**Current** Position

**Academic** Background

**Research** Interests

**Other** Interests

Hiking in nature with family is my favorite weekend activity.

**Spectral-infinite-element** Method

The spectral-infinite-element method combines the highly accurate spectral-element method with the mapped-infinite element method to solve the unbounded problems efficiently and accurately. Spectral elements represent the domain of interest, and a single layer of infinite elements captures outer space. To solve the weak form of the unbounded equation, we use Gauss-Legendre-Lobatto quadrature in spectral elements inside the domain of interest. Outside the domain, we use Gauss-Radau quadrature in the infinite direction, and Gauss-Legendre-Lobatto quadrature in the other directions.

The software package `SPECFEM-X` based on the SIEM aims to solve most (global) quasistatic problems.

**Earthquake-Induced** Gravity Perturbation

Although earthquake-induced gravity perturbations are frequently observed, numerical modeling of this phenomenon has remained a challenge. Due to the lack of reliable and versatile numerical tools, induced-gravity data have not been fully exploited to constrain earthquake source parameters. From a numerical perspective, the main challenge stems from the unbounded Poisson/Laplace equation that governs gravity perturbations. Additionally, the Poisson/Laplace equation must be coupled with the equation of conservation of linear momentum that governs particle displacement in the solid. Most existing methods either solve the coupled equations in a fully spherical harmonic representation, which requires models to be (nearly) spherically symmetric, or they solve the Poisson/Laplace equation in the spherical harmonics domain and the momentum equation in a discretized domain, a strategy that compromises accuracy and efficiency. We present a spectral-infinite-element approach that combines the highly accurate and efficient spectral-element method with a mapped-infinite-element method capable of mimicking an infinite domain without adding significant memory or computational costs. We solve the complete coupled momentum-gravitational equations in a fully discretized domain, enabling us to accommodate complex realistic models without compromising accuracy or efficiency. We present several coseismic and post-earthquake examples and benchmark the coseismic examples against the Okubo analytical solutions. Finally, we consider gravity perturbations induced by the 1994 Northridge earthquake in a 3D model of Southern California. The examples show that our method is very accurate and efficient, and that it is stable for post-earthquake simulations.

**Automated** Microearthquake Location

Most earthquake location methods require phase identification and arrival-time measurements. These methods are generally fast and efficient but not always applicable to microearthquake data with low signal-to-noise ratios because the phase identification might be very difficult. The migration-based source location methods, which do not require an explicit phase identification, are often more suitable for such noisy data. Whereas some existing migration-based methods are computationally intensive, others are limited to a certain type of data or make use of only a particular phase of the signal. We have developed a migration-based source location method especially applicable to data with relatively low signal-to-noise ratios. We projected seismograms on to the ray coordinate system for each potential source-receiver configuration and subsequently computed their envelopes. The envelopes were time shifted according to synthetic P- and S-wave arrival times (computed using an eikonal solver) and stacked for a predefined time window centered on the arrival time of the corresponding phase. This was done for each component and phase individually, and the squared sum of the stacks was defined as the objective function. We applied a robust global optimization routine called differential evolution to maximize the objective function and thereby locate the seismic event. Our source location method provides a complete algorithm with only a few control parameters, making it suitable for automatic processing. We applied this method to single and multicomponent data using P and/or S phases. We conducted controlled tests using synthetic seismograms contaminated with a minimum of 30% white noise. The synthetic data were computed for a complex and heterogeneous model of the Pyhäsalmi ore mine in Finland. We also successfully applied the method to real seismic data recorded with the in-mine seismic network of the Pyhäsalmi mine.

