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Elastic3D

sweep.equations.Elastic3D 

Elastic3D(spatial_order=4, device='cpu', backend='torch')

Bases: sweep.equations.base.FirstOrderEquation

First-order 3-D elastic wave equation on a staggered grid (Virieux 1986).

Three-dimensional velocity-stress formulation. The nine physical fields (vx, vy, vz, sxx, syy, szz, sxy, sxz, syz) are evolved together with eighteen CPML memory variables (one per first-derivative direction). Sources are typically an explosion (['sxx', 'syy', 'szz'] — the default) or a directional body force; receivers usually read particle velocities or stresses.

Reference: J. Virieux, 1986, P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method, Geophysics 51(4), 10.1190/1.1442147.

Models (constructor input order)

  • vp (m/s): 3D elastic P-wave velocity model.
  • vs (m/s): 3D elastic S-wave velocity model.
  • rho (kg/m^3): 3D density model.

Wavefields

  • vx (aliases: velocity_x): Particle velocity in the x direction; default receiver.
  • vy (aliases: velocity_y): Particle velocity in the y direction; default receiver.
  • vz (aliases: velocity_z): Particle velocity in the z direction; default receiver.
  • sxx (aliases: stress_xx): Normal stress in the x direction; default source.
  • syy (aliases: stress_yy): Normal stress in the y direction; default source.
  • szz (aliases: stress_zz): Normal stress in the z direction; default source.
  • sxy (aliases: stress_xy, shear_xy): Shear stress component.
  • sxz (aliases: stress_xz, shear_xz): Shear stress component.
  • syz (aliases: stress_yz, shear_yz): Shear stress component.
  • m_vxx: CPML memory variable for dvx/dx (internal).
  • m_vxy: CPML memory variable for dvx/dy (internal).
  • m_vxz: CPML memory variable for dvx/dz (internal).
  • m_vyx: CPML memory variable for dvy/dx (internal).
  • m_vyy: CPML memory variable for dvy/dy (internal).
  • m_vyz: CPML memory variable for dvy/dz (internal).
  • m_vzx: CPML memory variable for dvz/dx (internal).
  • m_vzy: CPML memory variable for dvz/dy (internal).
  • m_vzz: CPML memory variable for dvz/dz (internal).
  • m_sxxx: CPML memory variable for dsxx/dx (internal).
  • m_szzz: CPML memory variable for dszz/dz (internal).
  • m_sxyx: CPML memory variable for dsxy/dx (internal).
  • m_sxyy: CPML memory variable for dsxy/dy (internal).
  • m_sxzx: CPML memory variable for dsxz/dx (internal).
  • m_sxzz: CPML memory variable for dsxz/dz (internal).
  • m_syyy: CPML memory variable for dsyy/dy (internal).
  • m_syzy: CPML memory variable for dsyz/dy (internal).
  • m_syzz: CPML memory variable for dsyz/dz (internal).

Defaults

  • source_type: ['sxx', 'syy', 'szz']
  • receiver_type: ['vx', 'vy', 'vz']
  • pml_type: 'cpmls'

Build the 3-D elastic equation operator.

Parameters:

  • spatial_order –

    FD accuracy order of the staggered first-derivative operator — 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 — most visibly on the slower S-wave — at the cost of more compute per step and a wider PML halo. Performance note (impl='c' on CUDA): the compiled kernels are template-specialised only for spatial_order ∈ {2, 4, 6, 8}. Above 8 the dispatcher falls through to the generic order = -1 runtime path (see src/sweep/csrc/cuda/equations/elastic3d/forward.cu) which is noticeably slower; the PyTorch eager path is unaffected. Defaults to 4.

  • device –

    Device for the operator's static gradient kernels. Use 'cuda' / a torch.device for GPU runs so the propagator can follow without a host↔device copy. Defaults to 'cpu'.

  • backend –

    Array / programming backend, 'torch' or 'jax'. When you later want impl='c', leave this on 'torch'. Defaults to 'torch'.

C_NAME class-attribute 

C_NAME = 'elastic3d'

str(object='') -> str str(bytes_or_buffer[, encoding[, errors]]) -> str

Create a new string object from the given object. If encoding or errors is specified, then the object must expose a data buffer that will be decoded using the given encoding and error handler. Otherwise, returns the result of object.str() (if defined) or repr(object). encoding defaults to sys.getdefaultencoding(). errors defaults to 'strict'.

supports_image_topography class-attribute 

supports_image_topography = True

bool(x) -> bool

Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed.