Integrated high-resolution tomography

A common problem in seismic tomography is the inadequate amount of data required for accurate traveltime inversion. The inherent nature in which data is acquired and the subsurface velocities of the survey area can result in a nonuniform distribution of raypaths. In such instances the statistical nature of tomographic inversion biases the solution to reflect the acquisition instead of the geologic properties. This work outlines a method for using the quasi-null space, a measure of inversion reliability, to produce a more constrained solution. In this method, two seismic experiments with different acquisition geometries are used to determine velocity models over the same geologic region. Using the well-constrained portions of the two resulting velocity models, as determined from the quasi-null space, a final tomogram is determined. Testing shows that the combination of two seismic experiments over the same geologic model and null space analysis yield superior tomograms. INTRODUCTION Interpreting seismic data in complex structures requires accurate subsurface images, many times obtained only through prestack depth migration. Prestack depth migration inherently requires an accurate velocity model that can be determined via tomography. Tomographic methods use recorded traveltimes for velocity model estimation. An initial velocity model estimate is updated attempting to minimize the error between the modelled and observed traveltimes. It is assumed that the velocity model yielding the minimum residual traveltimes accurately represents the subsurface velocities. Two different types of tomography are utilized in this work: reflection and transmission. Transmission tomography and in this work consists of crosswell acquisition geometries and deals with purely transmitted signals. The direct traveltimes from source to receiver reveal information of the unknown parameters to be determined: the subsurface velocities of the survey area. Reflection tomography attempts to determine subsurface velocities from a signal that has been undergone reflection at seismologic impedance contrast along its travel path between source and receiver. In this case, recorded traveltimes reveal subsurface velocities as well as reflector positions. Bishop et al (1985) presented a classic paper outlining the basic theory of seismic reflection tomography. Parameterizing both the velocities and reflector positions as unknown quantities, a final multi-layered velocity function was determined after various iterations of modelling, solving a set of overdetermined equations and model parameter adjustment. Lines and LaFehr (1989) presented the basic theory of transmission tomography using a crosswell experiment. The same inversion process