Adaptive Elastic Modeling

Introduction:

Shear- and mode-converted waves provide rich information for further improving the image quality of complex geological structures and quantification of reservoir characterization. Multi-component seismic data acquisition has become more and more popular for surface seismic, Ocean Bottom Cable (OBC), and Vertical Seismic Profile (VSP) over the recent years.

Conventional elastic wave simulation uses fixed-grid discretization throughout the 3D volume. It requires a huge computing cost and encounters oversampling with high velocity.

In order to make elastic modeling more cost effective in marine environment, we propose a new hybrid method to perform 3D elastic modeling. We implement the
first-order acoustic wave equation used in water layer and the velocity-stress elastic wave equation with adaptive grid in solid sediment. The numerical result of the hybrid method matches very well with the conventional approach using fixed-grid implementation with full elastic wave equation. By applying the first-order acoustic/elastic perfectly matched layer (PML) boundary condition, the numerical boundary reflections are greatly absorbed.

Methods:

 

 

 

 

 

 

 

 

 

 

 

Above figure shows a grid layout of hybrid acoustic-elastic modeling method. In water layer, we apply the first-order acoustic wave equation:

In the solid-elastic medium, we apply the velocity-stress equations (for detail, please see published paper link at the end):

For the first-order acoustic wave equation, a PML boundary condition is described below:

 

 

 

Examples:

A simple two-layer model is introduced to verify the accuracy of this hybrid method. As shown in following Figure, the first layer is water, and the second layer is solid-elastic medium. The Ricker wavelet with a maximum frequency of 20 Hz is used. Figure 2b shows a snapshot of the vertical component of particle velocity at 0.7 s. Figure 2c shows the comparison of zero-offset traces of the vertical component obtained by analytical results generated by the Cagniard-De Hoop’s technique (de Hoop 1960), conventional elastic modelling result, and hybrid elastic modeling with adaptive grid result. The amplitudes of three traces are scaled for comparison. The direct arrival and reflected wave match well in terms of wave shape and travel time. The memory requirement of our method is 40% less than the conventional approach. The computation is also about 57% faster than the conventional approach.

 

 

 

 

 

 

 

 

 

Second example is a reality test on the 3D SEG Advanced Modeling Program (SEAM) dataset with OBC and VSP acquisition geometries. It contains a major salt body and suite of reservoirs. Following Figure shows a P-wave velocity model with a source and receivers’ position. S-wave velocity is set to half of the P-wave velocity. The computation aperture is limited to a crossline aperture of 8 km and an inline aperture of 6 km with modeling a depth of 10 km. The total recording time is 10 s with a 4-ms sample interval. The Ricker wavelet is used with a maximum frequency of 28 Hz. By applying our method, the velocity model is split into multiple subzones. The first zone is a water zone and the rest zones are elastic zones.

Conclusions:

To make elastic modeling more cost effective in marine environments, we proposed a hybrid method to combine the acoustic and elastic wave equations with adaptive grid implementation. An acoustic wave equation is used for simulating wave propagation in water layer, while the elastic wave equation is used in the solid-elastic medium below the water bottom. With implementing the adaptive grid scheme to acoustic/elastic wave propagation, oversampling in high-velocity areas is avoided, resulting in a tremendous improvement in computing efficiency. The numerical result of the hybrid method matches very well with the conventional approach using fixed-grid implementation with full elastic wave equation. The test on the SEAM model also demonstrates that this method is capable of modeling surface seismic, OBC, and VSP acquisition geometries with greatly improved efficiency and less frequently used computing resources.

Reference: 2013_Jiang_Hybrid Acoustic-Elastic Modeling Method Using Adaptive Grid Finite Difference Scheme