Analysis of the covariance matrix in FWI through density of covariance maps

  • Anyeres Neider Jimenez Universidad de Antioquia, Colombia https://orcid.org/0000-0003-3461-4927
  • Juan Carlos Muñoz Cuartas Universidad de Antioquia, FACoM, Colombia
  • Sheryl Avendaño Universidad de Antioquia, Colombia
  • Leonardo Gómez Bernal Instituto de Geociȇncias da Universidade Federal da Bahia
Keywords: Full Waveform Inversion, Resolution, Correlation Matrix

Abstract

Full waveform inversion (FWI) is a tool for the inversion of seismic data. There are several sources of uncertainty in the results provided by FWI. The quantification of such uncertainties has been studied through the resolution matrix (Res), which rests on a quadratic approximation that interprets the Hessian matrix as the posterior covariance matrix. Despite efforts in the use of Res, there is no published analysis of the uncertainties contained in the full correlation matrix, (R). Our approach leads to build the full R matrix, which, at the end of the day, is the final quantity that includes all the information associated with uncertainties.
We focused on uncertainties related to variation in the starting models of the FWI, and thus propose a method to study the full R matrix, which is-called the Density of Correlation Map, D. By using the D map, we found that the highest uncertainty zones in the FWI inverted model are near the sources, the model boundaries, and the interfaces. We argue that D can be a complement for the study and estimation of uncertainties in FWI.

Author Biography

Anyeres Neider Jimenez, Universidad de Antioquia, Colombia

Academics and employments

  1.  2007. Physicist, University of Antioquia. Monography: "Discos rotantes en relatividad General", Advisor: M.Sc. Alonso Sepúlveda Soto.
  2.  2011. M.Sc., University of Antioquia, Thesis: "Doubly special relativity theory by conformal transformations", Advisor: PhD Daniel Jaramillo.
  3.  2012. Temporary lecturer at University of Antioquia and Metropolitan Technological Institute. From 2007 to 2012.
  4.  2014. Academic Coordinator (Profesor Ocasional) of the Ocean Engineering Program, University of antioquia. Engineering Faculty. From 2012 to 2014.
  5.  2017. Internship: Universidade federal da Bahia, Bahia-Brasil. Centro de Pesquisa em Geofísica e Geologia da UFBA. Advisor: PhD Reynam Pestana. 
  6.  2018. PhD Thesis accepted, at University of Antioquia, “Full waveform inversion and uncertainties quantification”. 

International Events:

a) International School in physics education, Rionegro Antioquia, 2007.

b) Workshop on Physics and Technology at CERN, Bogotá Colombia. 2010-10-20, poster: "Conformal Transformations for Modified Lorentz symmetry of DSRMS Model”

c) Joint ICTP-Twas School on coherent state transforms, time-frequency and time-scale analysis, applications. June 2nd-20th 2014. ICTP, Trieste, Italy.

d) Educational tour, 2014, Paris. Professor: Tariq Alkhalifah.

Applied Courses

a) Geophysical inverse problems, professor: Mrinal Kanti Sen, april 2015.

b) Métodos de migración RTM y WWE 3D, January 2015, professor: Reynam da Cruz Pestana.

Works

a) 2012. Non Linear Lorentz Transformation and Doubly Special Relativity, https://arxiv.org/abs/1210.6261.

b) PNUD, “Employment Observatory, 2013”, Urabá: Región invencible. “Statistical study of employment in Antioquia Colombia”. Red de Observatorios Regionales del Mercado de Trabajo - Red ORMET Programa de las Naciones Unidas para el Desarrollo – PNUD. ISBN: 978-958-8815-09-1.

c) Creation of educational content for virtual education, “Guía de estudio para Aula Semilla, Ude@”, faculty of engineering, university of Antioquia. Mechanical physics.

d) Anyeres A. Jiménez, J. C. Muñoz-Cuartas, Sheryl Avendaño. “Integral modelling of propagation of incident waves in a laterally varying medium: An exploration in the frequency domain”, https://doi.org/10.29047/issn.0122-5383

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How to Cite
Jimenez, A. N., Muñoz Cuartas, J. C., Avendaño, S., & Gómez Bernal, L. (2020). Analysis of the covariance matrix in FWI through density of covariance maps. CT&F - Ciencia, Tecnología Y Futuro, 10(1), 93-105. https://doi.org/10.29047/01225383.163

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Published
2020-06-30
Section
Scientific and Technological Research Articles