<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0122-5383</journal-id>
<journal-title><![CDATA[CT&F - Ciencia, Tecnología y Futuro]]></journal-title>
<abbrev-journal-title><![CDATA[C.T.F Cienc. Tecnol. Futuro]]></abbrev-journal-title>
<issn>0122-5383</issn>
<publisher>
<publisher-name><![CDATA[Instituto Colombiano del Petróleo (ICP) - ECOPETROL S.A.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0122-53832018000200033</article-id>
<article-id pub-id-type="doi">10.29047/01225383.79</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[INTEGRAL MODELLING OF PROPAGATION OF INCIDENT WAVES IN A LATERALLY VARYING MEDIUM: AN EXPLORATION IN THE FREQUENCY DOMAIN]]></article-title>
<article-title xml:lang="es"><![CDATA[MODELADO INTEGRAL DE PROPAGACIÓN DE ONDAS INCIDENTES EN MEDIOS CON GRADIENTES LATERALES: UNA EXPLORACIÓN EN EL DOMINIO DE LA FRECUENCIA]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Jiménez]]></surname>
<given-names><![CDATA[Anyeres A]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Muñoz-Cuartas]]></surname>
<given-names><![CDATA[J. C]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Avendaño]]></surname>
<given-names><![CDATA[Sheryl]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Antioquia  ]]></institution>
<addr-line><![CDATA[Medellín ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2018</year>
</pub-date>
<volume>8</volume>
<numero>2</numero>
<fpage>33</fpage>
<lpage>45</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0122-53832018000200033&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0122-53832018000200033&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0122-53832018000200033&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT In this work we present a formalism that intends to solve the problem of modeling wave propagation in the context of seismic inversion. The formalism is based on the linear perturbation theory of Cauchy's equations. Based on the foregoing, we derived an equivalent Helmholtz equation for the propagation of waves in a variable density media. Then, we defined a solution, by using the boundary conditions on a half plane. This solution is of an integral nature and resembles expansion in a Neumann series. We implemented the solution of the first terms in the series, considering only the incident wavefield and neglecting the reflections. We show how this approximation works in different media that include lateral in homogeneities in the velocity. The method presented hereunder is intended as a first step in the modelling process for the full wavefield, to be used in seismic inversion methods, Full Waveform Inversion, for example.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN En esta investigación presentamos un formalismo que pretende contribuir al modelado de la propagación de ondas en el contexto de la inversión sísmica. El formalismo está basado en la teoría de perturbaciones lineales a las ecuaciones de Cauchy. Basados en este procedimiento derivamos una versión de la ecuación de Helmholtz que describe la propagación de ondas en un medio con densidad variable. Luego hallamos una solución en la cual se emplean condiciones de frontera de un plano semi infinito. Tal solución es expresada en forma de integral y recuerda la expansión en series de Neumann. Nosotros implementamos la solución del primer término de la serie, que considera únicamente el campo de onda incidente, sin considerar las reflexiones de onda. Mostramos que esta aproximación funciona en diferentes medios que incluyen variaciones in-homogeneidades laterales en el perfil de velocidad. Este método es presentado como un primer paso en el proceso de modelado del campo de onda completo el cual puede ser usado en métodos de inversión sísmica tales como "Inversión de onda completa", Full Waveform Inversion, (FWI).]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Neumann series]]></kwd>
<kwd lng="en"><![CDATA[Wave propagation]]></kwd>
<kwd lng="en"><![CDATA[Perturbative solutions]]></kwd>
<kwd lng="en"><![CDATA[Frequency domain]]></kwd>
<kwd lng="es"><![CDATA[Series de Neumann]]></kwd>
<kwd lng="es"><![CDATA[Propagación ondulatoria]]></kwd>
<kwd lng="es"><![CDATA[Soluciones perturbativas]]></kwd>
<kwd lng="es"><![CDATA[Dominio de la Frecuencia]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>[1]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[J. Virieux]]></surname>
<given-names><![CDATA[S. Operto]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An overview of full-waveform inversion in exploration geophysics]]></article-title>
