Browsing by Subject "computation"

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    Basis Pursuit Receiver Function
    (2014-12) Sen, Mrinal K.; Biswas, Reetam; Mandal, Prantik; Kumar, Prakash; Sen, Mrinal K.; Biswas, Reetam
    Receiver functions (RFs) are derived by deconvolution of the horizontal (radial or transverse) component of ground motion from the vertical component, which segregates the PS phases. Many methods have been proposed to employ deconvolution in frequency as well as in time domain. These methods vary in their approaches to impose regularization that addresses the stability problem. Here, we present application of a new time-domain deconvolution technique called basis pursuit deconvolution (BPD) that has recently been applied to seismic exploration data. Unlike conventional deconvolution methods, the BPD uses an L1 norm constraint on model reflectivity to impose sparsity. In addition, it uses an overcomplete wedge dictionary based on a dipole reflectivity series to define model constraints, which can achieve higher resolution than that obtained by the traditional methods. We demonstrate successful application of BPD based RF estimation from synthetic data for a crustal model with a near-surface thin layer of thickness 5, 7, 10, and 15 km. The BPD can resolve these thin layers better with much improved signal-to-noise ratio than the conventional methods. Finally, we demonstrate application of the BPD receiver function (BPRF) method to a field dataset from Kutch, India, where near-surface sedimentary layers are known to be present. The BPRFs are able to resolve reflections from these layers very well.
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    Numerical Boltzmann Equation Solutions for Secretly Asymmetric Dark Matter Scenarios
    (2017-05) Dessert, Christopher; Kilic, Can
    The Standard Model (SM) of particle physics was completed as we know it today in 1967, but experimental confirmation had to wait until 2012 when the Large Hadron Collider (LHC) announced the discovery of the Higgs boson. In the meantime many particle theorists have been searching for physics Beyond the Standard Model (BSM), one part of which is the search for a particle physics explanation of dark matter. One potential explanation is asymmetric dark matter (ADM), in which the initial amount of dark matter and antidark matter in the universe is unequal. What makes our model, one of several ADM models, special is that there are three flavors, or types, of dark matter and even though the initial amounts are unequal in each flavor, the total amount of dark matter is equal to that of antidark matter. The three flavors interact in various ways. These interactions serve to change the flavor of the dark matter particles or annihilate them altogether. One important interaction is the decay of the heavier flavors into lighter flavors, and after a long time only the light flavor will remain. In this case there will appear to only be one flavor of dark matter with equal amounts of dark matter and antidark matter. For this reason, the model is named "Secretly Asymmetric Dark Matter (SADM)." The results presented in this thesis are a direct followup to this work. We would like to understand if the model could be a realistic theory for dark matter. To do so, we use the interactions to write down a set of equations, known as Boltzmann equations, that model the density of the dark matter in the early universe as it expands and see if the results match experimental measurements today. The interactions are complicated and the resulting equations are impossible to solve by hand. I have written a program in Mathematica 11 that will solve them numerically.