Study On Numerical Simulation Of Whole-space Elastic Wave And Reverse Time Migration Imaging Method

The elastic wave advanced detection is one of the main methods to predict thegeological anomaly structures ahead of the tunneling or in the working face.Compared with the surface seismic exploration, this method has the advantage of highresolution. It has a good application prospect in the mining safety production. In thispaper, the high-order staggered grid finite difference method is used to simulate theseismic wave field under the conditions of the mining, and the pre-stack reverse timemigration is studied based on the vector wave field of the two-way wave equation.The isotropic medium wave equation is derived from the three basic equations ofthe elastic dynamics. The P-and S-waves separated first-order speed-stress elasticwave equation is derived from the divergence, the curl and the equilibrium differentialequation. This is the theoretical foundation for numerical simulation by the high-orderstaggered grid finite difference.The difference scheme of the P-and S-waves separated first-order speed-stresselastic wave equation is derived and the boundary conditions are analyzedtheoretically. It indicates that the effect of perfectly matched layer absorbing boundarycondition is good. The flux-corrected transport method is used to suppress thenumerical dispersion. The source and the stability of the numerical simulation are alsodiscussed in the paper.The attribute characteristics of the full space elastic wave field are studied. Thedip’s relative magnitude of the interface in front of the observation system can bederived by P-and S-waves maximum absolute amplitude. The lithology informationahead of the interface can be derived by P-and S-waves polarity.The models of vertical layered medium, tilted layered medium and compositetilted medium ahead of the observation system are simulated. It turned out that therecord reflected waves have a linear shape and the negative apparent velocity,multiple reflections appear on most records and the multiple reflections of the shearcomponent are obvious. The horizontal cylinder model is simulated. It turned out thatdiffracted waves appear at the near-source point and the most distal point, thediffracted wave field has the―X‖-type distribution affected by the upper and bottominterfaces of the cylinder.The elastic wave field characteristics on the condition of the coal seams existingare studied. The elastic wave diffracts at the breaking points of the single wing coalseams. The channel waves with high energy appear in the coal seams. The multiple reflected waves from the coal roof and floor are obvious. When the source is on thefloor, the differences of travel time between the direct wave from the tilted interfaceahead of the coal seam, the reflected wave from the floor and the reflected wave fromthe roof are very small. So there is a P wave-group. The reflected wave-group of theinterface in front can be identified on the record. When the coal seams break, the Pwave-group diffracts at the breaking point of the footwall. The primary diffraction canbe identified on the P wave record. The primary and secondary diffraction are obviouson the S wave record. The roof and floor reflections of the footwall can’t be identifiedon the record.Based on the Fermat’s principle and dichotomy theory, using nonlinearinterpolation method to calculate the first-arrival travel time, applying the Poynting’svector in the elastic wave pre-stack reverse time migration, the up-going wave,down-going wave, sped wave and back wave are separated in full space seismic wavefield. It overcomes the problem of ambiguity and pseudomorph of the full spacemigration result. The typical mining geological bodies migration processing indicatesthat the vertical interfaces in front appear as the―arc phenomenon‖. The interface iscloser to the observation system the―arc phenomenon‖is more obvious. The tiltedinterfaces in front appear as―smearing‖on the migrated section and the direction ofthe―smearing‖is related with the relative position between the interface and theobservation system. On the migrated section, the―two wings phenomenon‖appearsinside the interface position. The interface is closer to the observation system the―twowings phenomenon‖is more obvious.