<source><![CDATA[Geophysics]]></source>
<year>2009</year>
<volume>74</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>WCC1-WCC26</page-range></nlm-citation>
</ref>
<ref id="B2">
<label>[2]</label><nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kapoor]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Vigh]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Li]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Derharoutian]]></surname>
<given-names><![CDATA[D]]></given-names>
</name>
</person-group>
<source><![CDATA[Full waveform inversion for detailed velocity model building]]></source>
<year></year>
<conf-name><![CDATA[ 74EAGE Conference and Exhibition incorporating SPE EUROPEC 2012]]></conf-name>
<conf-loc>Copenhagen, Denmark </conf-loc>
<page-range>4-7</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>[3]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[dos Santos]]></surname>
<given-names><![CDATA[A. W. G]]></given-names>
</name>
<name>
<surname><![CDATA[Pestana]]></surname>
<given-names><![CDATA[R.C]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Time-domain multiscale full-waveform inversion using the rapid expansion method and efficient step-length estimation]]></article-title>
<source><![CDATA[Geophysics]]></source>
<year>2015</year>
<volume>80</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>R203-16</page-range></nlm-citation>
</ref>
<ref id="B4">
<label>[4]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tao]]></surname>
<given-names><![CDATA[Y]]></given-names>
</name>
<name>
<surname><![CDATA[Sen]]></surname>
<given-names><![CDATA[M. K]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Frequency-domain full wave inversion with scattering-intregral approach and its sensivity analysis]]></article-title>
<source><![CDATA[Journal of Geophysics and Engineering]]></source>
<year></year>
</nlm-citation>
</ref>
<ref id="B5">
<label>[5]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Richards]]></surname>
<given-names><![CDATA[Aki]]></given-names>
</name>
</person-group>
<source><![CDATA[Quantitative Seismology]]></source>
<year>2009</year>
<publisher-name><![CDATA[University Science Books]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<label>[6]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[De Santo]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Scalar Wave Theory Green's Functions Applications]]></source>
<year>1992</year>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<label>[7]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Anno]]></surname>
<given-names><![CDATA[P. D]]></given-names>
</name>
<name>
<surname><![CDATA[klein-gordon]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<source><![CDATA[Acoustic theory]]></source>
<year>1993</year>
<publisher-name><![CDATA[Faculty in the Board of Trustees of the Colorado School of Mines]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<label>[8]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mavko]]></surname>
<given-names><![CDATA[G D]]></given-names>
</name>
<name>
<surname><![CDATA[Mukerji T]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<source><![CDATA[The Rock Physics Handbook]]></source>
<year>2009</year>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<label>[9]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wang]]></surname>
<given-names><![CDATA[Y]]></given-names>
</name>
</person-group>
<source><![CDATA[Seismic Inverse Q Filtering]]></source>
<year>2009</year>
<publisher-name><![CDATA[Wiley]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<label>[10]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Polyanin]]></surname>
<given-names><![CDATA[A. D]]></given-names>
</name>
</person-group>
<source><![CDATA[Handbook of Linear Partial Differential Equations for engineers and scientists]]></source>
<year>2002</year>
<publisher-name><![CDATA[Chapman and Hall]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<label>[11]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Treves]]></surname>
<given-names><![CDATA[J.-F]]></given-names>
</name>
</person-group>
<source><![CDATA[Introduction to Pseudo-differential and Fourier Integral Operators: Pseudodifferential Operators]]></source>
<year>1980</year>
<publisher-name><![CDATA[University Series in Mathematics]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<label>[12]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Barrett]]></surname>
<given-names><![CDATA[K]]></given-names>
</name>
<name>
<surname><![CDATA[Myers]]></surname>
<given-names><![CDATA[H.H]]></given-names>
</name>
</person-group>
