Calculating off-Hugoniot states by the overtake method behind splitting waves

Overtake method is commonly used in impact experiments to determine and calibrate the equation of state outside the principle Hugoniot. The method is based on measuring the time of arrival of either consecutive shock waves or rarefaction waves from an impactor at targets of different thickness. In some cases, the leading shock wave that was created at the impact splits into two waves (e.g., elastic precursor or due to phase transition), so the speed of the second wave cannot be determined by the overtake method. In this work we investigate the difficulties that arise from such wave splitting, and specifically show that additional target widths do not add any new information that can be used when calculating wave velocities. We look at special cases where the speed of the second wave may nevertheless be approximated, albeit with lesser precision, and identify the main error sources. 1-dimensional simulations were carried out to support our calculations in good agreement. The present work may act as a basis for additional calculations that will expand our knowledge of equations of state in uncharted areas.