I work on applications of mechanics of solids and shear fractures to understand seismic and aseismic slip on faults; and, how fault slip evolution can be seamlessly posed in the broader framework of nonlinear dynamics. I am widely interested in mathematical modeling of various physical processes in the fields of tectonophysics, rock friction, and seismology; and, in turn, I often drift towards dynamical system theory, numerical methods for and approximate solutions of nonlinear partial differential equations. (Curriculum Vitae)

**R E S E A R C H**

**Earthquake nucleation with heterogeneous fault frictional strength**

We examine the development of instabilities of fault slip rate. We consider a slip rate and state dependence of fault frictional strength, in which frictional properties and normal stress are functions of position. We pose the problem for a slip rate distribution that diverges quasi-statically within finite time in a self-similar fashion. Scenarios of property variations are considered and the corresponding self-similar solutions found. We focus on variations of coefficients, a and b, respectively, controlling the magnitude of a direct effect on strength due to instantaneous changes in slip rate and of strength evolution due to changes in a state variable. These results readily extend to variations in fault-normal stress and the characteristic slip distance for state evolution, Dc. We find that heterogeneous properties lead to a finite number of self-similar solutions, located about critical points of the distributions: maxima, minima, and between them. We examine the stability of these solutions and find that only a subset is asymptotically stable, occurring at just one of the critical point types. Such stability implies that during instability development, slip rate and state evolution can be attracted to develop in the manner of the self-similar solution, which is also confirmed by solutions to initial value problems for slip rate and state. A quasi-static slip rate divergence is ultimately limited by inertia, leading to the nucleation of an outward expanding dynamic rupture: asymptotic stability of self-similar solutions then implies preferential sites for earthquake nucleation, which are determined by the distribution of frictional properties. [Ray and Viesca, JGR Solid Earth 2017].

**Homogenization of physical properties on faults**

Observations suggest that faults’ frictional properties are likely to be non-uniform over its extent. However, studies often consider properties to be homogeneous, or nearly so. Here, we highlight when it may not be appropriate to homogenize the frictional properties. We explore quasistatic slip evolution on faults with simple sinusoidal forms, with a characteristic wavelength of variation Λ, for variation of frictional properties. Interestingly, slip evolutions are almost identical in the limit of very small (highly heterogeneous) and large (almost homogeneous) wavelengths, compared to the nucleation length.

Therefore, in the limit of high and low wavelengths of variations, the using average estimate of an otherwise nonuniform strength parameter is appropriate. However, heterogeneity in fault frictional properties, or normal stress, is crucial to earthquake nucleation when Λ is comparable to the nucleation length or an elastofrictional scale.**Frictional heterogeneities can promote disordered slip evolution on faults**

Prior stability analyses, considering heterogeneous frictional properties revealed that stable blow-up solutions can predictably dictate earthquake-nucleating instabilities. In this prior analysis, the focus remained mainly on the attraction to stable blow-up solutions. Here, we shift the focus of discussion towards unstable blow-up solutions, in particular, we seek frictional heterogeneities that can make all blow-up solutions to lose stability. (We consider variations in direct and evolution effect parameters, $a(x)$ and $b(x)$, and pressume that $D_c$ and $\sigma$ are uniform). We find that faults that include rate-strengthening regions can lack attractive blow-up solutions. In such scenarios, a rate-weakening fault that includes appropriate rate-strengthening regions can significantly delay the development of an instability compared to a fault that is entirely rate-weakening. That delay can be attributed to the loss of stability of the blow-up solutions. Owed to the non-existence of attractive blow-up solutions, the developing slip velocity fails to converge to a specific distribution at a single location. The near-chaotic transient dynamics may give rise to tremor-like activities.

**Creeping landslides as diffusing slip on rate-strengthening frictional faults**.

Accelerating creep of landslides could be considered an evolution of slip of a deformable thin elastic layer over a rigid base such that basal friction strengthens with slip rate. We find self-similar solutions of nonlinear slip diffusion under relevant initial conditions of external stress or slip rate. A close analogy could be drawn with the Stokes’ first problem wherein a plate below a semi-infinite region of initially static incompressible fluid is suddenly moved to result in (self-similar) diffusion of momentum. Likewise, we find relevant lengthscale and nonlinear manner of diffusion of slip rate when a creeping slope is suddenly imposed with high stress or slip rate.

**T E A C H I N G**

- Fall 2016:
**Statics and dynamics**(TA) - Spring 2017:
**Strength of materials**(TA) - Fall 2017:
**Statics and dynamics**(TA)

**P U B L I C A T I O N S**

- S. Ray and Viesca R. C. (2017)
*,*Earthquake nucleation on faults with heterogeneous frictional properties, normal stress.*Journal of Geophysical Research: Solid Earth*,

DOI: 10.1002/2017JB014521. - S. Ray and Viesca R. C. (2019), Homogenization of fault frictional properties.
*Geophysical Journal International*, DOI: https://doi.org/10.1093/gji/ggz327. - S. Ray (2019), Frictional heterogeneities can promote disordered slip evolution on faults. EarthArXiv. September 3. doi:10.31223/osf.io/dcszm.
- Creeping landslides as diffusing slip on rate-strengthening frictional faults (in the works).

**C O N F E R E N C E S & M E E T I N G S**

- Stanford Earth, Department seminar, March 2019,

Nonlinear instability and diffusion of fault slip rate. - UMass Amherst, Nonlinear Waves Seminar, 2019,

Aseismic and seismic slip on geological faults - American Geophysical Union, 2018, Oral presentation, (Talk)

Slip instability and aseismic slip under multiple length scales of frictional heterogeneity. - Applied Math Seminar, Tufts University, 2018, Oral presentation,

Earthquake nucleation on faults: a finite-time instability problem. - Gordon Research Seminar/Conference, 2018, Oral/Poster,

Earthquake nucleation on faults under a multitude of length scales of frictional heterogeneity. GRS’18Talk - European Geophysical Union General Assembly, 2018,

Accelerated creep of a landslide with slip rate- and state-dependent basal friction

Lichen Wang, Sohom Ray, Pierre Dublanchet, and Robert C. Viesca - Dynamics Days, 2018, Ignite Talk and Poster,

The self-similar solution of diverging slip rate on faults with heterogeneous friction

Sohom Ray and Robert C. Viesca - Gordon Research Conference on Rock Deformation, 2016,

Preferential locations of slip-rate instabilities on faults determined by heterogeneous frictional properties.

Sohom Ray and Robert C. Viesca - Winter School, Cargese, Corsica, 2014, Oral,

Slip rate instability under heterogeneous fault friction - Southern California Earthquake Center, 2014 and 2015,

Preferential earthquake-nucleating locations on faults determined by heterogeneous direct-and evolution-effect parameters of rate-and state-dependent friction

Sohom Ray and Robert C. Viesca - American Geophysical Union, 2014 (and 2016) Oral (and Poster),

The evolution of earthquake-nucleating slip instabilities under spatially variable steady-state rate dependence of friction

Sohom Ray and Robert C. Viesca

**E D U C A T I O N & E M P L O Y M E N T**

- 2013-2019: Research/Teaching Assistant at Tufts University.
- 2011-13: Geophysicist at Coal India Limited.
- 2008-11: Masters (Geophysics) IIT Roorkee.
- 2005-08: Bachelors (Physics) Delhi University.

**C O N T A C T**

Email: Sohom.Ray at tufts.edu

Twitter: @RaySohom

Curriculum Vitae