## Alvarez Aramberri, Julen

**SHORT BIO:**
Julen Alvarez-Aramberri completed his degree in physics at the University of Basque Country in 2007 after concluding his last year as Erasmus student at the University of Florence. Then, he studied a M.S. in Quantitative Finance (2007-2009) and a M.S in ``Mathematical Modelization, Statistics and Computation'' (2010) at the University of Basque Country. In 2015, he received the Ph.D degree in Applied Mathematics in co-tutelage between the University of Basque Country and the University of Pau with the work entitled hp-Adaptive Simulation and Inversion of the Magnetotelluric Measurements. Since January 2016, he is a Postdoctoral Visiting Fellow in Computational and Applied Mathematics at the Basque Center for Applied Mathematics (BCAM).

**MAIN RESEARCH INTERESTS:**
I am mainly interested in the efficient implementation of the numerical schemes, methods, and tools developed with the
"Mathematical Modeling, Simulation, and Industrial Applications" group. My Ph.D focused in solving the direct
and inverse problems arising in the application of the magnetotelluric technique, which is used to retrieve information
about the resistivity distribution of the Earth's subsurface. In there, we tackled the problem via hp-adaptive goal-oriented
finite element methods for the direct problem and via classical and stochastic approaches for the inverse problem.

**MAIN RESEARCH PROJECTS:**
**Simulation and inversion of Magnetotelluric problems:**

In collaboration with Dr. David Pardo and Dr. Helene Barucq, we are simulating magnetotelluric phenomena a hp-adaptive goal-oriented finite element approach. Once this simulations are performed we are in position for developing new inversion algorithms that allow obtaining information about the minor constituents of the rock matrices beneath the surface.

** Dimensionally Adaptive Method (DAM) for inversion: **

In some scenarios, the dimension of the formation is unclear. Traditional inversion techniques usually select one fixed dimension for the forward and inverse problems. The dimensionality analysis of magnetotelluric measurements is an ongoing topic of study. Thus, a good dimensionality study of the problem may indicate specific areas of higher dimension, while others where lower dimension consideration of the problem may be sufficient.
In collaboration with Dr. David Pardo, we are developing an adaptive method in the spatial dimension for the inverse problem. The main idea of the method consists of performing adaptivity in the spatial dimension by starting with a low-dimensionality problem and use the corresponding results to minimize the computational cost of high-dimensionality problems.

** Goal-oriented adaptivity with nonlinear quantities of interest in the context of the magnetotelluric problem: **

The traditional goal-oriented strategies employ linear quantities of interest to bound the error. In the magnetotelluric problem this linear quantities would correspond to the electromagnetic fields. However, for these prospection method it is known that the impedance and/or apparent resistivities are proper physical magnitudes to be employed. In collaboration with Dr. Ignacio Muga and Dr. David Pardo, we are developing a goal-oriented adaptive procedure using highly nonlinear quantities of interest such as impedances or apparent resistivities.