Methods to estimate formation slowness from multi-borehole modes and of a multi-mode dispersion wave and multi-mode dispersion estimation systems

1. A method to estimate slowness from multi-borehole modes, the method comprising:

obtaining waveform data of a plurality of waves traversing through a downhole formation, wherein each wave of the plurality of waves has a different threshold cutoff frequency;

performing a multimode dispersion analysis of the waveform data to generate a semblance map of the plurality of waves;

obtaining a slowness dispersion of a wave of the plurality of waves;

determining a formation type of a formation the wave traverses based on one or more properties of the plurality of the waves;

determining an initial body wave slowness estimate of the wave;

determining an edge slowness of the wave;

in response to a determination that the formation type of the formation is a slow formation, designating the edge slowness of the wave as the initial body wave slowness estimate of the wave;

generating a modeling of the wave; and

reducing a mismatch between the modeling of the wave and the slowness dispersion of the wave to improve the modeling of the wave.

2. The method of claim 1 , wherein after reducing the mismatch between the modeling of the wave and the slowness dispersion of the wave, the method further comprising:

determining an actual body wave slowness from the modeling; and

determining an actual slowness dispersion of the wave from the modeling.

3. The method of claim 2 , further comprising:

obtaining a second slowness dispersion of a second wave of the plurality of waves;

generating a second modeling of a second wave; and

reducing a second mismatch between the second modeling and the second slowness dispersion to improve the second modeling.

4. The method of claim 1 , further comprising:

analyzing one or more peaks of the semblance map; and

extracting a slowness dispersion of the wave from the one or more peaks of the semblance map to obtain the slowness dispersion of the wave.

5. The method of claim 1 , further comprising removing a tool wave from the semblance map, wherein the formation type of the formation is determined after the tool wave is removed from the semblance map.

6. The method of claim 1 , further comprising:

determining a slowness of the wave; and

determining a slowness of a second wave of the plurality of waves,

wherein the slowness of the wave and the slowness of the second wave are properties of the one or more properties of the plurality of waves, and wherein the formation type of the formation is determined based on the slowness of the wave and the slowness of the second wave.

7. The method of claim 1 , wherein in response to a determination that the formation type of the formation is not a slow formation, the method further comprising:

obtaining waveform data of a second wave;

determining, from the waveform data of the second wave, whether a shear slowness peak of a shear of the second wave is coherent and continuous in a frequency axis; and

in response to a determination that the shear slowness peak is coherent and continuous in the frequency axis, designating a slowness of the shear of the second wave as the initial body wave slowness estimate of the wave.

8. The method of claim 7 , wherein in response to a determination that the shear slowness peak is not coherent and continuous in the frequency axis, the method further comprising:

determining whether a slowness of the second wave is within a threshold distance from the edge slowness of the wave;

in response to a determination that the slowness of the second wave is within a threshold distance from the edge slowness of the wave, designating a slowness of the shear of the second wave as the initial body wave slowness estimate of the wave, and

in response to a determination that the slowness of the second wave is not within a threshold distance from the edge slowness of the wave, designating the edge slowness of the wave as the initial body wave slowness estimate of the wave.

9. A multi-mode dispersion estimation system, comprising:

a storage medium; and

one or more processors configured to:

obtain waveform data of a plurality of waves traversing through a downhole formation, wherein each wave of the plurality of waves has a different threshold cutoff frequency;

perform a multimode dispersion analysis of the waveform data to generate a semblance map of the plurality of waves;

obtain a slowness dispersion of a wave of the plurality of waves;

determine a formation type of a formation the wave traverses based on one or more properties of the plurality of the waves;

determine an initial body wave slowness estimate of the wave;

determine an edge slowness of the wave;

in response to a determination that the formation type of the formation is a slow formation, designate the edge slowness of the wave as the initial body wave slowness estimate of the wave

generate a modeling of the wave; and

reduce a mismatch between the modeling of the wave and the slowness dispersion of the wave to improve the modeling of the wave.

10. The multi-mode dispersion estimation system of claim 9 , wherein the one or more processors are further configured to:

analyze one or more peaks of the semblance map; and

extract a slowness dispersion of the wave from the one or more peaks of the semblance map.

11. The multi-mode dispersion estimation system of claim 10 , wherein the one or more processors are further configured to:

obtain waveform data of a second wave;

perform a multimode dispersion analysis of the waveform data of the second wave to generate a second semblance map of the second wave;

analyze one or more peaks of the second semblance map;

extract a slowness dispersion of a second wave from the one or more peaks of the second semblance map;

generate a modeling of a second wave; and

reduce a mismatch between the modeling of the second wave and the slowness dispersion of the wave to improve the modeling of the second wave.

12. A non-transitory machine readable medium having one or more instructions which, when executed by a processor, cause the processors to perform operations comprising:

obtaining waveform data of a plurality of waves traversing through a downhole formation, wherein each wave of the plurality of waves has a different threshold cutoff frequency;

performing a multimode dispersion analysis of the waveform data to generate a semblance map of the plurality of waves;

obtaining a slowness dispersion of a wave of the plurality of waves;

determining a formation type of a formation the wave traverses based on one or more properties of the plurality of the waves;

determining an initial body wave slowness estimate of the wave;

determining an edge slowness of the wave;

in response to a determination that the formation type of the formation is a slow formation, designating the edge slowness of the wave as the initial body wave slowness estimate of the wave

generating a modeling of the wave; and

reducing a mismatch between the modeling of the wave and the slowness dispersion of the wave to improve the modeling of the wave.

13. The non-transitory machine readable medium of claim 12 , wherein the instructions which, when executed by the processor, cause the processor to further perform operations comprising:

obtaining waveform data of a second wave;

performing a multimode dispersion analysis of the waveform data of the second wave to generate a second semblance map of the second wave;

analyzing one or more peaks of the second semblance map;

extracting a slowness dispersion of a second wave from the one or more peaks of the second semblance map;

generating a modeling of a second wave; and

reducing a mismatch between the modeling of the second wave and the slowness dispersion of the wave to improve the modeling of the second wave.