arXiv subjects

Yukitoshi Fukahata

Publications and source records attributed to Yukitoshi Fukahata.

4 recordsLinked to original sources

arXiv2026

Smooth surface reconstruction of earthquake faults from distributed moment-potency-tensor solutions

Earthquake faults as observed by seismic motions primarily manifest as displacement discontinuities within elastic continua. The displacement discontinuity and the surface normal vector (n-vector) of such an idealized earthquake source are measured by the tensor of potency, which is seismic moment normalized by stiffness. This study formulates an inverse problem to reconstruct a smooth 3D fault surface from an areal density field of the potency tensor. Here, the surface is represented by an elevation field, while nodal planes of the potency density represent the surface normal (n-vector) field, reducing the problem to an n-vector-to-elevation transform. Although this transform is a one-to-one mapping in 2D, it becomes overdetermined in 3D because the n-vector has two degrees of freedom while the scalar elevation has only one, admitting no solution in general. This overdeterminacy originates from modeling the potency density, the inelastic strain with six degrees of freedom, as a displacement discontinuity of five degrees of freedom. Whereas this overdeterminacy appears as the violation of the determinant-free constraint in point potency sources, it raises a conflict with the global consistency of the n-vector field in areal potency densities. Recognizing this capacity of the potency density to describe inelastic strain incompatible with displacement discontinuity, we introduce an a priori constraint to define the fault as the smooth surface that best approximates inelastic strain as displacement discontinuity. We derive an analytical solution for this formulation and demonstrate its ability to reproduce 3D surfaces from noisy synthetic n-vectors. We integrate this formula into potency density tensor inversion and apply it to the 2013 Balochistan earthquake. The estimated 3D geometry shows better agreement with observed fault traces than previous quasi-2D methods, validating our proposal.

physics.geo-ph↗

arXiv2025

Differentiating frictionally locked asperities from kinematically coupled zones

Seismogenic areas on plate-boundary faults resist slipping until earthquakes begin. The delay in slip relative to plate motion, termed slip deficit, represents plate coupling as an interseismic proxy of seismic potential. However, when a part of a frictional interface sticks together (locked), the unlocked sliding surroundings are braked and slowed (coupled), causing coupled zones always wider than the locked zones that rupture during earthquakes. This study investigates the frictional physics that locked and unlocked zones should observe, laying the foundation for inferring frictionally locked segments, known as asperities in fault mechanics. Various friction laws are shown to have a unified representation of locking. (I) Locking means the pre-yield phase, where the fault interface does not slip, and unlocking means the post-yield phase, where stress on the interface equals strength. (II) For intersesismic periods, while locking still denotes constant slip, unlocking signifies quasi-steady creeping of constant stress. Locking inversion, a variant of conventional coupling inversion that incorporates this unified frictional physics, estimates the distribution of locking, determining slip and stress distributions consequently. We solve the locking inversion by a method that distributes circular asperities on unlocked interfaces. By applying this method to on-/off-shore GNSS data in southwestern Japan, we detect five primary locked segments along the Nankai subduction zone. Those segments accord with slip zones of historical megathrust earthquakes correlated with seafloor basins. Estimated locked zones avoid the occurrence zones of deep slow earthquakes, reproducing the hypothesis that the areas hosting slow earthquakes are normally, in interseismic timescales, coupled but unlocked.

physics.geo-ph↗

arXiv2022

A proof of consistency and model-selection optimality on the empirical Bayes method

We study the consistency and optimality of the maximum marginal likelihood estimate (MMLE) in the hyperparameter inference for large-degree-of-freedom models. We perform main analyses within the exponential family, where the natural parameters are hyperparameters. First, we prove the consistency of the MMLE for the general linear models when estimating the scales of variance in the likelihood and prior. The proof is independent of the number ratio of data to model parameters and excepts the ill-posedness of the associated regularized least-square model-parameter estimate that is shown asymptotically unbiased. Second, we generalize the proof to other models with a finite number of hyperparameters. We find that the extensive properties of cost functions in the exponential family generally yield the consistency of the MMLE for the likelihood hyperparameters. Besides, we show the MMLE asymptotically almost surely minimizes the Kullback-Leibler divergence between the prior and true predictive distributions even if the true data distribution is outside the model space under the hypothetical asymptotic normality of the predictive distributions applicable to non-exponential model families. Our proof validates the empirical Bayes method using the hyperparameter MMLE in the asymptotics of many model parameters, ensuring the same qualification for the empirical-cross-entropy cross-validation.

math.ST↗

arXiv2022

Appropriate reduction of the posterior distribution in fully Bayesian inversions

Bayesian inversion generates a posterior distribution of model parameters from an observation equation and prior information both weighted by hyperparameters. The prior is also introduced for the hyperparameters in fully Bayesian inversions and enables us to evaluate both the model parameters and hyperparameters probabilistically by the joint posterior. However, even in a linear inverse problem, it is unsolved how we should extract useful information on the model parameters from the joint posterior. This study presents a theoretical exploration into the appropriate dimensionality reduction of the joint posterior in the fully Bayesian inversion. We classify the ways of probability reduction into the following three categories focused on the marginalisation of the joint posterior: (1) using the joint posterior without marginalisation, (2) using the marginal posterior of the model parameters and (3) using the marginal posterior of the hyperparameters. First, we derive several analytical results that characterise these categories. One is a suite of semianalytic representations of the probability maximisation estimators for respective categories in the linear inverse problem. The mode estimators of categories (1) and (2) are found asymptotically identical for a large number of data and model parameters. We also prove the asymptotic distributions of categories (2) and (3) delta-functionally concentrate on their probability peaks, which predicts two distinct optimal estimates of the model parameters. Second, we conduct a synthetic test and find an appropriate reduction is realised by category (3), typified by Akaike's Bayesian information criterion (ABIC). The other reduction categories are shown inappropriate for the case of many model parameters, where the probability concentration of the marginal posterior of the model parameters is found no longer to mean the central limit theorem...

physics.geo-ph↗