Downhole receiver function: A case study

Receiver function is defined as the spectral ratio of the radial component and the vertical component of the ground motion. It is used to characterize converted waves. We extend the use of the receiver function to downhole data using waves recorded in a borehole, excited by an earthquake of magnitude 4.0 near San Francisco, California, on 26 June 1994. The focal depth of the event was 6.6 km and the epicenter was located at a distance of 12.6 km from the borehole array. Six three-component sensors were located at different depths in a borehole. To extract a coherent response of the near-surface from the incoherent earthquake waves, we deconvolve the waves recorded by the sensors at different depths with the waves recorded by the sensor on the surface. Deconvolution applied to the waves in the S-time window recorded by the radial component result in an upgoing and a downgoing wave propagating with S-wave velocity. For the waves in the P-time window recorded by the radial component, deconvolution also gives an upgoing and a down-going wave propagating with S-wave velocity. This interesting result suggests a P-to-S conversion at a depth below the deepest sensor. To diagnose this we compute the receiver function for the borehole recording of the earthquake waves. The receiver function shows an upgoing wave with an arrival close to time t = 0 for the deepest sensor. The agreement of the upgoing wave in the receiver function with the travel-time curve for the P-to-S converted wave, calculated using the P- and the S-wave velocity profile, supports the hypothesis of a pronounced P-to-S conversion. We present a synthetic example to illustrate that the first arrival of the receiver function applied to borehole data gives the upward-propagating P-to-S converted wave. To corroborate the observation of the mode conversion, we apply receiver function to a different earthquake data recorded by the same borehole array in 1998. The focal depth of the event was 6.9 km and the epicenter was located at a distance of 13 km from the borehole array. The receiver function for these data also show an upgoing wave with a pulse close to time t = 0 at the deepest sensor. The moveout of the upgoing wave agrees with the travel-time curve for the P-to-S converted wave, hence supporting our observation of the mode conversion.