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DAS family

Distributed Acoustic Sensing equations — strain / strain-rate forward operators for fiber-optic cable measurements. Both 2D and 3D variants are provided for the Zhao, Mu, elastic, and modeler formulations.

2-D

sweep.equations.DAS 

DAS(
    *,
    shape,
    method: str = "zhao",
    ndim: int | None = None,
    spatial_order: int = 4,
    source_type: Sequence[str] | None = None,
    receiver_type: Sequence[str] | None = None,
    gauge_cells: int | None = None,
    gauge_length: float | None = None,
    gauge_axis: int = -1,
    backend: str = "torch",
    impl: str | None = None,
    backend_options=None,
    eager_options=None,
    cuda_options=None,
    **propagator_kwargs
)

Bases: torch.nn.modules.module.Module

Unified Torch DAS (distributed acoustic sensing) modeling interface.

Facade nn.Module that wires one of the underlying DAS equations to a :class:PropTorch propagator and post-processes records into a uniform (batch, nt, nrec, nfield) layout. Two methods:

  • method="zhao" — runs the Zhao (2022) stress / normal-strain-rate equation (:class:DASZhao / :class:DASZhao3D); receivers are strain-rates already, no time differentiation needed.
  • method="mu" — runs the Mu (Mu & Hung 2022) velocity-stress equation augmented with integrated strain (:class:DASMu / :class:DASMu3D); strain-rate (exx_t etc.) and helical DAS receivers (das35_t, das54x_t, …) are derived by numerical time differentiation after the solve, which requires dt to be passed through propagator_kwargs.

Reference: Zhao Y. et al. 2022 (DAS strain-rate equation); Mu & Hung 2022 (velocity-stress-strain coupling).

Note

This class used to be called DASModeler; the shorter name mirrors the DAS field convention and matches the :class:AcousticAniso facade for anisotropic acoustic equations. DASModeler is kept as a back-compat alias at the bottom of this module.

Build the DAS facade.

Parameters:

  • shape –

    Spatial model shape (nz, nx) for 2-D or (nz, ny, nx) for 3-D.

  • method (str, default: 'zhao' ) –

    DAS formulation. One of 'zhao' (stress / normal-strain-rate, :class:DASZhao / :class:DASZhao3D) or 'mu' (velocity-stress + integrated strain, :class:DASMu / :class:DASMu3D). Defaults to 'zhao'.

  • ndim (int | None, default: None ) –

    Spatial dimensionality (2 or 3). Inferred from len(shape) when None. Defaults to None.

  • spatial_order (int, default: 4 ) –

    FD accuracy order — 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). Even integer. Defaults to 4.

  • source_type (Sequence[str] | None, default: None ) –

    Names of fields injected by the source. Defaults to the underlying equation's default_source_fields.

  • receiver_type (Sequence[str] | None, default: None ) –

    Names of receiver fields to extract. Mu can emit strain-rate (exx_t, ezz_t, …) and helical DAS-rate channels (das35_t, das54x_t, das54y_t, das54z_t); these require dt. Defaults to the underlying equation's default_receiver_fields.

  • gauge_cells (int | None, default: None ) –

    Gauge length in number of cells along the fibre axis for helical-fibre averaging. Mutually exclusive with gauge_length. Defaults to None (no averaging).

  • gauge_length (float | None, default: None ) –

    Gauge length in metres along the fibre axis; converted to cells using the propagator's dh. Defaults to None.

  • gauge_axis (int, default: -1 ) –

    Axis along which the gauge moving-average is applied. Defaults to -1.

  • backend (str, default: 'torch' ) –

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

  • impl (str | None, default: None ) –

    Propagator implementation. 'eager' for the PyTorch / JAX time loop, 'c' for the compiled CUDA kernel. Defaults to None (propagator decides).

  • backend_options –

    Forwarded to :class:PropTorch as backend-level options.

  • eager_options –

    Forwarded to :class:PropTorch for the eager path (e.g. checkpointing).

  • cuda_options –

    Forwarded to :class:PropTorch for the compiled CUDA path.

