Systems and methods for measuring cluster efficiency using broadband tube waves

A method for measuring cluster efficiency for a stage of a wellbore, wherein the wellbore comprises a fluid column that is defined by a surface casing string that couples the wellbore to a wellhead located at a surface and a production casing string that extends through a reservoir within a subsurface, and wherein the method comprises:

• selecting a frequency band for generating broadband tube waves within the fluid column of the wellbore;
• generating the broadband tube waves within the fluid column of the wellbore using a pressure pulse generator that is hydraulically coupled to the wellbore;
• recording data corresponding to the broadband tube waves and reflected broadband tube waves using a plurality of pressure receivers that are hydraulically coupled to the wellbore, wherein the plurality of pressure receivers are arranged into arrays with at least two pressure receivers in each array and with one array positioned on a same tubing as the pressure pulse generator and another array positioned on a separate offshoot of tubing, wherein the data recorded by the plurality of pressure receivers relate to characteristics of reflectors within the wellbore, and wherein the reflectors comprise perforation cluster/fracture interfaces within a stage of the wellbore;
• processing the recorded data using interferometry;
• and
• performing at least one full waveform inversion on the processed data to determine frequency-dependent, complex-valued reflection coefficients at each perforation cluster/fracture interface within the stage of the wellbore.