**Coseismic** Deformation & **Post-earthquake** Relaxation

Accurate and efficient simulations of coseismic and post-earthquake deformation are important for proper inferences of earthquake source parameters and subsurface structure. These simulations are often performed using a truncated halfspace model with approximate boundary conditions. The use of such boundary conditions introduces inaccuracies unless a sufficiently large model is used, which greatly increases the computational cost. To solve this problem, we develop a new approach by combining the spectral-element method with the mapped infinite-element method. In this approach, we still use a truncated model domain, but add a single outer layer of infinite elements. While the spectral elements capture the domain, the infinite elements capture the far-field boundary conditions. The additional computational cost due to the extra layer of infinite elements is insignificant. Numerical integration is performed via Gauss-Legendre-Lobatto and Gauss-Radau quadrature in the spectral and infinite elements, respectively. We implement an equivalent moment-density tensor approach and a split-node approach for the earthquake source, and discuss the advantages of each method. For post-earthquake deformation, we implement a general Maxwell rheology using a second-order accurate and unconditionally stable recurrence algorithm. We benchmark our results with the Okada analytical solutions for coseismic deformation, and with the Savage & Prescott analytical solution and the PyLith finite-element code for post-earthquake deformation.

**Gravity ** Anomalies

Gravity anomalies induced by density heterogeneities are governed by Poisson’s equation. Most existing methods for modelling such anomalies rely on its integral solution. In this approach, for each observation point, an integral over the entire density distribution needs to be carried out, and the computational cost is proportional to the number of observation points. Frequently, such methods are sensitive to high density contrasts due to inaccurate resolution of the volume integral. We introduce a new approach which directly solves a discretized form of the Poisson/Laplace equation. The main challenge in our approach involves the unbounded nature of the problem, because the potential exists in all of space. To circumvent this challenge, we combine a mapped infinite-element approach with a spectral-element method. Spectral elements represent the domain of interest, and a single layer of infinite elements captures outer space. To solve the weak form of the Poisson/Laplace equation, we use Gauss–Legendre–Lobatto (GLL) quadrature in spectral elements inside the domain of interest. Outside the domain, we use Gauss–Radau quadrature in the infinite direction, and GLL quadrature in the other directions. We illustrate the efficiency and accuracy of our method by comparing calculated gravity anomalies for various density heterogeneities with corresponding analytical solutions. Finally, we consider a complex 3-D model of an ore mine, which consists of both positive and negative density anomalies.

**Magnetic ** Anomalies

Magnetic anomalies induced by a magnetization distribution are governed by Poisson’s equation. Analogous to gravity anomalies, magnetic anomalies are frequently computed using a direct integral approach, involving an integral over the entire magnetization distribution for each observation point. Alternatively, magnetic anomalies can be computed using the so-called Poisson’s relation, in which the magnetic scalar potential is approximated by the derivative of the gravitational potential based on the analogy between the gravity and magnetic fields. However, this analogy is generally limited to simple isolated objects, and computing the magnetic field involves the second derivative of the gravitational potential. Both methods suffer from an often inaccurate volume integral over complex objects, and the computational cost scales with the number of observation points. We implement a spectral-infinite-element method to directly solve a discretized form of the Poisson/Laplace equation for magnetic anomalies. The spectral-infinite-element method combines the highly accurate spectral-element method with the mapped-infinite element method, which reproduces an unbounded domain accurately and efficiently. This combination is made possible by coupling Gauss-Legendre-Lobatto quadrature in spectral-elements with Gauss-Radau quadrature in infinite elements along the infinite directions. We illustrate the efficiency and accuracy of our method by comparing calculated magnetic anomalies for various magnetization heterogeneities with corresponding analytical and commonly used computational solutions. Finally, we consider a practical example involving a complex 3D model of an ore mine.

**Multistage** Excavation

We implement a 3D spectral-element method for multistage excavation problems. To simulate excavation in elastoplastic soils, we employ a Mohr–Coulomb yield criterion using an initial strain method. We parallelize the software based on non-overlapping domain decomposition using MPI. We verify the uniqueness principle for multistage excavation in linear elastic materials. We validate our serial and parallel programs, and illustrate several examples of multistage excavation in elastoplastic materials. Finally, we apply our software to a model of the Pyhäsalmi ore mine in Finland. Strong-scaling performance tests involving multistage excavation show that the parallel program performs reasonably well for large-scale problems.

