A method for converting seismic data recorded from marine streamers into deghosted seismic data, for imaging the earth's subsurface, comprising: using a programmable computer to perform the following: obtaining (11; 21) the seismic data recorded from the marine streamers, the seismic data representative of characteristics of subsurface earth formations and acquired by deployment of a plurality of seismic receivers overlying an area of the subsurface earth formations to be evaluated, the seismic receivers generating at least one of an electrical and optical signal in response to seismic energy; using a complex Laplace frequency parameter to transform the seismic data from a space-time domain to a spectral domain; applying an iterative conjugate gradient scheme, using a physically-based preconditioner, to the transformed seismic data, to provide a least squares solution to a normal set of equations for a deghosting system of equations; and inverse-transforming the solution back to a space-time domain to provide the deghosted seismic data, characterised in that using a complex Laplace frequency parameter comprises: determining a nonzero real part of the complex Laplace frequency parameter to transform the seismic data from a space-time domain to a spectral domain; obtaining recorded seismic data for a seismic source activation; using the complex Laplace frequency parameter to transform the recorded seismic data for a seismic source activation from the space-time domain to a Laplace space-frequency domain; obtaining transformed seismic data for a frequency; and using the complex Laplace frequency parameter to transform the transformed seismic data for a frequency from the Laplace space-frequency domain to the spectral domain. using a programmable computer to perform the following: obtaining (11; 21) the seismic data recorded from the marine streamers, the seismic data representative of characteristics of subsurface earth formations and acquired by deployment of a plurality of seismic receivers overlying an area of the subsurface earth formations to be evaluated, the seismic receivers generating at least one of an electrical and optical signal in response to seismic energy; using a complex Laplace frequency parameter to transform the seismic data from a space-time domain to a spectral domain; applying an iterative conjugate gradient scheme, using a physically-based preconditioner, to the transformed seismic data, to provide a least squares solution to a normal set of equations for a deghosting system of equations; and inverse-transforming the solution back to a space-time domain to provide the deghosted seismic data, obtaining (11; 21) the seismic data recorded from the marine streamers, the seismic data representative of characteristics of subsurface earth formations and acquired by deployment of a plurality of seismic receivers overlying an area of the subsurface earth formations to be evaluated, the seismic receivers generating at least one of an electrical and optical signal in response to seismic energy; using a complex Laplace frequency parameter to transform the seismic data from a space-time domain to a spectral domain; applying an iterative conjugate gradient scheme, using a physically-based preconditioner, to the transformed seismic data, to provide a least squares solution to a normal set of equations for a deghosting system of equations; and inverse-transforming the solution back to a space-time domain to provide the deghosted seismic data, characterised in that using a complex Laplace frequency parameter comprises: determining a nonzero real part of the complex Laplace frequency parameter to transform the seismic data from a space-time domain to a spectral domain; obtaining recorded seismic data for a seismic source activation; using the complex Laplace frequency parameter to transform the recorded seismic data for a seismic source activation from the space-time domain to a Laplace space-frequency domain; obtaining transformed seismic data for a frequency; and using the complex Laplace frequency parameter to transform the transformed seismic data for a frequency from the Laplace space-frequency domain to the spectral domain. determining a nonzero real part of the complex Laplace frequency parameter to transform the seismic data from a space-time domain to a spectral domain; obtaining recorded seismic data for a seismic source activation; using the complex Laplace frequency parameter to transform the recorded seismic data for a seismic source activation from the space-time domain to a Laplace space-frequency domain; obtaining transformed seismic data for a frequency; and using the complex Laplace frequency parameter to transform the transformed seismic data for a frequency from the Laplace space-frequency domain to the spectral domain.