Abstract: A method of determining the rate of penetration .DELTA.d of a drill bit at the end of a drill string while drilling a well, comprising:(a) measuring the vertical displacement S of the drill string at the surface,(b) determining a state space description of S comprising a state space measurement equation: ##EQU1## and a state evolution equation: ##EQU2## wherein S and .DELTA.d are as previously defined, .DELTA. is the difference operator for time .tau. between adjacent samples k and k+1, .LAMBDA. is the drill string compliance, .rho. is the noise term associated with the surface displacement measurement, r is the noise term associated with fluctuations in the state, and h is the hookload, and(c) applying a Kalman filter to said equations to obtain an estimate of the state parameters including .DELTA.d.

Abstract: A tool for measuring the mechanical properties of a formation through which a borehole has been drilled, comprising a tool body capable of being lowered into a borehole, the tool body having pads mounted on movable arms, each pad carrying a PDC type cutter which is urged against wall of the borehole so as to cut into the formation; transducers are provided for determining the depth of cut made by the cutter and for determining the resistance of the rock to cutting. The tool is connected to a wireline, enabling the cutter to be moved through the formation and the data from the transducers to be returned to the surface for analysing the depth of cut and resistance to cutting to determine the mechanical properties of the rock.

Abstract: A monopole transmitter for a sonic well tool includes an axial tube, a piezoceramic cylinder surrounding the axial tube, an endcap disposed at each end of and firmly contacting the cylinder, and an apparatus for holding the endcaps firmly against the axial tube. The endcaps firmly contact the axial tube without simultaneously contacting an upper bulkhead. The apparatus may include spring washers disposed between the bulkhead and at least one endcap, or it may include a spring disposed between a nodal mount and each endcap. A nodal mounting tube may be disposed around the axial tube, a ring being disposed at each end of the nodal mounting tube, each ring being disposed outside of the cylinder, the apparatus including a spring disposed between each ring and an endcap outside of the cylinder for biasing the endcaps in tension against a ring thereby holding each endcap firmly in contact against the axial tube.