the phase derivative of a complex signal sequence the phase derivative equals the phase of the autocorrelation r at 1 lag where n is the number of pixels in an estimator kernel and s a is the analytical signal of u m n r 2 combining equation 2 and equation 5 the 1 d shear wave velocity is estimated by in theory taking the derivative of a phase can provide a very high resolution but it is very sensitive to noise noise reduction is needed before calculating the gradient in the preferred embodiment a hand held ultrasound transducer is modified to include two parallel vibration sources the theory for waves produced by a thin beam in contact with the upper surface of a semi infinite elastic medium was derived by miller and pursey in 1954 when the thin bar presses tangentially into the surface of the medium shear waves are produced in a beam pattern that maximizes at around 45 degrees with respect to the surface the miller pursey solution has been extended in the preferred embodiment by including two sources and deriving the interference pattern between the two sources as a superposition the above will now be described with reference to fig2 consider a long thin strip 202 placed in close contact with a semi infinite large uniform homogeneous elastic solid 204 and vibrating normal to.