Silence out quiet periods in audio file with ffmpe

Question

I'm using ffmpeg to do some audio processing on phone calls. The raw calls have a left and right channel and my desired result is two mono files, one for each channel. I was able to use ffmpeg's map_channel to split the file by channel but I'm noticing the resulting files have a bit of cross talk that I would like to remove.

Each channel has the primary speaker talking very loud and clear but you can also hear the person from the other channel talking very quietly. I'd like to silence out these sections of the audio (i.e. make them perfectly silent but not remove them as I want to preserve the original length and pauses in the audio).

Does ffmpeg have a filter I can use to convert periods of low volume (or some other measurement that would isolate these sections of the recording) into total silence?