A variational formulation to image inclusions in 2D travel time cross hole tomography

• Autor(a) principal: Imhof,Armando Luis
• Data de Publicação: 2003
• Outros Autores: Calvo,Carlos Adolfo
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Revista Brasileira de Geofísica (Online)
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0102-261X2003000300006
• topic: Tomography; Cross Hole; Simplex Downhill; Variational; Nelder Mead

It was developed a simple and high speed method with the purpose to model inclusions of irregular forms (simply connected and convex domain) in the context of cross hole travel time 2D tomography. The extension to 3D can be easily implemented and is not covered in this paper. The following assumptions were made: a) Homogeneus host medium (therefore straight ray propagation assumed) b) Homogeneus inclusion. c) Not very high velocity contrast between host medium (V1) and the inclusion (V2). The algorithm calculate the host velocity V1 considering the (straight) ray between source 1 and receiver 1, and considering that this ray not intersect the anomaly. Then the velocity V2 of the inclusion is estimated upon determining the difference deltat among measured times source i - receiver j and corresponding calculated times. If the global difference is negative signifies that V2 will be greater than V1 and viceversa. The small values of deltat are treated as outliers and therefore eliminated. The last initial parameters needed by the algorithm are the coordinates of the center of the inclusion, which are estimated by a graphical procedure. Afterwards the program approximates the contour of the inclusion using the Nelder-Mead 'simplex' algorithm. At last the perfomance of the algorithm was applied with real data.