PhD Position Analytic Modeling of Greens Functions in 3D Heterogeneous Media Delft • TU Delft

Job description

We are looking for a PhD candidate who is keen to engage in fundamental acoustic and elastic wave theory and interested in developing analytical solution methods for calculating 3D Greens functions for smooth heterogeneous media.

For several seismic imaging and inversion applications, there is a need to know how the wave propagates in the background medium. To model this wavefield, various methods exist. With most frequency domain methods, analytic Green’s functions for a homogeneous medium are used. In situations where these Greens functions are not accurate enough, one needs to model the wave in the heterogeneous background medium via e.g. WRW, integral equations or WKBJ approaches. Unfortunately, these approaches are either computational expensive or inaccurate.

The goal of this PhD project is to develop a method that allows us to obtain analytical solutions for the 3D Green’s function in a smooth varying 3D heterogeneous medium. The backbone of the approach is to solve the acoustic Helmholtz equation using the quaternion number system, which allow for higher-dimensional complex-valued functions that can be used to obtain analytic solutions to the space-frequency domain Green’s function for such media. We foresee that such analytic Green’s functions enable various imaging and inversions applications, like Kirchhoff migration, reverse time migration, contrast-source acoustic and elastic scattering integral methods and forward modelling using physics-informed neural networks (PINNs).

During this four-year PhD project, you will have to familiarize yourself with wave theory and quaternions. You will expand the existing theory to increasingly more complex models and validate new concepts by developing and using simple numerical scattering and finite-difference models, eventually testing your approach on more complex synthetic (computationally modelled), as well as real acoustic or seismic data. We encourage you to develop and explore your own research ideas as well as ours following new discoveries and insights, while we will provide you with the necessary freedom and support to do so.

Job requirements 

Being creative and independent, you enjoy working on theoretical problems and are confident to master the challenges of organising a complex research project.

You also have:

• a MSc in a relevant field, such as physics, geophysics, applied mahtematics or similar,
• interest in mathematics, wave propagation phenomena and imaging methods,
• experience in scientific programming (preferably in Python or Matlab),
• good writing, commuincation and presenttion skills.

Experience in one or more of the fields below is considered an advantage:

• seismic methods (e.g., interferometry), ultrasound, scattering theory, or signal processing,
• modelling wave propagation.

TU Delft (Delft University of Technology) 

Delft University of Technology is built on strong foundations. As creators of the world-famous Dutch waterworks and pioneers in biotech, TU Delft is a top international university combining science, engineering and design. It delivers world class results in education, research and innovation to address challenges in the areas of energy, climate, mobility, health and digital society. For generations, our engineers have proven to be entrepreneurial problem-solvers, both in business and in a social context. 

At TU Delft we embrace diversity as one of our core values and we actively engage to be a university where you feel at home and can flourish. We value different perspectives and qualities. We believe this makes our work more innovative, the TU Delft community more vibrant and the world more just. Together, we imagine, invent and create solutions using technology to have a positive impact on a global scale. That is why we invite you to apply. Your application will receive fair consideration. 

Challenge. Change. Impact! 

Faculty of Civil Engineering and Geosciences 

The Faculty of Civil Engineering & Geosciences (CEG) is committed to outstanding international research and education in the field of civil engineering, applied earth sciences, traffic and transport, water technology, and delta technology. Our research feeds into our educational programmes and covers societal challenges such as climate change, energy transition, resource availability, urbanisation and clean water. Our research projects are conducted in close cooperation with a wide range of research institutions. CEG is convinced of the importance of open science and supports its scientists in integrating open science in their research practice. The Faculty of CEG comprises 28 research groups in the following seven departments: Materials Mechanics Management & Design, Engineering Structures, Geoscience and Engineering, Geoscience and Remote Sensing, Transport & Planning, Hydraulic Engineering and Water Management. 

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