Methods and systems with estimated synchronization between modular downhole logging system modules

A method that comprises:

• deploying a modular downhole logging system in a borehole, the modular downhole logging system having at least one transmitter module, at least one receiver module, and a processor;
• transmitting, by the at least one transmitter module, interrogation signals into a formation surrounding the borehole, wherein the interrogation signals are a function of a local frequency of the at least one transmitter module;
• receiving, by the at least one receiver module axially-spaced from the at least one transmitter module, response signals corresponding to the interrogation signals;
• performing sync estimation operations, by the at least one receiver module, wherein the sync estimation operations include estimating the local frequency of the at least one transmitter module based on analysis of response signal Fourier transform results corresponding to different frequencies;
• sampling, by the at least one receiver module, at least some of the response signals based on the estimated local frequency of the at least one transmitter module;
• and
• deriving, by the processor, formation property values using the sampled response signals.