**Slope** Stability

We implement a spectral‐element method for 3D time‐independent elastoplastic problems in geomechanics. As a first application, we use the method for slope stability analysis ranging from small to large scales. The implementation employs an element‐by‐element preconditioned conjugate‐gradient solver for efficient storage. The program accommodates material heterogeneity and complex topography. Either simple or complex water table profiles may be used to assess effects of hydrostatic pressure. Both surface loading and pseudostatic seismic loading are implemented. For elastoplastic behavior of slopes to be simulated, a Mohr–Coulomb yield criterion is employed using an initial strain method (i.e., a viscoplastic algorithm). For large‐scale problems, the software is parallelized on the basis of domain decomposition using Message Passing Interface. Strong‐scaling measurements demonstrate that the parallelized software performs efficiently. We validate our spectral‐element results against several other methods and apply the technique to simulate failure of an earthen embankment and a mountain slope.

**Reviewed** Articles

- Jeong, C., Manalaysay, A.,
**Gharti, H. N.**, Guan, S., and Vignola, J., 2019. Applicability of 3D spectral element method for computing close-range underwater piling noises,

*Journal of Theoretical and Computational Acoustics*. DOI:10.1142/S2591728519500129. **Gharti, H. N.**and Tromp, J., 2019. Spectral-infinite-element simulations of magnetic anomalies,

*Geophysical Journal International*, 217, 1656-1667. DOI:10.1093/gji/ggz107.- Langer, L.,
**Gharti, H. N.**, and Tromp, J., 2019. Impact of topography and three-dimensional heterogeneity on coseismic deformation,

*Geophysical Journal International*, 217, 866-878. DOI:10.1093/gji/ggz060. **Gharti, H. N.**, Langer, L., and Tromp, J., 2019. Spectral-infinite-element simulations of earthquake-induced gravity perturbations,

*Geophysical Journal International*, 217, 451-468. DOI:10.1093/gji/ggz028.- Vaaland, U. B.,
**Gharti, H. N.**, and Tromp, J., 2019. Simulations of seismic wave propagation using a spectral-element method in a Lagrangian framework with logarithmic strain,

*Geophysical Journal International*, 216, 2148-2157. DOI:10.1093/gji/ggy546. - Wang, N., Li, J., Borisov, D.,
**Gharti, H. N.**, Shen, Y., Zhang, W., and Savage, B., 2019. Modeling three-dimensional wave propagation in anelastic models with surface topography by the optimal strong stability preserving Runge-Kutta method,

*Journal of Geophysical Research - Solid Earth*, 124. DOI:10.1029/2018JB016175. **Gharti, H. N.**, Langer, L., and Tromp, J., 2019. Spectral-infinite-element simulations of coseismic and post-earthquake deformation,

*Geophysical Journal International*, 216, 1364-1393. DOI:10.1093/gji/ggy495.**Gharti, H. N.**, Tromp, J., and Zampini, S, 2018. Spectral-infinite-element simulations of gravity anomalies,

*Geophysical Journal International*, 215, 1098-1117. DOI:10.1093/gji/ggy324.- Lloyd, S. F., Jeong, C.,
**Gharti, H. N.**, Vignola, J., and Tromp, J., 2018. Spectral-element simulations of acoustic waves induced by a moving underwater source,

*Journal of Theoretical and Computational Acoustics*. DOI:10.1142/S2591728518500408. - Paap, B., Kraaijpoel, D., Bakker, M., and
**Gharti, H. N.**, 2018. Wave propagation modelling of induced earthquakes at the Groningen gas production site,

*Geophysical Journal International*, 214, 1947-1960. DOI:10.1093/gji/ggy225 - Lecomte, I., Lubrano-Lavadera, P., Wuestefeld, A., Kaschwich, T., Albaric, J., and
**Gharti, H. N.**, 2015. Focusing in migration-based location of weak microseismicity: modelling point-spread function for resolution analyses,

*SEG Technical Program Expanded Abstracts*, 2491-2495. DOI:10.1190/segam2015-5813282.1. **Gharti, H. N.**, Oye, V., Komatitsch, D., and Tromp, J., 2012. Simulation of multistage excavation based on a 3D spectral-element method,

