Abstract: A method of simulating response of a through casing electrical resistivity well logging instrument to a set of simulated earth formations, cement and casing. A model of the earth formations, casing, cement and a configuration of electrodes on the instrument is initialized. Space surrounding the instrument is divided into segments. Conductance of each of the segments is calculated. A system of linear equations describing the electrical potential at each junction of segments is set up. The system expresses the balance of electrical current at each junction disposed outside the instrument and satifies the conditions that the potential on an outer surface of the space is zero, that the current normal to an insulating part of the instrument is zero, and that the potential is substantially equal at all junctions contained within one of the electrodes. The system of linear equations is solved by the conjugate gradient method with Incomplete Cholesky preconditioning.

Abstract: A method for determining oil saturation in an earth formation penetrated by a wellbore. Measurements of relative amounts of carbon and oxygen are made by spectral analysis of neutron-induced inelastic gamma rays detected from the earth formation at spaced apart locations. The method includes calculating an apparent oil holdup in the wellbore at each of the spaced apart locations from the relative amounts of carbon and oxygen. A corrected oil holdup is calculated in the wellbore from differences between the apparent holdups determined at each of the spaced apart locations. An apparent oil saturation in the formation is determined at each of the spaced apart locations from the relative amounts of carbon and oxygen and the corrected oil holdup. A corrected formation oil saturation is determined from differences between the apparent oil saturations at each of the spaced apart locations.

Abstract: An apparatus for measuring the porosity of earth formations penetrated by a wellbore. The apparatus includes an elongated housing adapted to traverse the wellbore, a controllable source which emits bursts of high-energy neutrons, a near detector primarily sensitive to thermal neutrons and axially spaced apart from the source, a far detector also primarily sensitive to thermal neutrons and axially spaced apart from the source so that the near detector is axially disposed between the source and the far detector. The apparatus includes a neutron shield disposed between the near detector and the far detector, and a neutron scattering insert disposed inside the housing between the source and the near detector. The scattering insert consists of a material selected from the group of aluminum, beryllium, graphite, silicon, potassium, magnesium, lead and sulfur. In a preferred embodiment, the scattering insert consists of aluminum.

Abstract: A method for determining the permeability of earth formations penetrated by a wellbore from acoustic signals measured by an acoustic wellbore logging instrument. The method includes separating components from the measured acoustic signals which represent Stoneley waves propagating through the earth formations. Signals representing Stoneley waves propagating through the same earth formations are synthesized. The separated acoustic signal components and the synthesized Stoneley wave signals are compared. The permeability is determined from differences between the synthesized Stoneley wave signals and the separated acoustic signal components. In a preferred embodiment, the step of calculating the permeability includes inversion processing a wave center frequency shift and a wave travel time delay with respect to the permeability of the earth formations.

Abstract: A method of measuring the conductivity of earth formations penetrated by a wellbore. The method comprises selectively passing an alternating current through transmitter coils inserted into the wellbore. Each of the transmitter coils has a magnetic moment direction different from the magnetic moment direction of the other ones of the transmitter coils. The alternating current includes a first and a second frequency. The amplitude at the first frequency has a predetermined relationship to the amplitude at the second frequency. The relationship corresponds to the first and the second frequencies. The method includes selectively receiving voltages induced in a receiver coil having a sensitive direction substantially parallel to the axis of the corresponding transmitter coil through which the alternating current is passed.

Abstract: A method for correcting response of an induction logging instrument for inclination of earth formations with respect to an axis of the instrument. The instrument has a transmitter and a plurality of receivers at spaced apart locations. The method includes calculating expected receiver responses of simulated media having different conductivities. The calculations are performed for a plurality of different inclinations. The calculations are also performed for media having a plurality of different conductivity contrasts. 2-dimensional filters corresponding to a charge effect portion of each of the expected responses are calculated. 2-dimensional filters corresponding to a volumetric effect portion of each of the expected responses are calculated. An angle of inclination of the earth formations with respect to the instrument is determined. An approximate conductivity contrast of the earth formations is determined.

