Methods and devices using effective elastic parameter values for anisotropic media
Methods and devices for seismic exploration of an underground formation including an orthorhombic anisotropic medium or a tilted transverse isotropic medium are provided. Isotropic-type processing techniques use effective elastic parameter values calculated based on elastic parameter values, anisotropy parameter values and azimuth angle values for the orthorhombic anisotropic medium. For the tilted transverse isotropic medium, the effective elastic parameter values depend also on the tilt angle thereof.
1. A method for seismic exploration of an underground formation including an orthorhombic anisotropic medium with three mutually orthogonal planes of symmetry, the method comprising:
obtaining seismic data acquired for the underground formation, wherein the seismic data includes seismic amplitudes detected at plural values of an azimuth angle of a source-receiver direction relative to a principal axis of the orthorhombic anisotropic medium;
calculating elastic parameter values and anisotropy parameter values related to the orthorhombic anisotropic medium based on the seismic data;
calculating effective elastic parameter values for the orthorhombic anisotropic medium based on the elastic parameter values, the anisotropy parameter values and the azimuth angle, each elastic parameter E having a corresponding effective elastic parameter E eff expressed as:
E eff =ϵ r (2) X δ r (3) Y γ r (3) Z ϵ r (1) U δ r (1) V δ r (2) W E
wherein ϵ r (2) ,δ r (3) , γ r (3) ,ϵ r (1) ,δ r (1) ,δ r (2) are Thomson parameters, with (1), (2) and (3) indicating coordinate axes, and wherein X, Y, Z, U, V, W are constants;
performing an isotropic-type processing technique using the effective elastic parameter values, the isotropic-type processing technique yielding a quantitative model of the underground formation; and
locating hydrocarbon reservoirs based on the quantitative model of the underground formation.
2. The method of claim 1 , wherein the isotropic-type processing technique includes at least one of:
an isotropic seismic modeling method,
an isotropic seismic analysis and interpretation method,
an isotropic seismic wavelet estimation method,
an isotropic seismic inversion method, and
an isotropic method for analysis and interpretation of inversion results to produce processed effective elastic parameter data.
3. The method of claim 1 , wherein the elastic parameters values represent p-wave velocity, s-wave velocity and density.
4. The method of claim 1 , wherein the elastic parameters values represent p-wave impedance, s-wave impedance and density.
5. A method for seismic exploration of an underground formation including a tilted transverse isotropic, TTI, medium having a symmetry axis tilted at a tilt angle τ relative to a horizontal plane thereof, the method comprising:
obtaining seismic data acquired for the underground formation, wherein the seismic data includes seismic amplitudes detected at plural values of an azimuth angle, ω−φ, of a source-receiver direction relative to a projection of the symmetry axis in a horizontal plane;
calculating elastic parameter values and anisotropy parameter values related to the TTI medium based on the seismic data; and
performing an isotropic-type processing technique using effective elastic parameter values calculated based on the elastic parameter values, the anisotropy parameter values, the values of the azimuth angle and of the tilt angle for the TTI medium, the isotropic-type processing technique yielding a quantitative model of the underground formation; and
locating hydrocarbon reservoirs using the quantitative model of the underground formation.
6. The method of claim 5 , wherein the isotropic-type processing technique includes at least one of:
an isotropic seismic modeling method,
an isotropic seismic analysis and interpretation method,
an isotropic seismic wavelet estimation method,
an isotropic seismic inversion method, and
an isotropic method for analysis and interpretation of inversion results to produce processed effective elastic parameter data.
7. The method of claim 5 , wherein any elastic parameter E has a corresponding effective elastic parameter Eef eff expressed as:
E eff =ϵ r X δ r Y γ r Z E
wherein ϵ r X , δ r Y , γ r Z being Thomsen parameters and X, Y, Z being constants.
