<?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>1026-8774</journal-id>
<journal-title><![CDATA[Revista mexicana de ciencias geológicas]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. cienc. geol]]></abbrev-journal-title>
<issn>1026-8774</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Instituto de Geología]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1026-87742021000300152</article-id>
<article-id pub-id-type="doi">10.22201/cgeo.20072902e.2021.3.1641</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Spherical data validation of rock discontinuities orientation from Drone-derived 3D Point Clouds]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Mancera-Alejandrez]]></surname>
<given-names><![CDATA[Javier]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Macías-Medrano]]></surname>
<given-names><![CDATA[Sergio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Villarreal-Rubio]]></surname>
<given-names><![CDATA[Enrique]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Solano-Rojas]]></surname>
<given-names><![CDATA[Darío]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional Autónoma de México Facultad de Ingeniería ]]></institution>
<addr-line><![CDATA[Mexico City ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2021</year>
</pub-date>
<volume>38</volume>
<numero>3</numero>
<fpage>152</fpage>
<lpage>163</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1026-87742021000300152&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1026-87742021000300152&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1026-87742021000300152&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract This work presents a methodology for the statistical validation of discontinuity surfaces obtained from point clouds using digital photogrammetry from drones. Our methodology allows you to review the quality of the data obtained with photogrammetry and decide whether these measurements are representative of the discontinuity surfaces that they analyze. It consists of three steps, the first one being a shape analysis that allows defining which statistical model should be used: Fisher for circularly symmetric clusters or Bingham fits better for axially symmetric clusters. This step also makes the most significant difference to other works since our methodology starts from the premise that not all discontinuity surfaces are flat. Therefore, Fisher parameters do not allow validating data that do not correspond to a plane. In the second step of the methodology, we calculate the consistency parameters that depend on the statistical model defined in step 1. The parameters are similar for both models; both estimate &#954; which indicates how much the sample is concentrated around the mean orientation and validates the existence of this and which is the value of the generating angle of a cone with a 95 % confidence limit that it contains within the mean orientation. Finally, step 3 is used when there are control measurements to compare the point cloud data and define if both samples characterize the same discontinuity surface in the rock mass. The results obtained on a rock outcrop allowed us to observe that the measurements obtained from the drone faithfully represent the discontinuity surface analyzed when these were compared with the measurements made manually with the compass. Furthermore, the dispersion parameters (&#954; and &#945; 95) yielded results that make it possible to ensure that 1) there is a preferential direction (mean orientation) and 2) the mean orientation is representative of the entire measured surface.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Se presenta una metodología para la validación estadística para superficies de discontinuidad obtenidas de nubes de puntos utilizando fotogrametría digital a partir de drones. Esta metodología permite revisar la calidad de datos obtenidos con fotogrametría y decidir si estas mediciones son o no representativas de las superficies de discontinuidad que analizan. Esta metodología se compone de tres pasos, siendo el primero un análisis de forma que permite definir qué modelo estadístico se debe utilizar: Fisher para agrupaciones circularmente simétricas o Bingham que se ajusta mejor para agrupaciones axialmente simétricas. Este paso también es el elemento que marca la mayor diferencia con respecto a otros trabajos ya que nuestra metodología parte de la premisa de que no todas las superficies de discontinuidad son planas y, por lo tanto, los parámetros de Fisher no permiten validar datos que no corresponden a un plano. En el segundo paso de la metodología, se calculan los parámetros de consistencia que dependen del modelo estadístico que se definió en el paso 1. Los parámetros son similares para los dos modelos, en ambos se calcula &#954; que indica qué tanto se concentra la muestra alrededor de la orientación media y valida la existencia de esta y &#945;95 que es el valor del ángulo generador de un cono con un límite de confianza del 95 % de que contenga dentro la orientación media. Por último, el paso 3 se utiliza cuando se tienen medidas de control con las que comparar los datos de la nube de puntos y permite definir si ambas muestras caracterizan a la misma superficie de discontinuidad en el macizo rocoso. Los resultados obtenidos en una pared rocosa permitieron observar que las mediciones obtenidas a partir del dron representan fielmente a la superficie de discontinuidad analizada, cuando estas se compararon con las mediciones realizadas manualmente con la brújula. Además, los parámetros de dispersión (&#954; y &#945;95) arrojaron resultados que permiten asegurar que 1) existe una dirección preferencial (orientación promedio) y 2) que esta dirección es representativa de toda la superficie medida.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[rock-discontinuities]]></kwd>
<kwd lng="en"><![CDATA[spherical statistics models]]></kwd>
<kwd lng="en"><![CDATA[drone]]></kwd>
<kwd lng="en"><![CDATA[validation statistical]]></kwd>
<kwd lng="en"><![CDATA[point cloud]]></kwd>
<kwd lng="es"><![CDATA[discontinuidades]]></kwd>
<kwd lng="es"><![CDATA[modelos de estadística esférica]]></kwd>
<kwd lng="es"><![CDATA[dron]]></kwd>
<kwd lng="es"><![CDATA[validación estadística]]></kwd>
<kwd lng="es"><![CDATA[nubes de puntos]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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