  • **propagator_kwargs –

    Extra propagator kwargs (dh, dt, abcn, dev, …).

sweep.equations.DASZhao 

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

Bases: sweep.equations.base.FirstOrderEquation

First-order 2-D stress / normal-strain-rate DAS equation (Zhao 2022).

The dynamic variables are normal strain-rates exx_t, ezz_t, normal stresses sxx, szz, and auxiliary stress-like components txx, tzz. The system is the 2-D, y-invariant reduction of Eq. (9) of the Zhao et al. paper; helical-fibre strain-rate projections (das35_t, das54x_t, das54z_t) are computed inline from exx_t and ezz_t. Staggered-grid CPML (cpmls, 8 profiles).

Reference: Zhao Y. et al. 2022, DAS modelling using a stress and normal-strain-rate elastic formulation.

Models (constructor input order)

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

Wavefields

  • exx_t: Normal strain-rate in the x direction; default receiver.
  • ezz_t: Normal strain-rate in the z direction; default receiver.
  • sxx (aliases: stress_xx): Normal stress in the x direction; default source.
  • szz (aliases: stress_zz): Normal stress in the z direction; default source.
  • txx (aliases: tau_xx): Auxiliary stress-like variable tau_xx (internal).
  • tzz (aliases: tau_zz): Auxiliary stress-like variable tau_zz (internal).
  • m_sxx_xf: CPML memory variable for forward d(sxx)/dx (internal).
  • m_sxx_xb: CPML memory variable for backward d2(sxx)/dx2 (internal).
  • m_szz_zf: CPML memory variable for forward d(szz)/dz (internal).
  • m_szz_zb: CPML memory variable for backward d2(szz)/dz2 (internal).
  • m_txx_zf: CPML memory variable for forward d(txx)/dz (internal).
  • m_txx_zb: CPML memory variable for backward d2(txx)/dz2 (internal).
  • m_tzz_xf: CPML memory variable for forward d(tzz)/dx (internal).
  • m_tzz_xb: CPML memory variable for backward d2(tzz)/dx2 (internal).
  • das35_t: 35.3 degree helical-fiber axial strain-rate.
  • das54x_t: 54.7 degree helical-fiber axial strain-rate for x-oriented core.
  • das54z_t: 54.7 degree helical-fiber axial strain-rate for z-oriented core.

Defaults

  • source_type: ['sxx', 'szz']
  • receiver_type: ['exx_t', 'ezz_t']
  • pml_type: 'cpmls'

Build the 2-D Zhao DAS equation operator.

Parameters:

  • spatial_order –

    FD accuracy order of the staggered first-derivative operator (forward / backward FD pairs along x and z) — 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/das2d/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'. Defaults to 'torch'.

sweep.equations.DASMu 

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

Bases: sweep.equations.base.FirstOrderEquation

First-order 2-D velocity-stress-strain DAS equation (Mu).

Standard 2-D elastic velocity-stress system augmented with three integrated strain fields exx, ezz, exz that track the velocity-gradient sources: exx_t = d(vx)/dx, ezz_t = d(vz)/dz, exz_t = 0.5 · (d(vx)/dz + d(vz)/dx). The :class:DAS facade differentiates the integrated strains in time to produce strain-rate (exx_t, …) and helical DAS-rate (das35_t, das54x_t, das54z_t) receivers — which requires dt to be passed through the propagator. Staggered-grid CPML (cpmls, 8 profiles).

Reference: Mu & Hung 2022, Velocity-stress-strain coupling for DAS forward modelling.

Models (constructor input order)

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

Wavefields

  • vx (aliases: velocity_x): Particle velocity in the x direction.
  • vz (aliases: velocity_z): Particle velocity in the z direction.
  • sxx (aliases: stress_xx, sigma_xx): Normal stress in the x direction; default source.
  • szz (aliases: stress_zz, sigma_zz): Normal stress in the z direction; default source.
  • sxz (aliases: stress_xz, sigma_xz, sigma_zx): Shear stress component.
  • exx: Integrated normal strain in the x direction; default receiver.
  • ezz: Integrated normal strain in the z direction; default receiver.
  • exz: Integrated shear strain component; default receiver.
  • m_vxx: CPML memory variable for dvx/dx (internal).
  • m_vxz: CPML memory variable for dvx/dz (internal).
  • m_vzx: CPML memory variable for dvz/dx (internal).
  • m_vzz: CPML memory variable for dvz/dz (internal).
  • m_txxx: CPML memory variable for dsxx/dx (internal).
  • m_txxz: Reserved elastic auxiliary field (internal).
  • m_tzzx: Reserved elastic auxiliary field (internal).
  • m_tzzz: CPML memory variable for dszz/dz (internal).
  • m_txzx: CPML memory variable for dsxz/dx (internal).
  • m_txzz: CPML memory variable for dsxz/dz (internal).

