A theoretical correlation model is presented for spatially varying earthquake ground motion with the concept of a composite random process. It seeks to explain the fractal nature of the correlation structure contributed by the effects of the source, path of waves and the local site. The correlation model shows self-similarity in the logarithmic decay form with increasing distance. SMART-1 array data is used to verify the applicability of our model. The "apparent" correlation detected for the local average processes is realized as the "true" correlation incorporating the spatially averaged spectral density function.