arXiv subjects

Dye SK Sato

Publications and source records attributed to Dye SK Sato.

12 recordsLinked to original sources

arXiv2026

Diffusional earthquakes and their slip-distance scaling

The final size of an earthquake typically cannot be predicted from its ongoing seismic radiation. Expanding observations reveal distinct exceptions, such as slow earthquakes, injection-induced seismicity, and earthquake swarms, in which fault slip has an upper bound. A common thread among these anomalies is the diffusive migration of their active areas. Here, we report a unified scaling relation for these diffusional earthquakes. By tracking prolonged earthquake swarms in Northeast Japan, we constrained the time evolution of their active seismicity areas and cumulative seismic moments. Their moment-duration trajectories coincide with the final states documented for global swarms and induced seismicity across various scales. When plotted as seismic moment versus seismicity area, their trajectories collapse onto those of slow earthquakes, uniformly explained by a diffusional constant-slip model. This constant-slip scaling carves out a unique class of diffusional earthquakes, where the final available seismic energy is predetermined by slip distance.

physics.geo-ph↗

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↗

arXiv2026

A log-linear time algorithm for the elastodynamic boundary integral equation method

We present a fast and memory-efficient algorithm for transient, space-time-domain, and elastodynamic boundary-integral analysis. Associated data-sparse approximations and operations are named fast domain partitioning hierarchical matrices (FDP=H-matrices). The fast domain partitioning method (the FDPM) solves a known problem of hierarchical matrices (H-matrices) in compressing discretized elastodynamic kernel functions. A novel set of plane-wave approximations then unites the FDPM and H-matrices in an accurate analytic manner. Memory usage is $\mathcal O(N \log N)$ and computation time $\mathcal O(NM \log N)$ in our algorithm throughout one run with $N$ boundary elements and $M$ time steps. The amount of associated cost reduction is remarkable, as the memory usage and computational time have been originally $\mathcal O(N^2M)$ and $\mathcal O(N^2M^2)$, respectively, to run the orthodox time-marching implementation. Numerical experiments indicate that FDP=H-matrices achieve $\mathcal O(NM/\log N)$ times smaller memory and computation time while ensuring the accuracy of the analyses.

physics.comp-ph↗

arXiv2025

Postseismicity of slow-slip doublets discerned on the outermost of the Nankai Trough subduction megathrust

Despite dissimilar slip rates, slow earthquakes are faulting as ordinary earthquakes are. It is therefore physically natural that slow earthquakes also cause postseismic motions similarly to ordinary earthquakes, even though coseismic and postseismic slips remain undifferentiated for slow earthquakes. We pursue the slow-earthquake postseismicity based on the analysis of a fault slip beneath the Bungo Channel, the westernmost region of the Nankai Trough subduction zone in southwestern Japan. Its 2010 long-term slow slip event (SSE) was mispredicted by physics-based models, which concludes that the initial acceleration of this SSE was too abrupt for a slow variant of a fault rupture. We identify that a mispredicted GNSS signal evolves logarithmically in time, preceded by minor signals that evolve exponentially, lasting about two years west and about half a year east. By performing sparse inverse modeling on the GNSS, we have estimated that exponential slips occur at the same depth, bracketing a logarithmic slip that occurs beneath the channel. The regions of exponential slips match repeating slow-slip regions, and deep tremors synchronize exclusively with the logarithmic slip. This source complexity can be explained as a neighboring rupture doublet and its afterslip and aftershocks by the known mechanics of ordinary earthquakes. If slow earthquakes have a dual origin in exponentially nucleating slow rupture and logarithmically decelerating postseismic creep, it is possible to pick the slow earthquake nuclei that could accelerate into megathrust catastrophes.

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↗

arXiv2025

Reconciling aging and slip state evolutions from laboratory-derived canons of rate-and-state friction

