Geodetic inversion for spatial distribution of slip under smoothness, discontinuity, and sparsity constraints

Abstract

In geodetic data inversion, insufficient observational data and smoothness constraints for model parameters make it difficult to clearly resolve small-scale heterogeneous structures with discontinuous boundaries. We therefore developed a novel regularization scheme for the inversion problem that uses discontinuity, sparsity, and smoothness constraints. In order to assess its usefulness and applicability, the proposed method was applied to synthetic displacements calculated by a ring-shaped and sharply varying afterslip distribution on a plate interface. The afterslip was obtained from reasonable numerical simulation of earthquake generation cycle with a rate-and state-dependent friction law and realistic three-dimensional plate geometry. The obtained afterslip distribution was heterogeneous, and the discontinuous boundary was sharper than that obtained by using smoothness constraint only. The same inversion test was conducted with a smoothly varying circular slip distribution with large slips inside the ring-shaped distribution. The method accurately reproduces the smooth distribution of the slip area as well as the ring-shaped distribution. Therefore, the method could be applied to any slip distribution, with both discontinuous and continuous boundaries. Adopting this method for measured data will make it possible to obtain detailed heterogeneous distributions of physical structures on fault planes. The proposed method is therefore applicable to various geophysical inversion problems that exhibit discontinuous heterogeneity.

Discontinuous boundaries of slow slip events beneath the Bungo Channel, southwest Japan

“…In geophysics, sparsity constraints 18 have been introduced as a priori information into geodetic inversions instead of the commonly used smoothness constraints 22, 23 . Sparsity constraints have shown compact and sharply varying slip distributions with discontinuous boundaries, which are close to the end-member image of a slip distribution and previously unimaginable.…”

“…Recently, a sophisticated scientific information method using sparsity constraints 18 , 19 , which is referred to as compressed sensing, has been applied to various natural science fields 20 , 21 . In geophysics, sparsity constraints 18 have been introduced as a priori information into geodetic inversions instead of the commonly used smoothness constraints 22 , 23 . Sparsity constraints have shown compact and sharply varying slip distributions with discontinuous boundaries, which are close to the end-member image of a slip distribution and previously unimaginable.…”

Geodetic inversion for spatial distribution of slow earthquakes under sparsity constraints

“…We proposed a new evaluation function by incorporating three constraints: smoothness, discontinuity, and sparsity (SDS) constraints as prior information for inversion ( Figure 3) [4]. The new evaluation function can be expressed as: (2) where is a precision hyperparameter, is a smoothness hyperparameter for the non-zero-slip area, is a sparsity hyperparameter.…”

“…The first example is directly represented above, and our goal is to extract adequately both smoothness and abrupt change in slip distribution to the extent of observation data quality. We analyze afterslip on a plate interface following a moment magnitude (Mw) 6.8 earthquake beneath the Hyuga-nada offshore region [4]. On the other hand, the goal of the second example is to determine the presence of abrupt changes and detect their locations without detail slip distribution.…”

Locating Spatial Changes of Seismic Scattering Property by Sparse Modeling of Seismic Ambient Noise Cross‐Correlation Functions: Application to the 2008 Iwate‐Miyagi Nairiku (Mw6.9), Japan, Earthquake

“…LASSO has been widely used in sparse modeling. In recent years, this technique has been used for earthquake source inversions or geodetic inversions (e.g., Evans & Meade, 2012; Nakata et al, 2016; Yao et al, 2011). Yao et al (2011) estimated the distribution of source powers during the rupture of the 2011 Tohoku‐Oki, Japan, earthquake from teleseismic P waves recorded by an array of stations in the United States.…”