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...

Abstract We propose a new methodology for carrying out eikonal-based traveltime tomography arising from important applications such as seismic imaging and medical imaging. The new method formulates the traveltime tomography problem as a variational problem for a certain cost functional explicitly with respect to both traveltime and sound speed. Furthermore, the cost functional is penalized to e...

The first-arrival quasi-P wave traveltime field in an anisotropic elastic solid solves a first-order nonlinear partial differential equation, the q P eikonal equation. The difficulty in solving this eikonal equation by a finitedifference method is that for anisotropic media the ray (group) velocity direction is not the same as the direction of the traveltime gradient, so that the traveltime gra...

In the high frequency regime, the geometrical-optics approximation for the Helmholtz equation with a point source results in an eikonal equation for traveltime and a transport equation for amplitude. Because the point-source traveltime field has an upwind singularity at the source point, all formally high-order finite-difference eikonal solvers exhibit first-order convergence and relatively lar...