LINRORT - linearized P-P, P-S1 and P-S2 reflection coefficients for a horizontal interface separating two of any of the following halfspaces: ISOTROPIC, VTI, HTI and ORTHORHOMBIC. linrort [optional parameters] hspace1=ISO medium type of the incidence halfspace: =ISO ... isotropic =VTI ... VTI anisotropy =HTI ... HTI anisotropy =ORT ... ORTHORHOMBIC anisotropy for ISO: vp1=2 P-wave velocity, halfspace1 vs1=1 S-wave velocity, halfspace1 rho1=2.7 density, halfspace1 for VTI: vp1=2 P-wave vertical velocity (V33), halfspace1 vs1=1 S-wave vertical velocity (V44=V55), halfspace1 rho1=2.7 density, halfspace1 eps1=0 Thomsen's generic epsilon, halfspace1 delta1=0 Thomsen's generic delta, halfspace1 gamma1=0 Thomsen's generic gamma, halfspace1 ", for HTI: vp1=2 P-wave vertical velocity (V33), halfspace1 vs1=1 "fast" S-wave vertical velocity (V44), halfspace1 rho1=2.7 density, halfspace1 eps1_v=0 Tsvankin's "vertical" epsilon, halfspace1 delta1_v=0 Tsvankin's "vertical" delta, halfspace1 gamma1_v=0 Tsvankin's "vertical" gamma, halfspace1 ", for ORT: vp1=2 P-wave vertical velocity (V33), halfspace1 vs1=1 x2-polarized S-wave vertical velocity (V44), halfspace1 rho1=2.7 density, halfspace1 eps1_1=0 Tsvankin's epsilon in [x2,x3] plane, halfspace1 delta1_1=0 Tsvankin's delta in [x2,x3] plane, halfspace1 gamma1_1=0 Tsvankin's gamma in [x2,x3] plane, halfspace1 eps1_2=0 Tsvankin's epsilon in [x1,x3] plane, halfspace1 delta1_2=0 Tsvankin's delta in [x1,x3] plane, halfspace1 gamma1_2=0 Tsvankin's gamma in [x1,x3] plane, halfspace1 delta1_3=0 Tsvankin's delta in [x1,x2] plane, halfspace1 hspace2=ISO medium type of the reflecting halfspace (the same convention as above) medium parameters of the 2nd halfspace follow the same convention as above: vp2=2.5 vs2=1.2 rho2=3.0 eps2=0 delta2=0 eps2_v=0 delta2_v=0 gamma2_v=0 eps2_1=0 delta2_1=0 gamma2_1=0 eps2_2=0 delta2_2=0 gamma2_2=0 delta2_3=0 (note you do not need "gamma2" parameter for evaluation of weak-anisotropy reflection coefficients) a_file=-1 the string '-1' ... incidence and azimuth angles are generated automatically using the setup values below a_file=file_name ... incidence and azimuth angles are read from a file "file_name"; the program expects a file of two columns [inc. angle, azimuth] in the case of a_file=-1: fangle=0 first incidence phase angle langle=30 last incidence angle dangle=1 incidence angle increment fazim=0 first azimuth (in deg) lazim=0 last azimuth (in deg) dazim=1 azimuth increment (in deg) kappa=0. azimuthal rotation of the lower halfspace2 (e.t. a symmetry axis plane for HTI, or a symmetry plane for ORTHORHOMBIC) with respect to the x1-axis out_inf=info.out information output file out_P=Rpp.out file with Rpp reflection coefficients out_S=Rps.out file with Rps reflection coefficients out_SVSH=Rsvsh.out file with SV and SH projections of reflection coefficients out_Error=error.out file containing error estimates evaluated during the computation of the reflection coefficients; Output: out_P: inc. phase angle, azimuth, reflection coefficient; for a_file=-1, the inc. angle is the fast dimension out_S: inc. phase angle, azimuth, Rps1, Rps2, cos(PHI), sin(PHI); for a_file=-1, the inc. angle is the fast dimension ", out_SVSH: inc. phase angle, azimuth, Rsv, Rsh, cos(PHI), sin(PHI); for a_file=-1, the inc. angle is the fast dimension out_Error: error estimates of Rpp, Rpsv and Rpsh approximations; global error is analysed as well as partial contributions to the error due to the isotropic velocity contrasts, and due to anisotropic upper and lower halfspaces. The error file is self-explanatory, see also descriptions of subroutines P_err_2nd_order, SV_err_2nd_order and SH_err_2nd_order. Adopted Convention: The right-hand Cartesian coordinate system with the x3-axis pointing upward has been chosen. The upper halfspace (halfspace1) contains the incident P-wave. Incidence angles can vary from <0,PI/2), azimuths are unlimited, +azimuth sense counted from x1->x2 axes (azimuth=0 corresponds to the direction of x1-axis). In the current version, the coordinate system is attached to the halfspace1 (e.t. the symmetry axis plane of HTI halfspace1, or one of symmetry planes of ORTHORHOMBIC halfspace1, is aligned with the x1-axis), however, the halfspace2 can be arbitrarily rotated along the x3-axis with respect to the halfspace1. The positive weak-anisotropy polarization of the reflected P-P wave (e.t. positive P-P reflection coefficient) is close to the direction of isotropic slowness vector of the wave (pointing outward the interface). Similarly, weak-anisotropy S-wave reflection coefficients are described in terms of "SV" and "SH" isotropic polarizations, "SV" and "SH" being unit vectors in the plane perpendicular to the isotropic slowness vector. Then, the positive "SV" polarization vector lies in the incidence plane and points towards the interface, and positive "SH" polarization vector is perpendicular to the incidence plane, aligned with the positive x2-axis, if azimuth=0. Rotation angle "PHI", characterizing a rotation of "the best projection" of the S1-wave polarization vector in the isotropic SV-SH plane in the incidence halfspace1, is counted in the positive sense from "SV" axis (PHI=0) towards the "SH" axis (PHI=PI/2). Of course, S2 is perpendicular to S1, and the projection of S1 and S2 polarizations onto the SV-SH plane coincides with SV and SH directions, respectively, for PHI=0. The units for velocities are km/s, angles I/O are in degrees Additional Notes: The coefficients are computed as functions of phase incidence angle and azimuth (determined by the incidence slowness vector). Vertical symmetry planes of the HTI and ORTHORHOMBIC halfspaces can be arbitrarily rotated along the x3-axis. The linearization is based on the assumption of weak ", contrast in elastic medium parameters across the interface, and the assumption of weak anisotropy in both halfspaces. See the "Adopted Convention" paragraph below for a proper input. Author: Petr Jilek, CSM-CWP, December 1999.