On Seismic Wave Equation Gradiometric Inversion for Density

It is of interest for environmental and resource applications to better characterise dynamic processes and properties of the near-surface critical zone of the solid Earth. Seismic wavefield gradiometry refers to a class of imaging techniques that estimate properties of the subsurface by calculating temporal and spatial gradients of incoming wavefields using dense array measurements, usually recorded at the Earth’s surface. One such method called wave equation inversion (WEI) has been shown to require only a few minutes of ambient seismic noise recordings to produce phase velocity maps, and shows promise for rapid field deployment.

Previous applications of WEI are based on the assumption that the 2D scalar Helmholtz wave equation adequately describes the dynamics of recorded wavefields. This approximation is severe for seismic waves because the Helmholtz equation fails to describe elastic wave dynamics. Since ambient noise recordings contain all kinds of interfering elastic wave types, the accuracy of subsurface material property estimates is compromised.

To investigate the potential to enhance the information available from WEI, we test the method synthetically using more sophisticated wave equations that represent wave propagation in the subsurface more accurately. Starting from a 3D seismic array geometry which provides wavefield gradient information both at the surface and at depth, WEI can be formulated in terms of the full elastic wave equation. From there we track approximations in both wave physics and field acquisition geometries that deplete information about the medium, eventually arriving at the conventional 2D scalar wave equation. These experiments highlight approximations that most deteriorate the solution, allowing us to target future effort to remove them.

One approximation made in all previous WEI studies is to assume that density is constant across the local array. In reality, subsurface density varies both laterally and with depth, yet remains poorly constrained in seismic imaging problems. Accurate density estimates would provide important insight into subsurface properties. This prompts us to test wavefield sensitivities to subsurface density contrasts via WEI. Synthetic results for 3D acoustic media suggest that it is possible to estimate relative density structure with WEI by using a full acoustic formulation for wave propagation along the surface. We show that using a constant density assumption for the medium can be detrimental to subsurface images, whereas the full acoustic formulation of gradiometry improves our knowledge of material properties. It allows us to estimate density as an additional material parameter as well as to improve phase velocity estimates by incorporating approximations to the density structure. By expanding this methodology to the elastic case, we will discuss the feasibility of estimating density with gradiometric WEI in the solid Earth.