Kwangjin Yoon

Efficient calculation of a partial‐derivative wavefield using reciprocity for seismic imaging and inversion

Linearized inversion of surface seismic data for a model of the earth’s subsurface requires estimating the sensitivity of the seismic response to perturbations in the earth’s subsurface. This sensitivity, or Jacobian, matrix is usually quite expensive to estimate for all but the simplest model parameterizations. We exploit the numerical structure of the finite-element method, modern sparse matrix technology, and source–receiver reciprocity to develop an algorithm that explicitly calculates the Jacobian matrix at only the cost of a forward model solution. Furthermore, we show that we can achieve improved subsurface images using only one inversion iteration through proper scaling of the image by a diagonal approximation of the Hessian matrix, as predicted by the classical Gauss-Newton method. Our method is applicable to the full suite of wave scattering problems amenable to finiteelement forward modeling. We demonstrate our method through some simple 2-D synthetic examples.

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...

Waveform inversion using time‐windowed back propagation

Waveform inversion of reflection seismic data implicitly include non-uniqueness and local minima problems. To attack these obstacles, we suggest a new approach using time window and frequency band simultaneously. The number of local minima can be reduced by filtering and windowing measured and modeled data. With the filtered and windowed residual, we can begin by updating shallow velocity and then progressively update deeper velocity.

3-D Reverse-time Migration Using Acoustic Wave Equation: An Experience of SEG/EAGE Salt Data Set

Abstract Reverse-time migration has no dip limitations and one of the most promising methods to preserve true amplitudes. We applied 3-D prestack reverse time migration based on a pseudo-spectral implementation of the acoustic wave equation to the SEG/EAGE salt dome synthetic data set. We were able to illuminate sub salt reflectors of the SEG/EAGE salt model that were barely observable in the Kirchhoff migration images. Using the pseudo-spectral modeling technique, we could apply reverse-time migration to the SEG/EAGE data within the core memory, which could be equipped to a personal computer.

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.

Spectral Method in Scalar Wave Equation Modeling

ABSTRACT A new numerical method is proposed for the simulation of wave phenomena by applying the forward modeling of the scalar wave equation. In the computation of wavefield, the wave equation transformed into the frequency- wavenumber domain is utilized. A linear system composed of coefficients obtained by a discrete Fourier transform of discretized model parameters is solved to obtain the wavefield at each frequency. The wavefield in the time-space domain is obtained by inverse Fourier transforms of the wavefield computed in the frequency-wavenumber domain. This scheme has no numerical dispersion problems in the homogeneous media and can remove truncation errors originated in the finite-difference approximations to spatial and temporal derivatives. The accuracy of this scheme is confirmed through forward modeling with the Nyquist sampling limit. However, for solving in the linear system, lots of computation time and computer memory are required due to the huge resultant complex impedance matrix size. T...