Calculation method for theoretical dispersion curves of seismic channel waves considering variation of coal-seam thickness and analysis of dispersion characteristics

In channel-wave seismic exploration, dispersion features are used to invert structures of coal seams. So calculation of theoretical dispersion curves is an important subject. We can calculate dispersion curves when the coal-thickness keeps unchanged by utilizing the calculation method for surface wave dispersion of a horizontal stratified model. But this method is inapplicable when the coal-seam thickness changes. For a coal-bearing three-layer model, this work proposes a calculation method for theoretical dispersion curves when the coal-seam thickness fluctuates, which is based on the calculation method for dispersion curves of horizontal stratified models. We also analyze the characteristics of dispersion curves for different models of varied coal-seam thickness. Our research shows that unlike unchangeable coal-thickness model, group velocity of a changeable coal-thickness model becomes a function related to frequency and projective ray paths in horizontal plane. The change of coal-seam thickness along the ray route leads to squeezing effect of dispersion curves in velocity's direction, narrowing the range of group velocity and increasing the minimal group velocity at airy phase. The dispersion curve of the linearly changing coal-seam thickness model relates only to the thickness at the start and end of ray paths, while the curve shape does not change compared with the unchangeable coal-seam thickness model. The dispersion curve shape of a nonlinearly varied coal-seam thickness model may case change in the shape of dispersion curves with respect to the model with constant coal-seam thickness.