*Computers & Structures*, 100–101, 54–69. DOI:10.1016/j.compstruc.2012.03.005**Gharti, H. N.**, Komatitsch, D., Oye, V., Martin, R., and Tromp, J., 2012. Application of an elastoplastic spectral- element method to 3D slope stability analysis,

*International Journal for Numerical Methods in Engineering*, 91, 1–26. DOI:10.1002/nme.3374**Gharti, H. N.**; Oye, V.; Kühn, D., and Zhao, P., 2011. Simultaneous microearthquake location and moment-tensor estimation using time-reversal imaging,

*SEG Technical Program Expanded Abstracts*, 30, 1632-1637. DOI:10.1190/1.3627516**Gharti, H. N.**; Oye, V.; Roth, M., and Kühn, D., 2010. Automated microearthquake location using envelope stacking and robust global optimization,

*Geophysics*, 75, MA27-MA46. DOI:10.1190/1.3432784.- Oye, V.,
**Gharti, H. N.**, Aker, E., and Kühn, D., 2010. Moment tensor analysis and comparison of acoustic emission data with synthetic data from spectral element method,

*SEG Technical Program Expanded Abstracts*,29(1):2105–9. DOI:10.1190/1.3513260. - Kühn, D.,
**Gharti, H. N.**, Oye, V., and Roth, M., 2009, Analysis of mining-induced seismicity using focal mechanism and waveform computations in heterogeneous media.

*EAGE extended abstracts*, Amsterdam. DOI:10.3997/2214-4609.201400028 **Gharti, H. N.**, Oye, V., and Roth, M., 2008. Travel times and waveforms of microseismic data in heterogeneous media,

*SEG Tech Prog Expanded Abstracts*, 27(1):1337–41. DOI:10.1190/1.3059162.

**Other** Articles

**Gharti, H. N.**, Komatitsch, D., Langer, L., Martin, R., Oye, V., Tromp, J., Vaaland, U., and Yan, Z., 2017. SPECFEM 3D Geotech: an open-source, parallel and cross-platform geotechnical engineering application (Version v1.2.0),

*Zenodo*. DOI:10.5281/zenodo.820154**Gharti, H. N.**, Langer, L., Roth, M., Tromp, J., Vaaland, U., and Yan, Z., 2017. MeshAssist: an open-source and cross-platform meshing assistant tool,

*Zenodo*. DOI:10.5281/zenodo.883448**Gharti, H. N.**, and Tromp, J., 2017. A spectral-infinite-element solution of Poisson’s equation: an application to self gravity.

arXiv:1706.00855.**Gharti, H. N.**, Oye, V., Roth, M., and Kühn, D., 2017. Wave propagation modelling in various microearthquake environments using a spectral-element method.

arXiv:1706.05217

**Conferences** Presentations

**Gharti, H. N.**, Langer, L., Simons, F. J., Tromp, J, and Zampini, S., 2018. Spectral-Infinite-Element Simulation of Potential Field Problems in Geophysics,

*AGU Fall Meeting Abstracts*, DI24B-14.- Langer, L.,
**Gharti, H. N.**, and Tromp, J, 2017. Investigating the Importance of 3D Structure & Topography in Seismic Deformation Modeling: Case Study of the April 2015 Nepal Earthquake,

*AGU Fall Meeting Abstracts*, G43A-0915. - Manalaysay, A., Jeong, C., and
**Gharti, H. N.**, 2017. High-resolution spectral-element computation of underwater noises due to offshore piling,

*The Journal of the Acoustical Society of America*, 142, 2686. DOI:10.1121/1.5014798 - Lloyd, S., Jeong, C,
**Gharti, H. N.**, and Tromp, J., 2017. Computation of acoustic wave responses due to moving underwater acoustic sources in complex underwater environments using a spectral element method,

*The Journal of the Acoustical Society of America*, 141, 3531. DOI:10.1121/1.4987453 **Gharti, H. N.**, and Tromp, J, 2015. Spectral-infinite-element Simulations of Self-gravitating Seismic Wave Propagation,

*AGU Fall Meeting Abstracts*, S13C-04.- Langer, L.,
**Gharti, H. N.**, and Tromp, J, 2016. Investigating the Importance of 3D Structure in Seismic Deformation Modeling,

