Methods for compression of sonic log data include STC processing, sorting peak components in the sonic data; filtering the sorted peak components to remove high-frequency portions in the peak components; and decimating the filtered peak components according to a selected ratio to produce compressed data. One method for telemetry transmission of downhole sonic log data includes sorting peak components in the sonic log data; compressing the sorted peak components to produce compressed data; packing the compressed data to produce data packets for telemetry transmission; and sending the data packets using telemetry.