An ultrasound probe comprising: an ultrasound transducer configured to (i) fire pushing beams into a medium , wherein each pushing beam comprises a pushing beam focus which is at the end of the pushing beam, and wherein each pushing beam is configured to produce a respective shear wave along a propagation path through the medium, wherein the ultrasound transducer is further configured to (ii) issue tracking beams at different spatial locations , wherein said different spatial locations are disposed along the propagation path in a line perpendicular to the axis of the ultrasound probe and at a same depth as the pushing beam focus, receive respective echoes, and measure in response to issued tracking beams, previously emitted reference pulses to the different spatial locations and respective received echoes, shear-wave induced vertical displacement in the medium at the different spatial locations along the propagation path of the respective shear wave; characterized in that the ultrasound probe further comprises an in-place displacement based weighter operatively connected with all the tracking beams, wherein the in-place displacement based weighter is configured to use the shear-wave-induced displacement measured at the different spatial locations along the propagation path for determining a center of mass (COM) time value for each of the different spatial locations as a weighted average representative of an arrival time ( t COM ) of the corresponding shear wave at a respective location of the different spatial locations, by computing: t COM = ∑ disp peak × H disp × t ∑ disp peak × H disp , wherein disp peak is the peak displacement at the respective location, H disp is an instantaneous-displacement threshold factor that is either invariant with location or dynamically varying based on a criterion, t is the time at which the displacement is sampled. an ultrasound transducer configured to (i) fire pushing beams into a medium , wherein each pushing beam comprises a pushing beam focus which is at the end of the pushing beam, and wherein each pushing beam is configured to produce a respective shear wave along a propagation path through the medium, wherein the ultrasound transducer is further configured to (ii) issue tracking beams at different spatial locations , wherein said different spatial locations are disposed along the propagation path in a line perpendicular to the axis of the ultrasound probe and at a same depth as the pushing beam focus, receive respective echoes, and measure in response to issued tracking beams, previously emitted reference pulses to the different spatial locations and respective received echoes, shear-wave induced vertical displacement in the medium at the different spatial locations along the propagation path of the respective shear wave; characterized in that the ultrasound probe further comprises an in-place displacement based weighter operatively connected with all the tracking beams, wherein the in-place displacement based weighter is configured to use the shear-wave-induced displacement measured at the different spatial locations along the propagation path for determining a center of mass (COM) time value for each of the different spatial locations as a weighted average representative of an arrival time ( t COM ) of the corresponding shear wave at a respective location of the different spatial locations, by computing: t COM = ∑ disp peak × H disp × t ∑ disp peak × H disp , wherein disp peak is the peak displacement at the respective location, H disp is an instantaneous-displacement threshold factor that is either invariant with location or dynamically varying based on a criterion, t is the time at which the displacement is sampled. <EOS>