Defaults

  • source_type: ['sxx', 'szz']
  • receiver_type: ['exx', 'ezz', 'exz']
  • pml_type: 'cpmls'

Build the 2-D Mu DAS 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, …). 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/das_mu2d/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'. Defaults to 'torch'.

sweep.equations.DASElastic 

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

Bases: sweep.equations.base.FirstOrderEquation

First-order 2-D stress / normal-strain-rate DAS equation (Zhao 2022).

The dynamic variables are normal strain-rates exx_t, ezz_t, normal stresses sxx, szz, and auxiliary stress-like components txx, tzz. The system is the 2-D, y-invariant reduction of Eq. (9) of the Zhao et al. paper; helical-fibre strain-rate projections (das35_t, das54x_t, das54z_t) are computed inline from exx_t and ezz_t. Staggered-grid CPML (cpmls, 8 profiles).

Reference: Zhao Y. et al. 2022, DAS modelling using a stress and normal-strain-rate elastic formulation.

Models (constructor input order)

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

Wavefields

  • exx_t: Normal strain-rate in the x direction; default receiver.
  • ezz_t: Normal strain-rate in the z direction; default receiver.
  • sxx (aliases: stress_xx): Normal stress in the x direction; default source.
  • szz (aliases: stress_zz): Normal stress in the z direction; default source.
  • txx (aliases: tau_xx): Auxiliary stress-like variable tau_xx (internal).
  • tzz (aliases: tau_zz): Auxiliary stress-like variable tau_zz (internal).
  • m_sxx_xf: CPML memory variable for forward d(sxx)/dx (internal).
  • m_sxx_xb: CPML memory variable for backward d2(sxx)/dx2 (internal).
  • m_szz_zf: CPML memory variable for forward d(szz)/dz (internal).
  • m_szz_zb: CPML memory variable for backward d2(szz)/dz2 (internal).
  • m_txx_zf: CPML memory variable for forward d(txx)/dz (internal).
  • m_txx_zb: CPML memory variable for backward d2(txx)/dz2 (internal).
  • m_tzz_xf: CPML memory variable for forward d(tzz)/dx (internal).
  • m_tzz_xb: CPML memory variable for backward d2(tzz)/dx2 (internal).
  • das35_t: 35.3 degree helical-fiber axial strain-rate.
  • das54x_t: 54.7 degree helical-fiber axial strain-rate for x-oriented core.
  • das54z_t: 54.7 degree helical-fiber axial strain-rate for z-oriented core.

Defaults

  • source_type: ['sxx', 'szz']
  • receiver_type: ['exx_t', 'ezz_t']
  • pml_type: 'cpmls'

Build the 2-D Zhao DAS equation operator.

Parameters:

  • spatial_order –

    FD accuracy order of the staggered first-derivative operator (forward / backward FD pairs along x and z) — 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/das2d/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'. Defaults to 'torch'.

sweep.equations.DASModeler 

DASModeler(
    *,
    shape,
    method: str = "zhao",
    ndim: int | None = None,
    spatial_order: int = 4,
    source_type: Sequence[str] | None = None,
    receiver_type: Sequence[str] | None = None,
    gauge_cells: int | None = None,
    gauge_length: float | None = None,
    gauge_axis: int = -1,
    backend: str = "torch",
    impl: str | None = None,
    backend_options=None,
    eager_options=None,
    cuda_options=None,
    **propagator_kwargs
)

Bases: torch.nn.modules.module.Module

Unified Torch DAS (distributed acoustic sensing) modeling interface.

