Young Ho Cha

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.

Random‐beam full‐wavefield inversion

Full-wavefield inversion (FWI) of seismic data is computationally expensive due to the large number of shots that need to be simulated during the inversion process. Recently, a technique has been developed that reduces the computational cost of FWI significantly by encoding and simulating all shots recorded in a seismic survey simultaneously [Krebs et al., 2009]. This technique, however, is only directly applicable to surveys in which all receivers record signals from every shot. For the majority of current and legacy survey geometries this requirement is not met. Here we present a new method of FWI that can be applied to any survey geometry. When applied to marine streamer data a reduction to <5% of the computational cost of sequential-shot FWI is realizable. This method groups the data recorded during a seismic survey into several encoded multi-shot gathers each of which can be modeled using a single numerical simulation. These groups can either be constant or vary between inversion iterations. This grouping process also allows us to use an L2-norm for calculating data misfit. The computational speedup gained by using this method is constrained to be less than that provided by simulating all the shots in a survey simultaneously, which requires a seldom-used acquisition geometry.

The direct‐removal method of waveform inversion in the Laplace inversion for deep‐sea environments

Waveform inversion in the Laplace domain has the advantage of finding a smooth velocity structure including salt domes having a large velocity contrast to the background medium. In exploration, noises contaminate the data before and near the direct wave. The early time noises cause inaccuracy and instability of the Laplace transform of time signal, when we use the data for Laplace-domain waveform inversion. We developed an inversion algorithm using a method which removes the direct wave from common shot gather data. We performed velocity structure inversion and source estimation with a direct removed wavefield and we obtained the velocity model that was close to the true model. In this study, we developed an algorithm of waveform inversion in the Laplace domain which can be applied to a deep-sea survey and successfully applied to synthetic and field data.

2D Laplace-domain Waveform Inversion Using Adaptive Finite Element Method

Summary Waveform inversion in the Laplace domain has been proposed recently. The Laplace-domain waveform inversion is robust, is not sensitive to the initial model, and generates a long-wavelength velocity model for field data as it exploits a well behaved objective function. To improve the applicability of the waveform inversion, we adopted the adaptive finite element method to deal with the sources and receivers at shallow depths. Since the Laplace-domain wavefield damps out rapidly as a receiver becomes sufficiently far from a source, we applied the Dirichlet boundary condition on the edges of the extended model instead of using an absorbing boundary condition. By these two improvements in forward modeling, a numerical test was conducted on a time-domain original BP benchmark dataset. The Laplace-domain waveform inversion using the adaptive mesh successfully provided a long-wavelength velocity model of the true model. The inverted smooth velocity model was used as a good initial model for the frequency-domain waveform inversion. The followed frequency-domain inversion recovered almost every features of the BP model except some sub-salt structures.

2-D, Frequency-domain Waveform Inversion of Coupled Acoustic-elastic Media With an Irregular Interface

In order to correctly interpret marine exploration data, which contain many elastic signals such as S waves, surface waves and converted waves, we have developed both a frequency-domain modeling algorithm for acoustic-elastic coupled media with an irregular interface, and the corresponding waveform inversion algorithm. By applying the continuity condition between acoustic (fluid) and elastic (solid) media, wave propagation can be properly simulated throughout the coupled domain. The arbitrary interface is represented by tessellating square and triangular finite elements. Although the resulting complex impedance matrix generated by finite element methods for the acoustic-elastic coupled wave equation is asymmetric, we can exploit the usual back-propagation algorithm used in the frequency domain through modern sparse matrix technology. By running numerical experiments on a synthetic model, we demonstrate that our inversion algorithm can successfully recover Pand S-wave velocity and density models from marine exploration data (pressure data only).

A Comparative Study of Cascaded Frequency-selection Strategies For 2D Frequency-domain Acoustic Waveform Inversion

As a method to obtain a global minimum in waveform inversion, two kinds of frequency-selection strategy have been applied in waveform inversion. The two methods are similar to each other in that waveform inversion is performed sequentially by grouping frequencies into several groups and proceeding from the low frequencies to the high frequencies. The main difference between the two methods is that the first method employs the low frequencies repeatedly at every inversion stage, while the second method applies a range of frequencies at a stage that do not overlap with the frequencies used at other stages. By applying the two frequency-selection strategies to the logarithm waveform inversion, we examine their effectiveness. In the logarithm waveform inversion, the objective function is constructed by taking the logarithm of wavefields and the gradient is computed by the backpropagation technique of reverse-time migration. Numerical examples demonstrate that the two frequencyselection methods provide solutions closer to the global minimum compared with those of the simultaneously performed waveform inversion. Considering both computational efficiency and accuracy, the second method can be the method of choice for the logarithm waveform inversion.