A coil arrangement and method of collecting and processing data in induction logging of wells is disclosed. The coil arrangement includes three essentially identical coils made of elliptical conductive loops lying in a plane tilted from the axis of the logging tool. Each coil is centered on the same point in space. Data are preferably collected by using the coil arrangement for both transmitter and receiver, and transmitting at three closely-spaced frequencies, one from each of the transmitter coils. The transmitted signals are received and recorded, at which time they are operated on mathematically to create rotation of an after-the-fact virtual sonde for measuring desired earth formation properties.