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This paper presents a comprehensive and rational approach of synthesizing spatially correlated earthquake ground motions. The physically compliant seismological spectra, which have been used in simulating ground motion at a single location, is extended to synthesize spatially varying ground motion (SVGM). The seismological spectra are then related to Vector-valued Seismic Hazard Deaggregation, based on which a simulation framework is proposed to resolve the problem that a number of simulations need to be carried out for ground motion generation based on uniform hazard spectra. The proposed approach of synthesizing SVGMs accounts for local site effect, including consideration of random and spatially variable soil profiles, combined P-wave, shear horizontal (SH) wave and shear vertical (SV) wave motions for simulating tri-directional SVGMs, and the effect of degree of water saturation.