-ghosting seismic data related to a subsurface of a body of water, the method comprising:
 receiving input seismic data recorded by a plurality of seismic receivers, wherein the input seismic data is recorded in a time-space domain and the seismic receivers are located at different depths (z r ) in the body of water;   generating migration data (du) and mirror migration data (dd) from the seismic data;   computing, with a processor, cross-correlations of the migration data (du) with the mirror migration data (dd) to estimate first terms of a ghost lag model;   computing, with the processor, an autocorrelation of the migration data and an autocorrelation of the mirror migration data to generate second terms of the ghost lag model; and   deriving a ghost free model (m) based on simultaneously using the migration data (du), the mirror migration data (dd) and the ghost lag model.   
     
     
         2 . The method of  claim 1 , further comprising:
 using the ghost free model to generate a deghosted dataset; and   generating an image (f) of the subsurface using the deghosted dataset.   
     
     
         3 . The method of  claim 1 , wherein the step of computing cross-correlations comprises:
 finding a cross-correlation peak of the cross-correlations to provide an estimate of the first terms of the ghost lag model.   
     
     
         4 . The method of  claim 1 , wherein the first terms are linear terms and the second terms are non-linear terms. 
     
     
         5 . The method of  claim 1 , wherein the step of computing cross-correlations comprises:
 computing slant stacked correlations of the migration data with the mirror migration data.   
     
     
         6 . The method of  claim 5 , further comprising:
 correlating the migration data and the mirror migration data with various linear time shifts between the migration data and the mirror migration data.   
     
     
         7 . The method of  claim 6 , wherein a time shift is between columns of the migration data and the mirror migration data. 
     
     
         8 . The method of  claim 7 , wherein the time shift conforms to a linear time shift equation that depends on (i) the first terms and (ii) a horizontal offset between the source and the nth receiver. 
     
     
         9 . The method of  claim 1 , wherein the step of computing an autocorrelation of the migration data and an autocorrelation of the mirror migration data comprises:
 computing a curve stacked autocorrelation of the migration data and mirror migration data.   
     
     
         10 . The method of  claim 9 , further comprising:
 auto-correlating the migration data and auto-correlating the mirror migration data with various time shift curves between columns in the input seismic data and columns of a time-shifted copy of the input seismic data.   
     
     
         11 . A computing device for de-ghosting seismic data related to a subsurface of a body of water, the computing device comprising:
 an interface for receiving input seismic data recorded by a plurality of seismic receivers, wherein the input seismic data is recorded in a time-space domain and the seismic receivers are located at different depths (z r ) in the body of water; and   a processor connected to the interface and configured to,   generate migration data (du) and mirror migration data (dd) from the seismic data,   compute cross-correlations of the migration data (du) with the mirror migration data (dd) to estimate first terms of a ghost lag model,   compute an autocorrelation of the migration data and an autocorrelation of the mirror migration data to generate second terms of the ghost lag model, and   derive a ghost free model (m) based on simultaneously using the migration data (du), the mirror migration data (dd) and the ghost lag model.   
     
     
         12 . The computing device of  claim 11 , wherein the processor is further configured to:
 use the ghost free model to generate a deghosted dataset; and   generate an image (f) of the subsurface using the deghosted dataset.   
     
     
         13 . The computing device of  claim 11 , wherein the processor is further configured to:
 find a cross-correlation peak of the cross-correlations to provide an estimate of the first terms of the ghost lag model.   
     
     
         14 . The computing device of  claim 11 , wherein the first terms are linear terms and the second terms are non-linear terms. 
     
     
         15 . The computing device of  claim 11 , wherein the processor is further configured to:
 compute slant stacked correlations of the migration data with the mirror migration data.   
     
     
         16 . The computing device of  claim 15 , wherein the processor is further configured to:
 correlate the migration data and the mirror migration data with various linear time shifts between the migration data and the mirror migration data.   
     
     
         17 . The computing device of  claim 16 , wherein a time shift is between columns of the migration data and the mirror migration data. 
     
     
         18 . The computing device of  claim 17 , wherein the time shift conforms to a linear time shift equation that depends on (i) the first terms and (ii) a horizontal offset between the source and the nth receiver. 
     
     
         19 . The computing device of  claim 11 , wherein the processor is further configured to:
 compute a curve stacked autocorrelation of the migration data and mirror migration data, and   auto-correlate the migration data and auto-correlating the mirror migration data with various time shift curves between columns in the input seismic data and columns of a time-shifted copy of the input seismic data.   
     
     
         20 . A non-transitory computer readable medium including computer executable instructions, wherein the instructions, when executed by a processor, implement instructions for deghosting seismic data, the instructions comprising:
 receiving input seismic data recorded by a plurality of seismic receivers, wherein the input seismic data is recorded in a time-space domain and the seismic receivers are located at different depths (z r ) in the body of water;   generating migration data (du) and mirror migration data (dd) from the seismic data;   computing cross-correlations of the migration data (du) with the mirror migration data (dd) to estimate first terms of a ghost lag model;   computing an autocorrelation of the migration data and an autocorrelation of the mirror migration data to generate second terms of the ghost lag model; and   deriving a ghost free model (m) based on simultaneously using the migration data (du), the mirror migration data (dd) and the ghost lag model.