Bow tie for a GPR project

Hi guys I am designing a Bow-Tie antenna for a GPR. Since the GPR antennas should only radiate in one direction i have to design a back cavity with absorption material in it. But since the cavity acts as a reflector it changes all the S parameters of my antenna. I really don't have any idea on how to design this back cavity taking the reflections into consideration. Can someone give me a little help or a heads up? Thanks.