<source><![CDATA[Foundations of Image Science]]></source>
<year>2004</year>
<publisher-name><![CDATA[Wiley]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<label>[13]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[van den Berg]]></surname>
<given-names><![CDATA[P. M]]></given-names>
</name>
<name>
<surname><![CDATA[Kleinman]]></surname>
<given-names><![CDATA[R. E]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A contrast source inversion method]]></article-title>
<source><![CDATA[Inverse Problems]]></source>
<year>1997</year>
<volume>13</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>1607-20</page-range></nlm-citation>
</ref>
<ref id="B14">
<label>[14]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[van den Berg]]></surname>
<given-names><![CDATA[P. M]]></given-names>
</name>
<name>
<surname><![CDATA[van Broekhoven]]></surname>
<given-names><![CDATA[A. L]]></given-names>
</name>
<name>
<surname><![CDATA[Abubakar]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Extended contrast source inversion]]></article-title>
<source><![CDATA[Inverse Problems]]></source>
<year>1999</year>
<volume>15</volume>
<page-range>1325-43</page-range></nlm-citation>
</ref>
<ref id="B15">
<label>[15]</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ramirez]]></surname>
<given-names><![CDATA[A. B]]></given-names>
</name>
<name>
<surname><![CDATA[van Dongen]]></surname>
<given-names><![CDATA[K. W]]></given-names>
</name>
</person-group>
<source><![CDATA[Sparsity constrained Born inversion for breast cancer detection]]></source>
<year></year>
</nlm-citation>
</ref>
<ref id="B16">
<label>[16]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ramirez]]></surname>
<given-names><![CDATA[A. B]]></given-names>
</name>
<name>
<surname><![CDATA[van Dongen]]></surname>
<given-names><![CDATA[K. W. A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Sparsity constrained contrast source inversion]]></article-title>
<source><![CDATA[J. Acoust. Soc. Am]]></source>
<year>2016</year>
</nlm-citation>
</ref>
<ref id="B17">
<label>[17]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[dos Santos]]></surname>
<given-names><![CDATA[A. W. G]]></given-names>
</name>
<name>
<surname><![CDATA[Pestana]]></surname>
<given-names><![CDATA[R. C]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Time-domain multiscale full-waveform inversion using the rapid expansion method and efficient step-length estimation]]></article-title>
<source><![CDATA[Geophysics]]></source>
<year>2015</year>
<volume>80</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>R203-16</page-range></nlm-citation>
</ref>
<ref id="B18">
<label>[18]</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Chen]]></surname>
<given-names><![CDATA[G]]></given-names>
</name>
<name>
<surname><![CDATA[Wu]]></surname>
<given-names><![CDATA[R.-S]]></given-names>
</name>
<name>
<surname><![CDATA[Chen]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Full waveform inversion in time domain using time-damping filters]]></article-title>
<source><![CDATA[SEG technical Program Expanded Abstracts, Society of Exploration Geophysicists]]></source>
<year>2015</year>
<page-range>1451-5</page-range></nlm-citation>
</ref>
<ref id="B19">
<label>[19]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Murat]]></surname>
<given-names><![CDATA[Dogan a]]></given-names>
</name>
<name>
<surname><![CDATA[Fatih]]></surname>
<given-names><![CDATA[Dikmen]]></given-names>
</name>
<name>
<surname><![CDATA[Alkumru]]></surname>
<given-names><![CDATA[Ali]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Line source diffraction by perfectly conducting successive steps]]></article-title>
<source><![CDATA[Wave Motion]]></source>
<year>2017</year>
<numero>68</numero>
<issue>68</issue>
<page-range>253-71</page-range></nlm-citation>
</ref>
<ref id="B20">
<label>[20]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Versteeg]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<source><![CDATA[The marmousi experience: Velocity model determination on a synthetic complex data set]]></source>
<year>1994</year>
<page-range>927-36</page-range><publisher-name><![CDATA[The Leading Edge]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B21">
<label>[21]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jiménez]]></surname>
<given-names><![CDATA[A. A]]></given-names>
</name>
</person-group>
<source><![CDATA[Integral wave modelling and uncertainty quantification in full waveform inversion]]></source>
<year>2018</year>
<publisher-name><![CDATA[Universidad de Antioquia]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
