We propose an axis-transformation technique for modeling wave-propagation in the Laplace-domain using a finite-difference method. This technique enables us to use small grids near the surface and large grids at depth. Accordingly, we can reduce the number of grids and attain computational efficiency in modeling in the Laplace domain. We present comparisons between modeled wavefields obtained on the regular and transformed axes.
In this paper, we propose a new time-domain elastic migration technique. By exploiting the back-propagation technique, the excessive computational burden could be efficiently minimized. In addition, the implementation of the Helmholtz decomposition as the wavefield separation technique can enhance the accuracy of the final migrated images using the multi-component data in an elastic medium. Our migration algorithm is tested using the synthetic seismic data generated using the SEG/EAGE salt-dome and Overthrust models. Our new migration technique can image the location and shape of the target zone more clearly than conventional migration methods without wavefield separation.
When waveform inversion is performed in the Laplace-Fourier domain, wave propagation should be described through Laplace-Fourier domain modeling. However, because the modeling operator matrix organized by a complex-valued angular frequency is not satisfied with the positive definite, direct matrix solvers or iterative matrix solvers supporting nonsymmetrical linear systems should be used. In this study, 3D 2nd-order time-8th-order space-domain wave modeling with finite-difference stencils is employed in the waveform inversion instead of 3D complex-valued frequency-domain modeling, and the Graphic Processing Unit (GPU) architecture is used for higher speedup instead of the traditional CPU architecture. In this paper, Laplace-Fourier-domain waveform inversion with time-space wave modeling is called hybrid waveform inversion. To verify the feasibility of this technique, the waveform inversion is performed on the A1 line of the synthetic SEG/EAGE 3D salt model and 3D wide-azimuth real exploration data.
To obtain a reverse time migration image, we can display subsurface image by using a zero-lag cross-correlation between modeled and observed wavefields. However, reverse time migration based on the cross-correlation imaging condition can produce a distorted image when noise exists in the wavefield. Thus, we consider the application of the logarithm and the L1-norm to wavefields, as several earlier studies on waveform inversion applied the logarithm and the L1-norm to the objective functions. In this study, we propose an algorithm for frequency-domain reverse time migration using the logarithm and the L1-norm of a wavefield. We test our proposed algorithm on a synthetic dataset generated by the Marmousi model. After verifying the experiment with the synthetic data, we demonstrate the proposed algorithm on a real exploration dataset obtained from an area in the Gulf of Mexico. Through these numerical simulations, we verify the feasibility of the proposed algorithm. Moreover, we expect that the use of the proposed algorithm will reduce the effort of preprocessing procedures.
Since seismic modeling is conducted repeatedly in seismic inversion, efficiency and accuracy of inversion are affected by seismic modeling algorithm used in it. One of the main factors influencing accuracy of seismic modeling can be the boundary condition used to remove edge reflections arising from finite-size models. For elastic modeling and inversion algorithms free from edge reflections, we propose using the logarithmic grid set. In the logarithmic grid set, the origin is located in the middle of surface of a given model and grid interval increases logarithmically with distance from the origin. The logarithmic grid set enables us to incorporate huge boundary areas with fewer grid points than in the conventional grid set, so that edge reflections are not recorded within the recording duration. For elastic modeling and inversion in the logarithmic grid set, wave equations and source position are first transformed to the logarithm-scaled coordintate. To convert field data from the conventional grid set to the logarithmic grid set and transform inversion results from the logarithmic grid set to the conventional grid set, interpolation algorithms are needed. In the elastic modeling algorithm, the cell-based finite-difference method, which properly describes the free-surface boundary conditions, is used. For inversion process, we apply the gradient method based on the back-propagation method, the pseudo-Hessian matrix, and the conjugate-gradient method. We also employ the frequency-marching method. Numerical examples generated for the modified version of the Marmousi-2 model showed that the elastic modeling and inversion algorithms designed in the logarithmic grid set yield reasonable results.
We present a cyclic shot sampling method to make a full waveform inversion efficient while maintaining the quality of the inversion results. We compare the cyclic method with the regular and random sampling methods using a Laplace-domain full waveform inversion example of data from the Gulf of Mexico. The results can be obtained 7.1 times faster using the sampling methods. The random and cyclic methods yield similar results. However, the cyclic methods generated the best results when the number of shot samples was small.
We present a seismic waveform inversion using a weighting function. With the assumption that the source wavelet can be sufficiently estimated, we define the objective function as the L2-norm of the difference between the Green’s functions. We show the spectral analysis of the scaled gradient and use numerical examples to show that weighting can improve the inversion result.
It is difficult to apply the encoded simultaneous-source full waveform inversion technique to the marine-streamer data because of acquisition geometry. The difference of acquisition geometry between the observed and modeled data produces unwanted events in the residual seismogram. To avoid these unwanted residuals, the objective function based on global correlation was suggested by several researchers. However, the objective function based on global correlation unpredictably modifies the residual seismogram, which may result in distortion of inverted velocity model. In this paper, we propose an alternative approach to avoid these distorted residual seismograms and to properly cope with the acquisition geometry problem. Our algorithm modifies the offset-limited observed data to full-offset data by combining the original observed data with the modeled data. This modification leads to undistorted residual seismogram for the simultaneous multiple shot data. As a result, we can perform the effective simultaneous-source full waveform inversion even for the marine-streamer acquisition. Through the numerical examples, we show that our inversion algorithm better describes the velocity structure than the global correlation approach does.