The aging law and the slip law are two representative evolution laws of the rate- and state-dependent friction (RSF) law, based on canonical behaviors in three types of laboratory experiments: slide-hold-slide (SHS), velocity-step (VS), and steady-state (SS) tests. The aging law explains the SHS canon but contradicts the VS canon, and vice versa for the slip law. The later proposed composite law, which switches these two laws according to the slip rate $V$, explains both canons but contradicts the SS canon. The present study constructs evolution laws satisfying all three canons throughout the range of variables where experiments have confirmed the canons. By recompiling the three canons, we have derived constraints on the evolution law and found that the evolution rates in the strengthening phases of the SHS and VS canons are so different that complete reconciliation throughout the entire range of variables is mathematically impossible. However, for the limited range of variables probed by experiments so far, we have found that the SHS and VS canons can be reconciled without violating the SS canon by switching the evolution function according to $Ω$, the ratio of the state $θ$ to its steady-state value $θ_{\rm SS}$ for the instantaneous slip rate. We could generally show that, as long as the state evolution rate $\dot θ$ depends only on the instantaneous values of $V$ and $θ$, simultaneous reproduction of the three canons, throughout the experimentally confirmed range, requires the aging-law-like evolution for $Ω$ sufficiently below a threshold $β$ and the slip-law-like evolution for $Ω$ sufficiently above $β$. The validity of the canons in existing experiments suggests $β\lesssim 0.01$.

physics.geo-ph↗

arXiv2024

A comparative study on the self-similarity hypothesis of regular and slow earthquake growth

Fault ruptures of regular earthquakes typically grow in a self-similar manner, where the radiated energy is proportional to the seismic moment. Their proportionality factor, termed as scaled energy, has been conventionally described as the ratio of stress drop to stiffness. By analyzing the self-similar circular crack model by Sato and Hirasawa (1973), Matsu'ura (2024) found a correction prefactor for this theoretical representation of the scaled energy, the cubed ratio of the rupture speed to the S-wave speed. The stress drop times the cubed rupture speed is the scaling prefactor of the self-similar seismic moment, and thus, Matsu'ura's solution tells that the seismic moment rate is determined by the scaled energy in the self-similar rupture growth. We rearrange the properties of the self-similar solution from this perspective, apply this Sato-Hirasawa-Matsu'ura relation to a series of seismic events thought to be self-similar, and estimate their source parameters and scaled energies. According to our estimation using the above self-similarity model, seismologically detected low-frequency and very-low-frequency earthquakes have a common scaled energy, while geodetically detectable slow slip events indicate multiple modes with different scaled energies. Meanwhile, for very-low-frequency earthquakes and tectonic tremors, the seismic moments were significantly smaller than expected for self-similar ruptures despite their moments being proportional to cubed duration values. It keeps alive a hitherto less contemplated possibility: the proportionality of the moment to cubed duration may not be a manifestation of the self-similarity for slow earthquake rupture growth.

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↗

arXiv2020

Universal scaling for recovery of Fourier's law in low-dimensional solids under momentum conservation

Dynamic renormalization group (RG) of fluctuating viscoelastic equations is investigated to clarify the cause for numerically reported disappearance of anomalous heat conduction (recovery of Fourier's law) in low-dimensional momentum-conserving systems. RG flow is obtained explicitly for simplified two model cases: a one-dimensional continuous medium under low pressure and incompressible viscoelastic medium of arbitrary dimensions. Analyses of these clarify that the inviscid fixed point of contributing the anomalous heat conduction becomes unstable under the RG flow of nonzero elastic-wave speeds. The dynamic RG analysis further predicts a universal scaling of describing the crossover between the growth and saturation of observed heat conductivity, which is confirmed through the numerical experiments of Fermi-Pasta-Ulam $β$ (FPU-$β$) lattices.

cond-mat.stat-mech↗

arXiv2020

Paradox of Modeling Curved Faults Revisited with General Non-Hypersingular Stress Green's Functions

In a dislocation problem, a paradoxical discordance is known to occur between an original smooth curve and an infinitesimally discretized curve. To solve this paradox, we have investigated a non-hypersingular expression for the integral kernel (called the stress Green's function) which describes the stress field caused by the displacement discontinuity. We first develop a compact alternative expression of the non-hypersingular stress Green's function for general two- and three-dimensional infinite homogeneous elastic media. We next compute the stress Green's functions on a curved fault and revisit the paradox. We find that previously obtained non-hypersingular stress Green's functions are incorrect for curved faults, and that smooth and infinitesimally segmented faults are equivalent. Their compatibility bridges the gap between analytical methods featuring curved faults and numerical methods using subdivided flat patches.

physics.geo-ph↗

arXiv2016

Pressure-induced recovery of Fourier's law in one dimensional momentum-conserving systems

We report the two typical models of normal heat conduction in one dimensional momentum-conserving systems. They show the Arrhenius and the non-Arrhenius temperature dependence. We construct the two corresponding phenomenologies, transition-state theory of thermally activated dissociation and the pressure-induced crossover between two fixed points in fluctuating hydrodynamics. Compressibility yields the ballistic fixed point, whose scaling is observed in FPU-βlattices.

cond-mat.stat-mech↗