Depth Dependence of Signal-to-Noise Ratio in Shallow Seismic Monitoring

The signal-to-noise ratio (SNR) is a key parameter controlling the detectability, particularly for near-surface and shallow borehole seismic monitoring. While shallow borehole arrays are widely used to suppress surface noise and improve SNR, a physically consistent analytical description of SNR variation with depth has remained limited. Existing models typically assume an exponential decay of noise decay with depth and often neglect depth-dependent variations of the seismic signal itself. We developed a new analytical model describing the depth dependence of SNR in a homogeneous elastic half-space, explicitly accounting for the free-surface boundary condition. The signal is modelled as a superposition of upward- and downward-propagating body waves generated by reflection at the free surface. We modified already proposed noise model by Kalinichenko et al. (2025) that consistently links surface and shallow-borehole noise levels. The noise is represented as a superposition of an exponentially decaying surface-wave component and a slowly decaying body-wave component. We model depth dependence of noise as a superposition of exponentially decaying fundamental mode of surface waves and linearly decaying body waves. We show that the up- and down-going wave superposition results in frequency-dependent constructive and destructive interference of signal unsuitable for general microseismic monitoring. We show the depth of signal destructive interference, also known as a ghost, occurs also in a band-limited seismic signal and that its depth depends on the peak frequency of the signal. Furthermore, the complex SNR variations are limited to depths shallower than one-half of the wavelength of the peak frequency of the signal and SNR increases monotonically below this depth.