Acoustic logging apparatus and method for anistropic earth formations

In a system with a logging tool having a dipole transmitter pair and a plurality of dipole receiver pairs spaced apart from the dipole transmitter pair and from each other, and where the orientation of each dipole transmitter is known, and where each of the plurality of dipole receiver pairs has one dipole receiver axially parallel with one of the dipole transmitters and another dipole receiver axially parallel with another of the dipole transmitters, a method of determining a velocity of a fast and slow shear wave polarizations in an anisotropic earth formation comprising:

• transmitting acoustic signals with the dipole transmitters;
• receiving the acoustic signals as composite signals with the plurality of dipole receiver pairs;
• decomposing the composite signals into a plurality of decomposed signals;
• estimating a source signal for each of the plurality of decomposed signals to create a plurality of estimated source signals;
• and
• determining the acoustic velocity of the fast and slow polarized shear waves by comparison of the plurality of estimated source signals.

In an anisotropic earth formation where an induced shear wave breaks up into a fast polarization component and a slow polarization component, a method of determining characteristics of the earth formation comprising:

• a) generating acoustic signals with dipole transmitter pair by firing a first dipole transmitter, then firing a second dipole transmitter;
• b) receiving at a first dipole receiver pair acoustic energy composite signals containing information about both the fast and slow polarization components;
• c) receiving at a second dipole receiver pair acoustic energy composite signals containing information about both the fast and slow polarization components;
• d) decomposing the signals of the first dipole receiver pair into a first decomposed signal for a strike angle;
• e) decomposing the signals of the second dipole receiver pair into a second decomposed signal for the strike angle;
• f) estimating a an assumed slowness of the earth formation;
• g) estimating a first source wavelet based on the first decomposed signal;
• h) estimating a second source wavelet based on the second decomposed signal;
• i) comparing the first and second source wavelets to obtain an objective function;
• j) plotting the objecting function as a function of slowness of the assumed transfer function, a start time within the decomposed signals, and strike angle;
• k) repeating steps f) through j) for a plurality of assumed transfer functions;
• l) repeating steps f) through k) for a plurality of start times within the decomposed signal;
• and
• m) repeating steps d) through 1) for a plurality of strike angles.

A method of determining an orientation of fast and slow polarized shear waves in an anisotropic earth formation, the method comprising:

• transmitting acoustic energy into the earth formation, and wherein the earth formation breaks the acoustic energy into the fast polarization shear wave and the slow polarization shear wave;
• receiving composite waveforms comprising components of both the fast and slow polarization shear waves;
• decomposing the composite waveforms into decomposed waveforms;
• estimating source waveforms from the decomposed waveforms to create estimated source waveforms;
• and
• comparing the estimated source waveforms to determine the orientation of fast and slow polarized shear waves.