Facade nn.Module that wires one of the underlying DAS equations to a :class:PropTorch propagator and post-processes records into a uniform (batch, nt, nrec, nfield) layout. Two methods:

  • method="zhao" — runs the Zhao (2022) stress / normal-strain-rate equation (:class:DASZhao / :class:DASZhao3D); receivers are strain-rates already, no time differentiation needed.
  • method="mu" — runs the Mu (Mu & Hung 2022) velocity-stress equation augmented with integrated strain (:class:DASMu / :class:DASMu3D); strain-rate (exx_t etc.) and helical DAS receivers (das35_t, das54x_t, …) are derived by numerical time differentiation after the solve, which requires dt to be passed through propagator_kwargs.

Reference: Zhao Y. et al. 2022 (DAS strain-rate equation); Mu & Hung 2022 (velocity-stress-strain coupling).

Note

This class used to be called DASModeler; the shorter name mirrors the DAS field convention and matches the :class:AcousticAniso facade for anisotropic acoustic equations. DASModeler is kept as a back-compat alias at the bottom of this module.

Build the DAS facade.

Parameters:

  • shape –

    Spatial model shape (nz, nx) for 2-D or (nz, ny, nx) for 3-D.

  • method (str, default: 'zhao' ) –

    DAS formulation. One of 'zhao' (stress / normal-strain-rate, :class:DASZhao / :class:DASZhao3D) or 'mu' (velocity-stress + integrated strain, :class:DASMu / :class:DASMu3D). Defaults to 'zhao'.

  • ndim (int | None, default: None ) –

    Spatial dimensionality (2 or 3). Inferred from len(shape) when None. Defaults to None.

  • spatial_order (int, default: 4 ) –

    FD accuracy order — 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). Even integer. Defaults to 4.

  • source_type (Sequence[str] | None, default: None ) –

    Names of fields injected by the source. Defaults to the underlying equation's default_source_fields.

  • receiver_type (Sequence[str] | None, default: None ) –

    Names of receiver fields to extract. Mu can emit strain-rate (exx_t, ezz_t, …) and helical DAS-rate channels (das35_t, das54x_t, das54y_t, das54z_t); these require dt. Defaults to the underlying equation's default_receiver_fields.

  • gauge_cells (int | None, default: None ) –

    Gauge length in number of cells along the fibre axis for helical-fibre averaging. Mutually exclusive with gauge_length. Defaults to None (no averaging).

  • gauge_length (float | None, default: None ) –

    Gauge length in metres along the fibre axis; converted to cells using the propagator's dh. Defaults to None.

  • gauge_axis (int, default: -1 ) –

    Axis along which the gauge moving-average is applied. Defaults to -1.

  • backend (str, default: 'torch' ) –

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

  • impl (str | None, default: None ) –

    Propagator implementation. 'eager' for the PyTorch / JAX time loop, 'c' for the compiled CUDA kernel. Defaults to None (propagator decides).

  • backend_options –

    Forwarded to :class:PropTorch as backend-level options.

  • eager_options –

    Forwarded to :class:PropTorch for the eager path (e.g. checkpointing).

  • cuda_options –

    Forwarded to :class:PropTorch for the compiled CUDA path.

  • **propagator_kwargs –

    Extra propagator kwargs (dh, dt, abcn, dev, …).

3-D

sweep.equations.DASZhao3D 

DASZhao3D(spatial_order=4, device='cpu', backend='torch')

Bases: sweep.equations.base.FirstOrderEquation

First-order 3-D stress / normal-strain-rate DAS equation (Zhao 2022).

Three-dimensional generalisation of :class:DASZhao from Eq. (9) of the Zhao et al. paper. The dynamic variables are normal strain-rates exx_t, eyy_t, ezz_t, normal stresses sxx, syy, szz, and auxiliary stress-like components txx, tyy, tzz. Helical-fibre strain-rate projections are computed inline using all three normal strain-rates. Staggered-grid CPML (cpmls, 12 profiles).

Reference: Zhao Y. et al. 2022.

