| CPC G01V 1/50 (2013.01) [E21B 47/14 (2013.01); G01V 1/307 (2013.01); G01V 2210/47 (2013.01); G01V 2210/63 (2013.01)] | 11 Claims |
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1. A method of invertibly transforming acoustic log signals comprising the steps of:
a) inserting into a borehole, forming part of a borehole-formation system in which the borehole penetrates a rock formation, an elongate acoustic logging tool, the acoustic logging tool including at least one acoustic source and, spaced from the acoustic source along the logging tool, a sequential array of two or more acoustic signal receiver stations, the receiver stations each including at least one receiver and being spaced along the logging tool from the acoustic source by successively greater known transmitter-receiver distances whose minimum separation is greater than the minimum detectable wavelength corresponding to a formation slowness range of interest;
b) causing the acoustic source to emit acoustic energy in a manner (I) effecting the propagation in the borehole-formation system towards the receiver stations of plural signal packets exhibiting paths characteristic of at least first and second respective modes one or more of which is dispersive and (II) stimulating at least two receivers of respective, sequential, spaced receiver stations to generate at least one output signal per receiver station that is indicative of the signal packets, received at the at least one receiver of each respective receiver station, representing the modes in combination with one another;
c) transforming the output signals into respective transformed mode signals containing phase and amplitude information of each respective mode across the array and in which estimated phase and amplitude information are linked by an operator to the slowness and attenuation characteristics of the respective mode and the transmitter-receiver distance of the respective receiver station;
d) using the estimated phase and amplitude information for each mode from each receiver in the acoustic array to extract slowness and attenuation information for each mode from the output signals and generating signals indicative of the slowness and/or attenuation characteristics; and
e) using the signals indicative of the slowness and/or attenuation characteristics in plotting, storing; transmitting, displaying, printing or further processing the slowness and/or attenuation characteristics,
wherein the Step d) of using the estimated phase and amplitude information for each mode to extract slowness and attenuation information for each mode from the output signals includes f) generating complex spectra information from the receiver array signals and taking the real and imaginary parts of the transformed mode signals containing respective amplitude and phase components of the respective modes;
wherein the method includes the steps of:
g) in cases where the number of receivers exceeds the minimum necessary to determine slowness and amplitude values for each frequency and mode of interest, solving for mode amplitude and slowness by minimizing in a least squares sense the differences between real and imaginary mode amplitudes and the real and imaginary amplitudes of the combined modes observed in the spectra of received signals for each frequency, and
h) representing the real and imaginary parts between estimated and received signals as objective function signals and summing the squares of the objective function signals over the two or more receiver stations; and
wherein the Step g) includes minimizing the error between terms representing the amplitude and phase detected at the receivers and terms representing amplitude and phase components in the real and imaginary parts, including using initial estimates of the amplitude and phase components of the respective modes, and using a search method to minimize the said error.
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