Seungwon Ko

Traveltime and amplitude calculations using the damped wave solution

Because of its computational efficiency, prestack Kirchhoff depth migration remains the method of choice for all but the most complicated geological depth structures. Further improvement in computational speed and amplitude estimation will allow us to use such technology more routinely and generate better images. To this end, we developed a new, accurate, and economical algorithm to calculate first-arrival traveltimes and amplitudes for an arbitrarily complex earth model. Our method is based on numerical solutions of the wave equation obtained by using well-established finite-difference or finite-element modeling algorithms in the Laplace domain, where a damping term is naturally incorporated in the wave equation. We show that solving the strongly damped wave equation is equivalent to solving the eikonal and transport equations simultaneously at a fixed reference frequency, which properly accounts for caustics and other problems encountered in ray theory. Using our algorithm, we can easily calculate first-arrival traveltimes for given models. We present numerical examples for 2-D acoustic models having irregular topography and complex geological structure using a finite-element modeling code.

Traveltime calculations from frequency‐domain downward‐continuation algorithms

We present a new, fast 3D traveltime calculation algorithm that employs existing frequency‐domain wave‐equation downward‐continuation software. By modifying such software to solve for a few complex (rather than real) frequencies, we are able to calculate not only the first arrival and the approximately most energetic traveltimes at each depth point but also their corresponding amplitudes. We compute traveltimes by either taking the logarithm of displacements obtained by the one‐way wave equation at a frequency or calculating derivatives of displacements numerically. Amplitudes are estimated from absolute value of the displacement at a frequency.By using the one‐way downgoing wave equation, we also circumvent generating traveltimes corresponding to near‐surface upcoming head waves not often needed in migration. We compare the traveltimes computed by our algorithm with those obtained by picking the most energetic arrivals from finite‐difference solutions of the one‐way wave equation, and show that our trave...

Wave equation calculation of most energetic traveltimes and amplitudes for Kirchhoff prestack migration

Because of its computational efficiency, Kirchhoff migration is the method of choice for 3D prestack depth migration, particularly in the initial velocity model-building stages where several iterations of migration are necessary. In the beginning, Kirchhoff migration used traveltimes calculated by either eikonal solvers or asymptotic ray theory, while amplitudes were calculated using relatively smooth geometrical spreading and obliquity considerations. More recently, Kirchhoff migration has been generalized to include more than one arrival time, with amplitudes calculated from geometrical optics, solution of the transport equations, or Gaussian beams (e.g., Hill, 2001).

Improved logarithmic waveform inversion considering the power‐spectrum of the wavefield

Local minima of an objective function often prevent solutions of logarithmic waveform inversions from converging to the global minimum in cases where an initial velocity model for the inversion is not close to the true velocity structure. In particular, forward-modeled wave fields with small power-spectrum values influence the numerical stability of the gradient direction. Accordingly, it is important to remove these small values to allow a solution to the misfit function to converge to the global minimum. Therefore, we developed a waveform-inversion technique using forward-modeled wavefields with relatively large values of the power-spectrum.

Traveltime and amplitude calculation using a perturbation approach

Accurate amplitudes and correct traveltimes are critical factors that govern the quality of prestack migration images. Because we never know the correct velocity initially, recomputing traveltimes and amplitudes of updated velocity models can dominate the iterative prestack migration procedure. Most tomographic velocity updating techniques require the calculation of the change of traveltime due to local changes in velocity. For such locally updated velocity models, perturbation techniques can be a significantly more economic way of calculating traveltimes and amplitudes than recalculating the entire solutions from scratch. In this paper, we implement an iterative Born perturbation theory applied to the damped wave equation algorithm. Our iterative Born perturbation algorithm yields stable solutions for models having velocity contrasts of 30% about the initial velocity estimate, which is significantly more economic than recalculating the entire solution.

A Robust and Accurate Traveltime Calculation from Frequency-domain Two-way Wave-equation Modeling Algorithm

ABSTRACT We improve the accuracy and stability of traveltime calculation method using frequency-domain modeling algorithm. We perform a parameter analysis to obtain the optimum combination of frequency and damping factor and thus improve the accuracy of traveltime. Then we obtain the empirical formula for our numerical algorithm. Lastly, we propose the adaptive frequency and the adaptive damping factor for an inhomogeneous model to eliminate the distortion in the traveltime contour. Two-dimensional numerical examples verify that the proposed algorithm gives a much smaller traveltime error and a better traveltime contour for the complex model. Compared to the other two methods, this algorithm computes traveltime that is close to a directly transmitted wave. We demonstrated our algorithm on 2D IFP Marmousi models, and the numerical results show that our algorithm is a faster traveltime calculation method of a directly transmitted wave for imaging the subsurface and transmission tomography.