Borehole dispersive wave processing with automatic dispersion matching for compressional and shear slowness

A system for real-time determination of one or more geophysical or mechanical properties of an underground formation, the system comprising:

• an acoustic logging tool having an array of receivers configured to acquire acoustic waveforms, the acoustic logging tool comprising:
• at least one transmitter for transmitting acoustic signals of different azimuthal orders;
• a receiver array comprising a plurality of receivers spaced along the acoustic logging toll for receiving different acoustic waveforms containing variations introduced by the one or more geophysical or mechanical properties of the underground formation as the acoustic signals propagate along the borehole, wherein a first receiver of the plurality of receivers is spaced from the at least one transmitter by a first spacing and each receiver of the plurality of receivers is spaced apart by a second spacing;
• a telemetry sub communicatively coupling the acoustic logging tool and a surface logging facility, the telemetry sub configured to send the acoustic waveforms received by each of the plurality of receivers of the receiver array to at least one processor within the surface logging facility, and wherein an axial resolution of the extracted slowness-frequency curve is a function of the second spacing and a size of the receiver array;
• and
• at least one non-transitory computer-readable storage medium having stored therein instructions which, when executed by the at least one processor, cause the at least one processor to:
• obtain, from an acoustic logging tool in a borehole, acoustic waveforms;
• extract a slowness-frequency curve from the acoustic waveforms, wherein the slowness-frequency curve is generated based at least in part upon a dispersion analysis;
• calculate a slowness density log of the slowness-frequency curve;
• obtain an initial shear slowness estimate based on the slowness density log;
• perform edge fitting to obtain the initial shear slowness estimate by:
• determining a fitting range including a slowness fitting maximum and a slowness fitting minimum, wherein the edge fitting function is
• f(s, β)=ρ(smax)cos2(smaxβ−sβ)
• where denotes a fitting parameter, s is the slowness and ρ(s) is the slowness density log;
• minimizing a misfit between an edge of the slowness density log and an edge fitting function based on the slowness fitting maximum and the slowness fitting minimum;
• and
• calculating the initial shear slowness estimate based on the minimized misfit;
• generate a dispersion model comprising a plurality of model parameters;
• and
• perform a dispersion auto match inversion to obtain a final shear slowness estimate, wherein the dispersion auto match inversion is performed based on at least the slowness-frequency curve and the estimated slowness-frequency curve simulated by the dispersion model;
• and
• displaying a slowness density image based on the final shear slowness estimate that is more representative of the underground formation than the acoustic waveforms.

A non-transitory computer-readable device having stored therein instructions which, when executed by at least one processor, cause the at least one processor to perform operations for real-time determination of one or more geophysical or mechanical properties of an underground formation, the operations comprising:

• exciting, via at least one transmitter of an acoustic logging tool in a borehole, acoustic signals of different azimuthal orders;
• receiving, via a receiver array comprising a plurality of receivers spaced along the acoustic logging tool, different acoustic waveforms containing variations introduced by the one or more geophysical or mechanical properties of the underground formation as the acoustic signals propagate along the borehole, wherein a first receiver of the plurality of receivers is spaced from the at least one transmitter by a first spacing and each receiver of the plurality of receivers is spaced apart by a second spacing;;
• transmitting, via a communicative coupling between the acoustic logging tool and a surface logging facility, the acoustic waveforms received by each of the plurality of receivers of the receiver array to a processor within the surface logging facility;
• extracting a slowness-frequency curve from the acoustic waveforms, wherein the slowness-frequency curve is generated based at least in part upon a dispersion analysis, and wherein an axial resolution of the extracted slowness-frequency curve is a function of the second spacing and a size of the receiver array;
• calculating a slowness density log of the slowness-frequency curve;
• obtaining an initial shear slowness estimate based on the slowness density log, wherein obtaining the initial shear slowness estimate further comprises performing edge fitting by:
• determining a fitting range including a slowness fitting maximum and a slowness fitting minimum, wherein the edge fitting function is
• f(s, β)=ρ(smax)cos2(smaxβ−sβ),
• where β denotes a fitting parameter, s is the slowness and ρ(s) is the slowness density log;
• minimizing a misfit between an edge of the slowness density log and an edge fitting function based on the slowness fitting maximum and the slowness fitting minimum;
• and
• calculating the initial shear slowness estimate based on the minimized misfit;
• generating a dispersion model comprising a plurality of model parameters;
• performing a dispersion auto match inversion to obtain a final shear slowness estimate, wherein the dispersion auto match inversion is performed based on at least the slowness-frequency curve and an estimated slowness-frequency curve simulated by the dispersion model dispersion model;
• and
• displaying a slowness density image based on the final shear slowness estimate that is more representative of the underground formation than the acoustic waveforms.