*AGU Fall Meeting Abstracts*, G51B-1104. - Wang, N., Li, J., Borisov, D.,
**Gharti, H. N.**, Shen, Y., Zhang, W., Savage, and B. K., 2016. Three-dimensional wave field modeling by a collocated-grid finite-difference method in the anelastic model with surface topography,

*AGU Fall Meeting Abstracts*, S23C-2781. -
Kühn, D., Vavrycuk, V., Aker, E.,
**Gharti, H. N.**, Oye, V., and Huynh, K., 2013, Source Mechanisms of Acoustic Emissions due to Failure Around a Borehole in a Triaxial Lab Experiment,

*4th EAGE Passive Seismic Workshop*. DOI:10.3997/2214-4609.20142348 **Gharti, H. N.**, Austermann, J., Komatitsch, D., Lau, H., Mitrovica, J. X., Peter, P., Tromp, J., Xie, Z., and Zampini, S., 2013. Efficient Numerical Solution of Global Dynamic and Quasistatic Problems Using a Spectral-Element Method Coupled with an Infinite-Element Approach,

*AGU Fall Meeting Abstracts*, DI34B-03.**Gharti, H. N.**, Oye, V., and Roth, M., 2009. Automated Event Location for Noisy Microearthquake Data Using Envelope Stacking and Robust Global Optimization,

*AGU Fall Meeting Abstracts*, S32B-04.-
Kühn, D.,
**Gharti, H. N.**, Oye, V., and Roth, M., 2009. Analysis of Mining-induced Seismicity Using Focal Mechanism and Waveform Computations in Heterogeneous Media,

*71st EAGE Conference and Exhibition incorporating SPE EUROPEC 2009*. DOI:10.3997/2214-4609.201400028 -
Kühn, D., Gharti, H. N., Oye, V., and Roth, M., 2009, Microseismic Deformation Rate Monitoring,

*Second EAGE Passive Seismic Workshop - Exploration and Monitoring Applications 2009*. DOI:10.3997/2214-4609.20146744 -
Kühn, D., Gharti, H. N., Oye, V., Roth, M., 2009, Automatic determination of full moment tensor solution from P-wave first motion amplitudes,

*Second EAGE Passive Seismic Workshop - Exploration and Monitoring Applications 2009*. DOI:10.3997/2214-4609.20146731 - Oye, V. and
**Gharti, H. N.**, 2009. Location of Microearthquakes in Various Noisy Environments Using Envelope Stacking,

*AGU Fall Meeting Abstracts*, S23B-1751.

Please visit my Google Scholar and/or ResearchGate profile for more detailed publication list.

I have (co)developed a number of software packages for engineering and geoscientific applications for research and class lectures. Depending on the requirements and the applications, I mostly use Fortran 2008, C, C++, Python, Matlab, and Mathematica.

**SPECFEM-X**

- Coseismic and post-earthquake deformation
- Earthquake-induced gravity perturbation
- Gravity anomalies
- Magnetic anomalies
- Generalized viscoelastic rheology
- Glacial isostatic adjustment
- Slow slip events
- Thermomechanical simulations
- Generalized source implementation
- Builtin and externally ported solvers
- Parallelization based on the MPI and domain decomposition

**SPECFEM 3D** Geotech

- Elastoplastic failure
- Parallelization based on the MPI and domain decomposition
- Slope stability analysis
- Multistage excavation
- Ground water table
- Crossplatform compatibility
- Element-by-element solver

**MeshAssist**

- Convert complex geological surfaces to meshable ACIS surface
- Convert vector graphics to ACIS geometry
- Convert AUTOCAD files to ACIS geometry
- Convert DEM or XYZ data to ParaView and CUBIT/Trelis files
- Several functions for 1D/2D/3D geometry data
- Convert Exodus mesh files to SPECFEM(-X) files

Please visit my GitHub profile for more detailed list of my software contributions.

CIG Webinar

Hom Nath Gharti gave a CIG webinar talk on "Introduction to the Spectral-Infinite-Element Method" on March 09, 2017.