Arion is looking at using differences between air pressure and density to fly at speeds of up to Mach 1.2 without a boom. (Paid Subscription Required)

Basically, the speed of sound goes down as altitude goes up, and if the shock wave enters air where the speed is no longer supersonic, it cuts off.

Needless to say, the implementation would be problematic. You would need accurate real time temperature and barometric data to ensure that your shock would not hit the ground:

“We see no difficulties in its application,” says Richard Tracy, Aerion’s chief technology officer. “It requires atmospheric information, which is available over populated areas where it is needed. It’s a matter of accessing that data from the aircraft.” To ensure the sonic boom never reaches the ground, the company has picked a Mach cutoff altitude—the height at which the shockwave goes subsonic—of 5,000 ft., to provide a wide margin for uncertainty caused by aging or gaps in the data.

Based on temperatures and winds at or near the surface, the aircraft would be flown at a GPS speed relative to the airmass that ensures its shockwave never intersects with the surface. “With no wind, in a standard atmosphere, we could fly at Mach 1.15-1.16,” says Tracy. But the exact speed would vary with winds, season, time of day and direction of flight. “The Mach number in the cockpit could be Mach 1.03 to 1.3 or so.”

If supersonic flight was to be permitted over the U.S., Aerion calculates Mach cutoff would slice 1 hr. and 18 min. off a New York to Los Angeles flight compared with a conventional Mach 0.85 business jet, and trim 40 min. if compared with the Aerion SSBJ’s Mach 0.99 subsonic overland cruise speed.