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In the present paper, a general integral expression is derived and discussed for the cross-correlation function (CCF) of speckle patterns in synthetic aperture radar (SAR) images processed by using partially overlapped subapertures of arbitrary Doppler center frequencies (or equivalent azimuth times). It is shown that, under the white noise approximation for the backscattered field, the CCF of the interlook speckle intensity patterns is given by the squared modulus of the autocorrelation function of the amplitude weighting function of subapertures where the time lag is the center time difference. It is also shown that the CCF of the interlook speckle patterns is independent of the surface coherence time of sea surface. The integral expression for the intensity CCF is then evaluated for a rectangular weighting function, and comparison is made with Japanese Earth Resources Satellite-1 (JERS-1) L-band and RADARSAT-1 C-band SAR images of sea surface to test the theory. The CCFs computed from the JERS-1 SAR data show excellent agreement with the theory, and good agreement is obtained with the RADARSAT-1 data.