8. The method of claim 5 , wherein an elastic parameter E has a corresponding effective elastic parameter Eef eff expressed as:
ln E eff =b 0 +b 2 cos(2(ω−φ))+ b 4 cos(4(ω−φ))
wherein b 0 , b 2 and b 4 are coefficients depending on the elastic parameter values, the anisotropy parameter values and the tilt angle.
9. The method of claim 5 , wherein the elastic parameters values represent p-wave velocity, s-wave velocity and density.
10. The method of claim 5 , wherein the elastic parameters values represent p-wave impedance, s-wave impedance and density.
11. A seismic data processing apparatus for exploration of an underground formation, the apparatus comprising:
an interface configured to obtain seismic data acquired for the underground formation, wherein the seismic data includes seismic amplitudes detected at plural values of an azimuth angle, ω−φ, of a source-receiver direction
relative to a principal axis of the orthorhombic anisotropic medium if the underground formation includes an orthorhombic anisotropic medium, or
relative to a projection of a symmetry axis in a horizontal plane, if the underground formation includes a tilted transverse isotropic, TTI, medium having a symmetry axis tilted at a tilt angle τ relative to an isotropy plane thereof; and
a central processing unit, CPU, which has one or more processors and is connected to the interface, the CPU being configured
to calculate elastic parameter values and anisotropy parameter values related to the orthorhombic anisotropic medium or to the TTI medium based on the seismic data;
to calculate effective elastic parameter values, wherein the effective elastic parameter values are based on the elastic parameter values, the anisotropy parameter values and the azimuth angle, for the orthorhombic anisotropic medium, and the effective elastic parameter values are based on the elastic parameter values, the anisotropy parameter values, the azimuth angle and the tilt angle for TTI medium,
to perform an isotropic-type processing technique using the effective elastic parameter values, the isotropic-type processing technique yielding a quantitative model of the underground formation, and
to locate hydrocarbon reservoirs using the quantitative model of the underground formation.
12. The seismic data processing apparatus of claim 11 , wherein the isotropic-type processing technique includes at least one of:
an isotropic seismic modeling method,
an isotropic seismic analysis and interpretation method,
an isotropic seismic wavelet estimation method,
an isotropic seismic inversion method, and
an isotropic method for analysis and interpretation of inversion results to produce processed effective elastic parameter data.
13. The seismic data processing apparatus of claim 11 , wherein for the orthorhombic anisotropic medium, an elastic parameter E has a corresponding effective elastic parameter E eff expressed as:
E eff =ϵ r (2) X δ r (3) Y γ r (3) Z ϵ r (1) U δ r (1) V δ r (2) W E
wherein ϵ r (2) δ r (3) γ r (3) ϵ r (1) δ r (1) δ r (2) are Thompsen parameters, with (1), (2,) and (3) indicating coordinate axes, and wherein X, Y, Z, U, V, W are constants.
14. The method of claim 11 , wherein, for the TTI medium, any elastic parameter E has a corresponding effective elastic parameter E eff expressed as:
E eff =ϵ r X δ r Y γ r Z E
wherein ϵ r X , δ r Y , γ r Z being Thomsen parameters and X, Y, Z being constants.
15. The method of claim 11 , wherein, an elastic parameter E has a corresponding effective elastic parameter E eff expressed as:
ln E eff =b 0 +b 2 cos(2(ω−φ))+ b 4 cos(4(ω−φ))
wherein b 0 , b 2 and b 4 are coefficients depending on a combination of the elastic parameter values, the anisotropy parameter values and the tilt angle.
16. The seismic data processing apparatus of claim 11 , wherein the elastic parameters values represent p-wave velocity, s-wave velocity and density.
17. The seismic data processing apparatus of claim 11 , wherein the elastic parameters values represent p-wave impedance, s-wave impedance and density.
18. The seismic data processing apparatus of claim 11 , wherein the CPU includes an interface to a non-transitory computer readable recording medium storing executable codes, which, when executed by the CPU, make the CPU to calculate the elastic parameter values and the anisotropy parameter values, to calculate the effective elastic parameter values and to perform an isotropic-type processing technique using the effective elastic parameter values.