Traveltime calculations amount to solving the nonlinear eikonal equation for a given source location. We analyze the relationship between the eikonal solution and its perturbations with respect to the source location and develop a partial differential equation that relates the traveltime field for one source location to that for a nearby source. This linear first-order equation in one form depe...

In this paper, we give a theoretical analysis of the crosswell traveltime tomography. In the single arrival case, we prove that the objective function is smooth, and every critical point is a kinematically correct velocity model. A numerical example is presented to demonstrate the properties we prove and the diierence between traveltime tomography and waveform inversion via the output least squ...

Prestack Kirchhoff migration using first arrival traveltimes has been shown to fail in areas of complex structure. I propose a new method for calculating traveltimes that estimates the traveltime of the maximum energy arrival, rather than the first arrival. The method estimates a traveltime that is valid in the seismic frequency band, not the usual high frequency approximation. Instead of solvi...

Reconstruction of acoustic, seismic, or electromagnetic wave speed distribution from rst arrival traveltime data is the goal of traveltime tomography. The reconstruction problem is nonlinear, because the ray paths that should be used for tomographic backprojection techniques can depend strongly on the unknown wave speeds. In our analysis, Fermat's principle is used to show that trial wave speed...

In complex areas, residual vertical movement is not an effective method to calculate traveltime errors for image domain tomography. By scanning over velocity ratios using residual Stolt migration, a different criteria for a coherent image can be defined, and a traveltime error approximated. The resulting traveltime errors are more accurate, therefore the tomography procedure is more robust than...

Joint inversion of different geophysical datasets is an effective way to eliminate non-uniqueness in geophysical inversion problems. In this paper, we focus on a case study of joint inversion of seismic traveltime and gravity observations. The results are encouraging and we can have confidence that, comparing traveltime tomography alone, joint inversion of seismic traveltime and gravity data im...

Constructing the seismic image in vertical time, as opposed to depth, eliminates the inherent ambiguity of resolving the vertical P -wave velocity from surface seismic data in transversely isotropic media with a vertical axis of symmetry (VTI media). By ray tracing in the space-time (x-τ)-domain, a traveltime map is built by interpolating the traveltime information along the rays onto a regular...

Event picking is used in many steps of seismic processing. We present an automatic event picking method that is based on a new attribute of seismic signals, the instantaneous traveltime. The calculation of the instantaneous traveltime consists of two separate but interrelated stages. First, a trace is mapped onto the time-frequency domain. Then the time-frequency representation is mapped back o...