Models (constructor input order)

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

Wavefields

  • exx_t: Normal strain-rate in the x direction; default receiver.
  • eyy_t: Normal strain-rate in the y direction; default receiver.
  • ezz_t: Normal strain-rate 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.
  • txx (aliases: tau_xx): Auxiliary stress-like variable tau_xx (internal).
  • tyy (aliases: tau_yy): Auxiliary stress-like variable tau_yy (internal).
  • tzz (aliases: tau_zz): Auxiliary stress-like variable tau_zz (internal).
  • m_sxx_xf: CPML memory variable for forward d(sxx)/dx (internal).
  • m_sxx_xb: CPML memory variable for backward d2(sxx)/dx2 (internal).
  • m_syy_yf: CPML memory variable for forward d(syy)/dy (internal).
  • m_syy_yb: CPML memory variable for backward d2(syy)/dy2 (internal).
  • m_szz_zf: CPML memory variable for forward d(szz)/dz (internal).
  • m_szz_zb: CPML memory variable for backward d2(szz)/dz2 (internal).
  • m_txx_yf: CPML memory variable for forward d(txx)/dy (internal).
  • m_txx_yb: CPML memory variable for backward d2(txx)/dy2 (internal).
  • m_txx_zf: CPML memory variable for forward d(txx)/dz (internal).
  • m_txx_zb: CPML memory variable for backward d2(txx)/dz2 (internal).
  • m_tyy_xf: CPML memory variable for forward d(tyy)/dx (internal).
  • m_tyy_xb: CPML memory variable for backward d2(tyy)/dx2 (internal).
  • m_tyy_zf: CPML memory variable for forward d(tyy)/dz (internal).
  • m_tyy_zb: CPML memory variable for backward d2(tyy)/dz2 (internal).
  • m_tzz_xf: CPML memory variable for forward d(tzz)/dx (internal).
  • m_tzz_xb: CPML memory variable for backward d2(tzz)/dx2 (internal).
  • m_tzz_yf: CPML memory variable for forward d(tzz)/dy (internal).
  • m_tzz_yb: CPML memory variable for backward d2(tzz)/dy2 (internal).
  • das35_t: 35.3 degree helical-fiber axial strain-rate.
  • das54x_t: 54.7 degree helical-fiber axial strain-rate for x-oriented core.
  • das54y_t: 54.7 degree helical-fiber axial strain-rate for y-oriented core.
  • das54z_t: 54.7 degree helical-fiber axial strain-rate for z-oriented core.

Defaults

  • source_type: ['sxx', 'syy', 'szz']
  • receiver_type: ['exx_t', 'eyy_t', 'ezz_t']
  • pml_type: 'cpmls'

Build the 3-D Zhao DAS 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, …). 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/das3d/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'. Defaults to 'torch'.

sweep.equations.DASMu3D 

DASMu3D(spatial_order=4, device='cpu', backend='torch')

Bases: sweep.equations.base.FirstOrderEquation

First-order 3-D velocity-stress-strain DAS equation (Mu).

Three-dimensional generalisation of :class:DASMu. Standard 3-D elastic velocity-stress system (nine physical fields) augmented with six integrated strain fields tracking the velocity gradients. The :class:DAS facade differentiates the integrated strains in time to produce strain-rate and helical DAS-rate receivers — which requires dt to be passed through the propagator. Staggered-grid CPML (cpmls, 12 profiles).

Reference: Mu & Hung 2022.

Models (constructor input order)

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

Wavefields

  • vx (aliases: velocity_x): Particle velocity in the x direction.
  • vy (aliases: velocity_y): Particle velocity in the y direction.
  • vz (aliases: velocity_z): Particle velocity in the z direction.
  • sxx (aliases: stress_xx, sigma_xx): Normal stress in the x direction; default source.
  • syy (aliases: stress_yy, sigma_yy): Normal stress in the y direction; default source.
  • szz (aliases: stress_zz, sigma_zz): Normal stress in the z direction; default source.
  • sxy (aliases: stress_xy, sigma_xy, sigma_yx): Shear stress xy component.
  • sxz (aliases: stress_xz, sigma_xz, sigma_zx): Shear stress xz component.
  • syz (aliases: stress_yz, sigma_yz, sigma_zy): Shear stress yz component.
  • exx: Integrated normal strain in the x direction; default receiver.
  • eyy: Integrated normal strain in the y direction; default receiver.
  • ezz: Integrated normal strain in the z direction; default receiver.
  • exy: Integrated shear strain xy component; default receiver.
  • exz: Integrated shear strain xz component; default receiver.
  • eyz: Integrated shear strain yz component; default receiver.
  • 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: ['exx', 'eyy', 'ezz', 'exy', 'exz', 'eyz']
  • pml_type: 'cpmls'

