Adjoint sensitivity kernels for receiver functions
Authors:   , de Jong Janneke Helena Elizabeth 
Published: May 2024

In Groningen, the state of the subsurface has been a cause for concern for many years. Earthquakes, induced by local gas production, have caused significant economic damage, and disturbed the lives of local communities. Even though gas production has stopped, it remains important to monitor the area such that proper estimations of the risks can be made. In Groningen, most monitoring is focused on detection, localization, and classification of induced seismic events. However, it is also important to monitor gradual changes in the subsurface in order to detect the release or build-up of stress, and better estimate the earthquake risk. This thesis aims to answer whether it is possible to adapt the method of receiver functions from global seismology to a smaller scale, so that it can be used to detect small, gradual changes in the near subsurface.
Imaging interfaces and their topography is an important part of understanding the subsurface of our Earth. Discontinuities are marked by a stark contrast of the physical properties between two adjacent layers. To image discontinuities, seismologists can use converted waves. The arrivals of these converted waves contain information on the depth and topography of the discontinuity. Receiver functions are adapted waveforms that enhance the generally weak signals from converted. They have been used by the global seismological community for the past five decades to image discontinuities.
Before I can assess the possibility of applying this global method to the small scale setting of Groningen. I investigate what precisely contributes to a receiver function’s waveform. Using the adjoint method developed for full waveform inversion, I calculate the sensitivity kernels for a receiver function’s waveform to the volumetric parameters of P- and S-wave velocity and impedance or to the discontinuity’s topography.I calculated synthetic receiver functions for a 3D, global, realistic setting and for a 2D, regional scale, synthetic model. In both cases I found that receiver functions are sensitive to discontinuity topography. However, I also found a strong trade-off between the sensitivity to velocity and discontinuity depth. Lastly, I found that, contrary to previous assumptions, receiver functions are sensitive to the structural parameters along the entire wave path of the converted wave..
Then, I applied my method to data from the small scale setting in Groningen. I investigated receiver functions recorded with geophones located in the gas reservoir at 3km depth. In this unconventional set-up, I used receiver functions to look upward, so that I could monitor the depths and topography of the interfaces of the overburden.
I found that, although it is unlikely that the signal from subsidence in Groningen is large enough to be detected directly, it can be observed by exploiting the linear behaviour of receiver function sensitivity. This means that it is possible to isolate the receiver function sensitivity to the subsurface change. Because of this linearity, borehole receiver functions are well suited for time lapse monitoring of overburden subsidence if data from a constant signal or a repetitive source is available.