Forward Simulation Of Wave Equation In Three-dimensional Viscoelastic Media

Absorption attenuation is an inherent feature of seismic wave propagation in the actual earth medium.In seismic exploration,quality factor Q is usually used to quantify the degree of seismic wave absorption attenuation in the stratum.Studies show that the attenuation of seismic wave energy can be regarded as a linear combination of two components: Q does not change with frequency and Q changes with frequency.In view of the above two changes of Q values,the forward modeling of three-dimensional viscoelastic wave equation is helpful to study the influence of different absorption attenuation laws on seismic wave propagation characteristics,and is of great significance to the acquisition,processing and interpretation of actual seismic data.At present,the three dimensional viscoelastic medium time domain wave equation forward modeling mainly low attenuation model,and Q value on frequency change law of seismic wave propagation characteristics of the influence of the research is not enough in-depth,the paper USES the high order generalized standard linear model,within the expected frequency band by a least squares fitting method to calculate each standard linear independent characterization parameters,implementation of Q does not change with frequency and Q on frequency change characteristics of two kinds of high precision.In this paper,the degree of accurate fitting of the above two Q value characteristics by different order generalized standard linear model is analyzed.On the basis of weighing the calculation accuracy and the forward simulation efficiency of three-dimensional wave equation,the fifth order generalized model and the ninth order generalized model are selected to simulate the two characteristics of Q not changing with frequency and Q changing with frequency respectively.On this basis,a three-dimensional viscoelastic wave equation based on generalized standard linear model was derived.CPML boundary conditions were used to absorb the reflection at the boundary,and MPI+Open MP was used for parallel acceleration to realize the forward modeling of three-dimensional viscoelastic media wave equation.To solve the problem that the change of Q value with frequency is affected by physical parameters such as porosity and permeability,this paper constructs a three-dimensional stratigraphic framework with seismic interpretation horizon and fault according to the characteristics of actual seismic working area,and establishes a three-dimensional physical parameter model with logging data under the constraint of seismic phase.The layered media model with pore period was used to characterize the change rule of Q value with physical parameters.Based on the 3d physical parameter modeling,3d Q value data bodies with different frequencies were established.On this basis,the forward modeling of three-dimensional viscoelastic medium wave equation is carried out,and the influence of different Q values on the absorption attenuation characteristics of seismic waves in different seismic frequency bands is analyzed,and the variation law of seismic wave amplitude with porosity and permeability is discussed.Study shows that the quality factor Q directly influenced by the inherent nature of strata and seismic wave frequency band range of influence,therefore,in the viscoelastic medium wave equation forward modeling should fully consider the impact of Q value and frequency,for fine characterization of absorption attenuation of seismic waves in the actual medium characteristics has important theoretical significance and practical application value.