Q estimation based on logarithmic spectral areas with different high and low frequencies

When a seismic wave propagates through subsurface viscoelastic media,the formation absorbs the high-frequency energy of the seismic wave more strongly than the low-frequency energy.As the depth and the off set increase,the diff erence between the logarithmic spectral areas with high and low frequencies gradually increases.Based on this seismic wave characteristic,we have developed a novel Q-estimation method based on logarithmic spectral area diff erence of high and low frequencies(referred to as the LSAD_LH method).In this paper,we derive the theoretical relationship between the Q value and difference of logarithmic spectral areas with high and low frequencies and prove the applicability of the LSAD_LH method using a single-layer medium numerical model.To verify the sensitivity of the LSAD_LH method to bandwidth selection and noise,we compare the LSAD_LH method with two credible methods—the logarithmic spectral ratio(LSR)and logarithmic spectral area diff erence(LSAD)methods using a synthetic model containing the random noise.The results demonstrate that the LSAD_LH method is not highly dependent on bandwidth,and in terms of noise immunity,it is signifi cantly better than the LSR method and has the same advantages as the LSAD method.To further highlight the advantages of the LSAD_LH method,we apply the LSAD_LH and LSAD methods to the vertical seismic profi ling(VSP)numerical simulation of the multilayer media and the fi eld zero-off set VSP data.The application of the two cases proves the applicability of the LSAD_LH method and the accuracy of the high Q-value estimation relative to the LSAD method.Moreover,via the transmission coeffi cient,the LSAD_LH method overcomes the weakness of the LSAD method.