Abstract: A method of determining the number of exponential decay modes in spin echo amplitude signals from a nuclear magnetic resonance well logging instrument. The method includes dividing the time interval between initiation and termination of measurement of the spin echo amplitude signals into 2r-1 equal length segments, where r is a positive integer. Integrals of the spin echo amplitude signals with respect to time in each of the segments are calculated. Best fit functions are calculated for the spin echo amplitude signals, and integrals with respect to time of apparent amplitudes of the best fit functions at each time corresponding to a time at which the spin echo amplitude signals were generated. The integrals of the spin echo amplitude signals and the integrals of the apparent amplitudes from each segment are arranged into symmetric matrices each having dimensions r.times.r. A norm and a standard deviation of the matrix of the spin echo amplitude integrals is calculated.

Abstract: A method of compressing digital signals for transmission and/or storage. The method includes lossy compressing the digital signal to generate a lossy compressed signal. The compressed signal is decompressed locally to generate a local lossy decompressed signal. An error signal is calculated as the difference between the original digital signal and the local lossy decompressed signal. The power in the original digital signal and in the error signal is determined. A minimum resolution for quantizing the error signal is determined from a ratio of the power of the original signal with respect to power of the error signal. The error signals is lossy compressed by quantizing to at least the minimum resolution. Both the compressed digital signal and the compressed error signal are transmitted and/or stored. The lossy compressed error signal and the lossy compressed signal are recovered from storage or transmission.

Abstract: A nuclear magnetic resonance sensing apparatus including a magnet for inducing a static magnetic field in materials to be analyzed, the magnetic field having uniform field strength around, being substantially rotationally symmetric and perpendicular to a longitudinal axis of the magnet. The apparatus includes means for generating a radio frequency magnetic field in the materials to be analyzed. The radio frequency magnetic field is substantially rotationally symmetric about the longitudinal axis and is parallel to the longitudinal axis within a sensitive volume containing the materials to be analyzed. The apparatus includes means for receiving a nuclear magnetic resonance signal from the sensitive volume. In a preferred embodiment, the means for generating and means for receiving include an antenna coil wound so that turns of the coil lie in planes perpendicular to the longitudinal axis of the magnet.

Abstract: A method of determining the continuity of earth formations between wellbores by analyzing seismic energy imparted to the formations. The energy is imparted to the formations at a plurality of depths in one wellbore and is received at a plurality of depths in another wellbore. Compressional and shear components of the seismic energy received in the other wellbore are separated. A frequency spectrum is determined for the compressional component and the shear component of the seismic energy at each selected depth. Common imparted depth stacks of the compressional components and shear components are assembled at the depths at which the seismic energy is imparted. Common received depth stacks of the compressional components and the shear components are assembled at the selected depths at which the energy is received.

Abstract: A method of determining the acoustic propagation velocities of earth formations using signals generated by an acoustic array well logging instrument. The method includes generating a model of the acoustic velocities including a value of velocity for each propagation mode for which the velocity is to be determined Acoustic waveforms are synthesized for a plurality of receiver locations on the acoustic logging instrument by using the values of the acoustic velocities in the model. A difference is determined between the synthesized waveforms and measured waveforms generated by acoustic energy detected at corresponding receiver locations on the acoustic logging instrument. The model is adjusted and the waveforms are resynthesized until the difference is determined to be at a minimum. The step of adjusting the model is performed by very fast simulated annealing.

Abstract: A method for using geometrical data to determine characteristics of a wellbore penetrating a subterranean formation is disclosed. The method involves converting data obtained from acoustic well logging into cartesian coordinates and solving a general quadratic equation by a least squares fit to an elliptical or circular model. More specific information, such as tensor strain and formation compaction along the wellbore may then be obtained from the geometrical data.

Abstract: A dipole acoustic well logging instrument including an acoustic transmitter. Receiver sections are disposed at axially spaced apart locations from the acoustic transmitter. Each receiver section includes an outer shoulder at each end adapted to be placed in acoustically isolated contact with an internal shoulder of a connector coupling when the instrument is in tension. The outer shoulders have an acoustically isolating material disposed on their surfaces. The receiver sections include an inner shoulder at each end adapted to be placed in direct contact with an external shoulder of the connector coupling when the instrument is in compression. The instrument includes one connector couplings disposed at each end of each receiver section to couple the receiver sections to each other and to the remainder of the instrument. At least one receiver element is disposed in a passage formed into each of the receiver sections.

