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ElasticTTI

sweep.equations.ElasticTTI 

ElasticTTI(spatial_order=8, device='cpu', backend='torch')

Bases: sweep.equations.base.FirstOrderEquation

First-order 2-D three-component elastic TTI wave equation (RSG).

Velocity-stress formulation for a fully anisotropic 2-D three-component medium (8 stiffness parameters reduced to the 15 independent components C11…C66 via Bond rotation from the Thomsen-style VTI parameters). Derivatives are taken on a rotated staggered grid (RSG: cell-corner ↔ cell-centre with diagonal stencils) so no interpolation is required between staggered locations; CPML is the recursive variant cpmlr (six profiles).

Reference: Bond-rotated VTI stiffness with RSG operators (Saenger / Bohlen rotated staggered grid).

Models (constructor input order)

  • vp0 (m/s): VTI-frame vertical P velocity.
  • vs0 (m/s): VTI-frame vertical S velocity.
  • rho (kg/m^3): Density.
  • epsilon: Thomsen epsilon.
  • delta: Thomsen delta.
  • gamma: Thomsen gamma.
  • theta (rad): Tilt angle.
  • phi (rad): Azimuth angle.

Wavefields

  • vx (aliases: velocity_x): Particle velocity in x; default receiver.
  • vy (aliases: velocity_y): Particle velocity in y.
  • vz (aliases: velocity_z): Particle velocity in z; default receiver.
  • sxx (aliases: stress_xx): Normal stress xx; default source.
  • szz (aliases: stress_zz): Normal stress zz; default source.
  • syz (aliases: stress_yz): Shear stress yz.
  • sxz (aliases: stress_xz): Shear stress xz.
  • sxy (aliases: stress_xy): Shear stress xy.
  • m_vxx: CPML memory for dvx/dx (internal).
  • m_vxz: CPML memory for dvx/dz (internal).
  • m_vyx: CPML memory for dvy/dx (internal).
  • m_vyz: CPML memory for dvy/dz (internal).
  • m_vzx: CPML memory for dvz/dx (internal).
  • m_vzz: CPML memory for dvz/dz (internal).
  • m_txxx: CPML memory for dsxx/dx (internal).
  • m_txzz: CPML memory for dsxz/dz (internal).
  • m_txyx: CPML memory for dsxy/dx (internal).
  • m_tyzz: CPML memory for dsyz/dz (internal).
  • m_txzx: CPML memory for dsxz/dx (internal).
  • m_tzzz: CPML memory for dszz/dz (internal).

Defaults

  • source_type: ['sxx', 'szz']
  • receiver_type: ['vx', 'vz']
  • pml_type: 'cpmlr'

Build the 2-D-3C elastic TTI equation operator (RSG variant).

Parameters:

  • spatial_order –

    FD accuracy order of the rotated staggered-grid (RSG) first derivative — e.g. spatial_order=4 is fourth-order accurate. Internally the half-stencil width is M = spatial_order // 2 (used for loop bounds and PML padding). Must be an even integer (2, 4, 6, 8, 10, …). Higher orders reduce grid dispersion at the cost of more compute per step and a wider PML halo. This equation has no compiled impl='c' path; use impl='eager' (the SG variant :class:ElasticTTISG does have a CUDA kernel). Defaults to 8.

  • device –

    Device for the operator's static RSG kernels. Use 'cuda' / a torch.device for GPU eager runs. Defaults to 'cpu'.

  • backend –

    Array / programming backend, 'torch' or 'jax'. Defaults to 'torch'.