AcousticVRZ / AcousticVRZ3D

sweep.equations.AcousticVRZ

AcousticVRZ(spatial_order=4, device='cpu', backend='torch', dim=2)

Bases: sweep.equations.base.SecondOrderEquation

Second-order 2-D acoustic wave equation in variable-density VRZ form.

Pressure-only scalar acoustics with explicit density coupling through an impedance-like auxiliary parameter z. The Laplacian carries an extra term ∇b · ∇p (with b = vp / z, κ = z · vp), so the propagator is a single second-order PDE in h1 that correctly refracts at sharp impedance contrasts without needing a staggered velocity field. Absorbing boundaries via split-step CPML (cpmlr).

Reference: 10.3997/2214-4609.202010332.

Models (constructor input order)

• vp (m/s): Acoustic velocity model.
• z: Auxiliary parameter used by the VRZ formulation.

Wavefields

• h1 (aliases: pressure, p): Primary VRZ acoustic pressure-like wavefield; default source and receiver.
• h2 (aliases: pressure_prev): Previous-step VRZ acoustic pressure-like wavefield (internal).
• psix: CPML memory variable for the x-derivative term (internal).
• psiz: CPML memory variable for the z-derivative term (internal).
• zetax: CPML auxiliary wavefield for the x-direction update (internal).
• zetaz: CPML auxiliary wavefield for the z-direction update (internal).

Defaults

• source_type: ['h1']
• receiver_type: ['h1']
• pml_type: 'cpmlr'

Build the 2-D VRZ acoustic equation operator.

Parameters:

• spatial_order –

  FD accuracy order of the spatial Laplacian and the auxiliary first-derivative kernels used by the ∇b · ∇p term — 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, …). Performance note (impl='c' on CUDA): the compiled kernels ship template specialisations only for spatial_order ∈ {2, 4, 6, 8}. Above 8 the dispatcher drops to a generic runtime path (order = -1 in src/sweep/csrc/cuda/equations/acoustic_vrz2d/forward.cu) which uses more registers and runs 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' — the compiled CUDA kernels go through the Torch binding. Defaults to 'torch'.

• dim –

  Stored dimensionality. Always 2 for this class; use :class:AcousticVRZ3D for 3-D. Defaults to 2.

BOUNDARY_BUFFER_REACH class-attribute

BOUNDARY_BUFFER_REACH = 1

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal.

int('0b100', base=0) 4

C_NAME class-attribute

C_NAME = 'acoustic_vrz2d'

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'.

sweep.equations.AcousticVRZ3D

AcousticVRZ3D(spatial_order=4, device='cpu', backend='torch', dim=3)

Bases: sweep.equations.base.SecondOrderEquation

Second-order 3-D acoustic wave equation in variable-density VRZ form.

Three-dimensional generalisation of :class:AcousticVRZ: a single pressure-like field h1 is propagated with an extra ∇b · ∇p coupling term (with b = vp / z, κ = z · vp) so that impedance contrasts refract correctly without needing a separate velocity field. Absorbing boundaries on every face via split-step CPML (cpmlr).

Reference: 10.3997/2214-4609.202010332.

Models (constructor input order)

• vp (m/s): 3D acoustic velocity model.
• z: Auxiliary parameter used by the 3D VRZ formulation.

Wavefields

• h1 (aliases: pressure, p): Primary 3D VRZ acoustic pressure-like wavefield; default source and receiver.
• h2 (aliases: pressure_prev): Previous-step 3D VRZ acoustic pressure-like wavefield (internal).
• psix: CPML memory variable for the x-derivative term (internal).
• psiy: CPML memory variable for the y-derivative term (internal).
• psiz: CPML memory variable for the z-derivative term (internal).
• zetax: CPML auxiliary wavefield for the x-direction update (internal).
• zetay: CPML auxiliary wavefield for the y-direction update (internal).
• zetaz: CPML auxiliary wavefield for the z-direction update (internal).

Defaults

• source_type: ['h1']
• receiver_type: ['h1']
• pml_type: 'cpmlr'

Build the 3-D VRZ acoustic equation operator.

Parameters:

• spatial_order –

  FD accuracy order of the spatial Laplacian and the auxiliary first-derivative kernels used by the ∇b · ∇p term — 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, …). Performance note (impl='c' on CUDA): the compiled kernels ship template specialisations only for spatial_order ∈ {2, 4, 6, 8}. Above 8 the dispatcher drops to a generic runtime path (order = -1 in src/sweep/csrc/cuda/equations/acoustic_vrz3d/forward.cu) which uses more registers and runs 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' — the compiled CUDA kernels go through the Torch binding. Defaults to 'torch'.

• dim –

  Stored dimensionality. Always 3 for this class; use :class:AcousticVRZ for 2-D. Defaults to 3.

BOUNDARY_BUFFER_REACH class-attribute

BOUNDARY_BUFFER_REACH = 1

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal.

int('0b100', base=0) 4

C_NAME class-attribute

C_NAME = 'acoustic_vrz3d'

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'.