Abstract: A nuclear magnetic resonance apparatus including a magnet generating a static magnetic field in a first region containing materials to be analyzed. The magnet generates zero static magnetic field in a second region. The magnet has generally homogeneous magnetization along a longitudinal axis and is magnetized substantially perpendicular to the axis. The apparatus includes means for generating a radio frequency magnetic field in the first region for exciting nuclei of the materials. The means for generating the radio frequency magnetic field includes an antenna disposed within the second region. The apparatus includes means for receiving a nuclear magnetic resonance signal from the excited nuclei. The means for receiving also provides an output indication of properties of the materials to be analyzed. In a preferred embodiment, the means for generating and receiving include an antenna at least partially disposed within the second region.

Abstract: A method for determining orientations and velocities of slow and fast waves in an anisotropic earth formation. Signals are used from an acoustic logging tool including dipole transmitters and receiver arrays. An initial value of angle subtended between orientation of the fast wave and one of the transmitters is selected. A waveform of a fast principal wave and slow principal wave at first and second selected receiver positions are calculated from received signals at each of these positions and the selected subtended angle. A derivative waveform with respect to subtended angle is calculated for both fast and slow principal waves. An initial velocity of slow waves is selected and the calculated waveforms of the slow principal wave and its derivative waveform at the first position are time shifted by a time corresponding to distance between first and second receiver positions and the selected value of velocity.

Abstract: An electromagnetic wellbore logging tool including an elongated sonde adapted for traversing the wellbore, a source of alternating current, an antenna connected to the source of alternating current, and a receiver circuit connected to the antenna. The receiver circuit provides an output corresponding to electromagnetic signals induced in the antenna. The invention includes at least one insulating insert disposed in an annular space between the exterior of the sonde and the wall of the wellbore. The insert extends in a direction so as to segment the paths of eddy current which would otherwise flow in the annular space. In a preferred embodiment, the logging tool includes a nuclear magnetic resonance apparatus having a longitudinal dipole antenna. The insulating inserts extend along the longitudinal axis of the tool so as to segment eddy current paths perpendicular to the longitudinal axis of the tool.

Abstract: The invention is a method of determining the permeability of an earth formation using a wireline formation testing instrument. The method includes measuring pressure with respect to time at a probe in hydraulic communication with the earth formation, calculating time derivatives of the measured pressure, withdrawing fluid from the earth formation by increasing a volume of a chamber in hydraulic communication with the probe, measuring the volume of the chamber with respect to time, and calculating time derivatives of the measured volume. Increasing the volume of the chamber is stopped. The permeability is calculated when the measured pressure substantially stops increasing, by determining a slope of a linear relationship of the measured pressure with respect to a fluid flow rate calculated from the time derivative of the volume and the time derivative of the pressure.

Abstract: A method of determining amplitude and phase response of a receiver amplifier in an induction well logging instrument including the steps of generating an oscillating current at least one frequency, energizing a transmitter coil instrument with the oscillating current, generating a first test signal having a known phase and amplitude relationship with respect to the oscillating current and a different frequency than any frequency in the oscillating current, amplifying and detecting voltages induced in a receiver coil corresponding to electrical properties of an earth formation, conducting a portion of the first test signal to the receiver amplifier causing the amplifier to generate a combined output including the first test signal and a signal resulting from the induced voltages, combining the oscillating current with the first test signal to form a combined test/reference signal, spectrally analyzing the combined test/reference signal and spectrally analyzing the combined output, and comparing spectral analys

Abstract: The invention is a method of inversion processing signals from an induction well logging instrument including a transmitter and a plurality of receivers at spaced apart locations. The method includes skin effect correcting the responses of the receivers by extrapolating the receiver responses to zero frequency. A model is generated of the media surrounding said instrument. Conductivities of elements in the model are then adjusted so that a measure of misfit between the skin-effect corrected receiver responses and simulated receiver responses based on the model is minimized. The geometry of the model is then adjusted so that the measure of misfit between the skin-effect corrected receiver responses and the simulated receiver responses based on the model is further minimized.

Abstract: A method of measuring motion properties of nuclei within pore spaces of a porous medium. The method includes applying a static magnetic field to the medium to polarize the nuclei, generating a first magnitude of magnetic field gradient within the pore spaces of the medium, applying a radio frequency magnetic field to excite the nuclei, receiving nuclear magnetic resonance signals from the nuclei, and calculating the motion properties from rates of decay of the amplitude of the nuclear magnetic resonance signals.