Build the 3-D Mu DAS 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, …). 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/das_mu3d/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'. Defaults to 'torch'.

sweep.equations.DASElastic3D 

DASElastic3D(spatial_order=4, device='cpu', backend='torch')

Bases: sweep.equations.base.FirstOrderEquation

First-order 3-D stress / normal-strain-rate DAS equation (Zhao 2022).

Three-dimensional generalisation of :class:DASZhao from Eq. (9) of the Zhao et al. paper. The dynamic variables are normal strain-rates exx_t, eyy_t, ezz_t, normal stresses sxx, syy, szz, and auxiliary stress-like components txx, tyy, tzz. Helical-fibre strain-rate projections are computed inline using all three normal strain-rates. Staggered-grid CPML (cpmls, 12 profiles).

Reference: Zhao Y. et al. 2022.

Models (constructor input order)

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

Wavefields

  • exx_t: Normal strain-rate in the x direction; default receiver.
  • eyy_t: Normal strain-rate in the y direction; default receiver.
  • ezz_t: Normal strain-rate 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.
  • txx (aliases: tau_xx): Auxiliary stress-like variable tau_xx (internal).
  • tyy (aliases: tau_yy): Auxiliary stress-like variable tau_yy (internal).
  • tzz (aliases: tau_zz): Auxiliary stress-like variable tau_zz (internal).
  • m_sxx_xf: CPML memory variable for forward d(sxx)/dx (internal).
  • m_sxx_xb: CPML memory variable for backward d2(sxx)/dx2 (internal).
  • m_syy_yf: CPML memory variable for forward d(syy)/dy (internal).
  • m_syy_yb: CPML memory variable for backward d2(syy)/dy2 (internal).
  • m_szz_zf: CPML memory variable for forward d(szz)/dz (internal).
  • m_szz_zb: CPML memory variable for backward d2(szz)/dz2 (internal).
  • m_txx_yf: CPML memory variable for forward d(txx)/dy (internal).
  • m_txx_yb: CPML memory variable for backward d2(txx)/dy2 (internal).
  • m_txx_zf: CPML memory variable for forward d(txx)/dz (internal).
  • m_txx_zb: CPML memory variable for backward d2(txx)/dz2 (internal).
  • m_tyy_xf: CPML memory variable for forward d(tyy)/dx (internal).
  • m_tyy_xb: CPML memory variable for backward d2(tyy)/dx2 (internal).
  • m_tyy_zf: CPML memory variable for forward d(tyy)/dz (internal).
  • m_tyy_zb: CPML memory variable for backward d2(tyy)/dz2 (internal).
  • m_tzz_xf: CPML memory variable for forward d(tzz)/dx (internal).
  • m_tzz_xb: CPML memory variable for backward d2(tzz)/dx2 (internal).
  • m_tzz_yf: CPML memory variable for forward d(tzz)/dy (internal).
  • m_tzz_yb: CPML memory variable for backward d2(tzz)/dy2 (internal).
  • das35_t: 35.3 degree helical-fiber axial strain-rate.
  • das54x_t: 54.7 degree helical-fiber axial strain-rate for x-oriented core.
  • das54y_t: 54.7 degree helical-fiber axial strain-rate for y-oriented core.
  • das54z_t: 54.7 degree helical-fiber axial strain-rate for z-oriented core.

Defaults

  • source_type: ['sxx', 'syy', 'szz']
  • receiver_type: ['exx_t', 'eyy_t', 'ezz_t']
  • pml_type: 'cpmls'

Build the 3-D Zhao DAS 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, …). 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/das3d/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'. Defaults to 'torch'.