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	Alison Malcolm amalcolm [at] mit.edu Department of Earth, Atmospheric and Planetary Sciences Massachusetts Institute of Technology 77 Massachusetts Ave, 54-522 Cambridge, MA, 02139 617-324-1974

       Research        Publications        Teaching        Personal

Research Overview

Each of my current research projects is described briefly below. If you're interested in my past work, have a look at my CV (pdf), for my guess at what I might be up to in the future, you can check out my research statement.

Collaborators: Fernando Reitich , Jiaqi Yang, Fanbin Bu in the School of Mathematics at the University of Minnesota and James Greenleaf, Mostafa Fatemi , Farid Mitra at the Mayo Clinic.

Ultrasound vibro-acoustography is a new imaging modality developed at the Mayo Clinic that combines the high resolution possible with high-frequency imaging methods with the clean (scatter-free) images possible using low-frequency waves. It was first introduced by Fatemi and Greenleaf in 1999; that paper can be found here . We are working to model these experiments with the goal of improving the understanding of the underlying physics which we hope will result in improved images of abnormal tissue. The image below shows the current state of our model, on the left is an experimental image of an aluminum rod submerged in water and on the right is the result of our model for the same configuration. More details can be found in a conference proceedings paper we wrote about a year ago, or email me and I will send a copy of our book chapter.

Collaborators: Bjørn Ursin at the Technical University in Trondheim and Maarten de Hoop in the Center for Computational and Applied Math at Purdue University

In typical seismic experiments for oil prospecting sources and receivers are restricted to lie on the Earth's surface. Waves are also typically assumed to reflect only once in the subsurface and to travel primarily downwards into the Earth before reflecting and upwards afterwards. The combination of these restrictions limits the region of the Earth imaged. We are working to extend this region by relaxing the restriction that waves scatter only once in the subsurface. From doubly scattered waves this improves images of steeply dipping structures and from triply scattered waves we are able to image some structures from below. A summary of this work can be found on this poster or in this SEG abstract . The image below shows an example of imaging a fault, with a standard image on the left and our improved image on the right; this example is similar to that presented by Jin, Xu and Walraven at SEG in 2006, available through the Society of Exploration Geophysicists.

Collaborators: Jeannot Trampert at Utrecht University and Jesper Spetzler at Delft Technical University.

Wavefront healing is the name given to the phenomena by which traveltime delays decay, from the interference of diffractions with direct arrivals, as waves travel over long distances. We are studying the physics and underlying mathematics of this problem to better understand the seismological implications of this effect.

Collaborators: Bojan Guzina University of Minnesota.

The topological derivative is a method of locating variations in material parameters relatively quickly. The basic idea is to define a cost function and then compute the derivative of this cost function with respect to the introduction of an infinitesimal inclusion (variation from the background parameters). This concept was first introduced in the PhD thesis of Schumacher in 1995 and has been extensively studied since then, primarily in the frequency domain. We have extended it to the time-domain, focusing on acoustic obstacles to more closely correspond to seismic applications. Below you can see the utility of the method in that we are able to locate two inclusions (outlined in black) with this method; the negative regions (blue) indicate points expected to be within the inclusion.

Publications

Journal Articles:

Malcolm, A. E., Ursin, B. and de Hoop, M. V. Seismic imaging and illumination with internal multiples, Geophysical Journal International, submitted.

Malcolm, A. E., Reitich, F., Yang, J., Greenleaf, J. F. and Fatemi, M. A combined parabolic-integral equation approach to the acoustic simulation of vibro-acoustic imaging, Ultrasonics, in press.

Malcolm, A. E. & Guzina, B. On the Topological Sensitivity of Transient Acoustic Fields, Wave Motion, in press.

Malcolm, A. E., de Hoop, M. V., & Calandra, H. (2007), Identifying imaging artifacts from internal multiples, Geophysics, 72 S123.

Malcolm, A. E., & de Hoop, M. V., (2005), A method for inverse scattering based on the generalized Bremmer coupling series, Inverse Problems 21 No. 3 pp 1137-1167.

Malcolm, A. E., de Hoop, M. V., & Le Rousseau, J. H. (2005), The applicability of DMO/AMO in the presence of caustics, Geophysics 70 S1.

Malcolm, A. E., Scales, J. A. & van Tiggelen, B. A. (2004), Retrieving the Green function from diffuse, equipartitioned waves , Phys. Rev. E. 70.

de Hoop, M. V., Malcolm, A. E., & Le Rousseau, J. H. (2003), Seismic wavefield `continuation' in the single scattering approximation: A framework for dip and azimuth moveout,Can. Apply. Math. Q. 10 199-238.

Scales, J. A. & Malcolm, A. E. (2003), Laser characterization of ultrasonic wave propagation in random media , Phys. Rev. E. 67.

Book Chapter:

A. Malcolm, F. Reitich, J. Yang, J. F. Greenleaf, M. Fatemi (2007) "Numerical Modeling for Assessment and Design of Ultrasound Vibroacoustography Systems" in "Biomedical Applications of Vibration and Acoustics in Imaging and Characterisations" editors: M. Fatemi, A. Al-Jumaily and A. Alizad.

Theses:

A. Malcolm, (2005) "Data Regularization for Data Continuation and Internal Multiples," Ph.D. Thesis, Colorado School of Mines, supervisor M. V. de Hoop.

A. Malcolm, " Algorithm Development for the Fast Computation of the Fourier Transform of Unequally Sampled Data with Applications to Seismic and Sediment Core Data" BSc Thesis, University of British Columbia, supervisor T. J. Ulrych.

Teaching Overview

I've not yet had the opportunity to teach a class of my own, though I used to lecture fairly regularly when Martijn was travelling. If you are interested you can check out my teaching statement.

Personal

My husband, Scott, and I both hail from the Vancouver area in western Canada, where we still enjoy visiting our families and gawking at the lovely scenery. We are now excited to be exploring the other coast of the continent! Both of us like to travel and spend most of our non-working hours outdoors.

I used to be an avid figure skater and spent an enjoyable year skating with the Starlight Ice Dance club whilst living in Minneapolis in 2006/7, no ice capades, just lots of good fun! I'm also a hockey fan, but get more excited about world hockey tournaments than the NHL.

When I'm not working or running around outside I can usually be found, reading, knitting or cooking with my husband and our friends.