RESPONSE OF ELECTROMAGNETIC-PULSE LOGGING SONDE IN AXIALLY SYMMETRICAL FORMATION

The time-domain response of an electromagnetic-pulse logging sonde in axially symmetrical formations is obtained using the transmission-line-matrix (TLM) technique. The sonde consists of transmitting and receiving coils that are placed on the axis of the borehole. The formation is assumed to have horizontal layers with or without invasion zones. The transmitting coil emits an electromagnetic pulse of known shape. Using the TLM technique, the transient response of the receiver has been computed. The technique calls for dividing the formation into small cells. Each cell is simulated with a matrix of transmission lines which are connected to those of the adjacent cells. The voltage and current in the transmission line network are proportional to the electric and magnetic fields. The parameters of the transmission lines are so adjusted that the resulting transmission line equations correspond exactly to the Maxwell equations in the cell. Propagation of an electromagnetic pulse in the formation is then equivalent to the propagation of a pulse in the transmission line network. The latter has been obtained in a simple and systematic way with accurate results. Examples are given to show that the TLM technique is well-suited to solving time-domain well-logging problems in complex environments.