1. A method for seismic inversion of vertical seismic profile (VSP) data in an oilfield having a subterranean formation penetrated by a wellbore, comprising: obtaining an initial velocity model of the subterranean formation, the initial velocity model comprising acoustic velocities of wave propagation in proximity to the wellbore; determining an acquisition geometry for obtaining the VSP data, the acquisition geometry comprising a plurality of receiver locations within the wellbore and a source location; performing a seismic survey to obtain the VSP data based on the acquisition geometry; analyzing, using a central processing unit (CPU) of a computer system, direct arrival signals of the VSP data to generate transit time data for wave propagation from the source location to the plurality of receiver locations; modifying, using the CPU, the initial velocity model to generate an updated velocity model by performing a tomographic inversion of the transit time data; generating, using the CPU, an elastic model of the subterranean formation by performing the seismic inversion of the VSP data using the updated velocity model; and adjusting the operations of the oilfield based on the elastic model.