An approach to 2.5-D crosswell seismic transmission tomography

We present an approach to crosswell transmission travel time tomography in this article. The trajectory of a real well varies in three dimensions. The crosswell seismic rays are severely insufficient to cover the 3-D model. Thus the 2.5-D crosswell velocity model is constructed and then is divided into a set of 2.5-D horizontally trapezoid prism elements in the light of the prior data of stratigraphy and structures from the drilling or logging and so on. Each element has the slope top and bottom planes with different angles, two vertical side planes in x direction and two vertical side planes in y direction. The velocity of each element is represented as a linear polynomial of x, which is determined using the velocity values at its two side planes in x direction. We also proposed a 3-D raytracing algorithm for this 2.5-D discrete model. And the tomographic inversion is implemented using precondition conjugate gradients algorithm. The tomography approach here can handle severe well deviations, describe effectively the undulation of the layer interfaces and the variations of the velocity, use conveniently the prior geologic and geophysical information as the constraints, and improve thus greatly the reliability and the resolution of the tomograms.