I am a Ph.D. student at Tufts University working on applications of mechanics of solid and shear fractures to understand seismic and aseismic slip on faults under various possible fault frictional scenarios. Laboratory rock friction experiments show that fault friction could possibly have a next-to-leading order dependence on the rate of slip and its history or state. Such rate- and state-dependent fault frictional strength, coupled with the elasticity of fault governing traction-slip relations, leads to interesting nonlinear system of PDEs that govern the evolution of slip on a fault that could manifest in a seismic or aseismic manner depending upon the underlying fault frictional properties. As a result, my interests often shift towards numerical methods for and approximate solutions of nonlinear parabolic partial differential equations and also include the application of dynamical systems in problems related to nonlinear instabilities. (Curriculum Vitae)

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

**Earthquake nucleation with heterogeneous fault frictional strength**

We examine the development of an instability 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 distribution of frictional properties. [Ray and Viesca, JGR Solid Earth 2017].

**When is heterogeneity relevant?**

Heterogeneity in frictional properties leads to preferential locations on fault wherein an unstable slip rate most likely to nucleate. Those preferential locations are otherwise lost when heterogeneity in fault frictional properties are neglected or homogenized for model simplification purposes. The length scales over which slip rate diverges are determined by the magnitude of elastic and frictional properties of the fault. Additional length scales are introduced in the dynamics when the frictional properties are considered to be variable over the extent of the fault with a characteristic wavelength. The dynamics of interaction those two independent length scales, the elasto-frictional lengthscale and the wavelength of parameter variation, heavily depends upon their contrast and subsequently dictates the favorable locations of earthquake nucleating slip instabilities. Here, we explore how the favorable nucleation sites could be a function of the similarity or disparity between the elasto-frictional lengthscales and the wavelength of the parameter variation.

- Aseismic slip on the fault under various fault loading conditions (in preparation).

**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.
*,*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.
*, Earthquake nucleation under diverse length scales of fault frictional heterogeneity.*In preparation to be submitted in Geophysical Journal International.

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

- 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-present: 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