GeophyAI · Oct 26, 2026 · Oct 23, 2026 · Oct 24, 2026 · Oct 26, 2026 · Oct 26, 2026
diff --git a/CHANGELOG.md b/CHANGELOG.md
@@ -65,6 +65,28 @@ and this project adheres to
   local-window FWI and an x-strip domain decomposition (`SEMModelParallel`).
   User guide: `docs/user-guide/sem.md`; examples: the SEM section (notebooks
   41-44).
+- **`BiotVSSEM2DDeformed`: Biot poroelastic waves on the SEM.**  The FD `Biot`'s
+  velocity-stress-pressure form with the Darcy flux on the Quad9 mesh, its eight
+  coefficients and its `source_type` / `receiver_type` names through `PropSEM`.  The
+  pore pressure is continuous and the flux element-local, so the pore fluid is the
+  acoustic pressure SEM (with the flux continuous, as in SPECFEM2D, a point source
+  excites grid-scale modes along its grid lines); the viscous drag integrated
+  exactly per node, C-PML, an open-pore free surface (`p = 0`) that a `topography`
+  carries too.  Checked against analytic and wavenumber-integration solutions, the
+  FD records and SPECFEM2D's `poroelastic_semi_infinite_homogeneous` example.  2-D,
+  eager, no boundary saving.  The receiver gather now also reads element-local
+  fields (the flux and the stresses).  With SPECFEM2D's other poroelastic
+  features: a point force `fx` / `fz` and flux sources `qx` / `qz`; an anisotropic
+  permeability (`BiotAnisoPermSEM2DDeformed`, the drag a tensor); the viscous
+  attenuation (`equation_options={"viscous_q": (Q0, f0)}`, a standard linear
+  solid); fluid (`rho = 0`) and dry elastic (`M = 0`) regions in one model, coupled
+  as in SPECFEM2D (open pores to a fluid, sealed to a dry solid), sources loading
+  only the fields of their medium.  `sweep.equations.biot_params`: the drag tensor,
+  the fluid and dry-solid coefficients, and the parameter families of Morency, Luo &
+  Tromp (2009) with their kernels by the exact chain rule.  Checked against
+  SPECFEM2D runs of each and its `poroelastic_acoustic` example.
+- **`PropSEM(equation_options=...)`**: an equation's own `build` keywords; a name the
+  equation does not take is refused.
 - **`impl='c'` for `sweep.sem`.**  The SEM CUDA kernels are 43 entries of the
   core (kind 3 of the C API, called through `sweep_sem_call`), their input
   structs generated from `cuda/equations/sem{2,3}d/*_types.h` like the FD ones.

diff --git a/docs/api/index.md b/docs/api/index.md
@@ -228,7 +228,7 @@
     </a>
     <a class="sweep-api__card" href="sem/equations/">
       <div class="sweep-api__card-hd"><code>SEM equations</code><div class="sweep-api__card-tags"><span>2D + 3D</span></div></div>
-      <p>Acoustic, elastic (displacement and velocity-stress, VTI) and coupled fluid-solid, on flat and curved meshes.</p>
+      <p>Acoustic, elastic (displacement and velocity-stress, VTI), coupled fluid-solid and poroelastic (Biot), on flat and curved meshes.</p>
       <div class="sweep-api__card-models">registry: <span class="sweep-api__chip teal">equation_classes</span> <span class="sweep-api__chip teal">describe</span></div>
     </a>
     <a class="sweep-api__card" href="sem/mesh/">

diff --git a/docs/api/sem/equations.md b/docs/api/sem/equations.md
@@ -159,3 +159,25 @@ each; records `chi`, `u_x`, `u_z` and the derived `p`, `vx`, `vz`.
       members: [build]
       inherited_members: true
       show_if_no_docstring: true
+
+## Poroelastic (Biot)
+
+The FD `sweep.equations.Biot` on the spectral-element mesh: solid velocity
+and pore pressure on the continuous nodes, Darcy flux and total stress in the
+elements, with the same eight coefficients `[H, mu, C, M, rho, rho_f, m, b]`
+and the same source and receiver names. See
+[Poroelastic waves (Biot)](../../user-guide/sem.md#poroelastic-waves-biot).
+
+::: sweep.sem.BiotVSSEM2DDeformed
+    options:
+      heading_level: 3
+      members: [build]
+      inherited_members: true
+      show_if_no_docstring: true
+
+::: sweep.sem.BiotAnisoPermSEM2DDeformed
+    options:
+      heading_level: 3
+      members: [build]
+      inherited_members: true
+      show_if_no_docstring: true
diff --git a/docs/user-guide/cli.md b/docs/user-guide/cli.md
@@ -75,22 +75,24 @@ Finite difference (sweep.equations, run with PropTorch):
 
 Spectral element (sweep.sem, run with PropSEM):
 
-  Equation                 Mesh                   Models                                   Torch Binding  Binding Ready
-  -----------------------  ---------------------  ---------------------------------------  -------------  -------------
-  AcousticElasticSEM2D     quad9 2-D, topography  ['vp', 'vs', 'rho']                      yes            yes
-  AcousticPotentialSEM2D   quad9 2-D, topography  ['vp']                                   yes            yes
-  AcousticSEM2D            quad4 2-D              ['vp']                                   no             no
-  AcousticSEM2DDeformed    quad9 2-D, topography  ['vp']                                   no             no
-  AcousticSEM3D            hex8 3-D               ['vp']                                   yes            yes
-  AcousticSEM3DDeformed    hex27 3-D, topography  ['vp']                                   yes            yes
-  ElasticSEM2D             quad4 2-D              ['vp', 'vs', 'rho']                      no             no
-  ElasticSEM2DDeformed     quad9 2-D, topography  ['vp', 'vs', 'rho']                      yes            yes
-  ElasticSEM3D             hex8 3-D               ['vp', 'vs', 'rho']                      yes            yes
-  ElasticSEM3DDeformed     hex27 3-D, topography  ['vp', 'vs', 'rho']                      yes            yes
-  ElasticVSSEM2DDeformed   quad9 2-D, topography  ['vp', 'vs', 'rho']                      no             no
-  ElasticVSSEM3D           hex8 3-D               ['vp', 'vs', 'rho']                      yes            yes
-  ElasticVSSEM3DDeformed   hex27 3-D, topography  ['vp', 'vs', 'rho']                      no             no
-  ElasticVTISEM2DDeformed  quad9 2-D, topography  ['vp', 'vs', 'rho', 'epsilon', 'delta']  no             no
+  Equation                    Mesh                   Models                                                              Torch Binding  Binding Ready
+  --------------------------  ---------------------  ------------------------------------------------------------------  -------------  -------------
+  AcousticElasticSEM2D        quad9 2-D, topography  ['vp', 'vs', 'rho']                                                 yes            yes
+  AcousticPotentialSEM2D      quad9 2-D, topography  ['vp']                                                              yes            yes
+  AcousticSEM2D               quad4 2-D              ['vp']                                                              no             no
+  AcousticSEM2DDeformed       quad9 2-D, topography  ['vp']                                                              no             no
+  AcousticSEM3D               hex8 3-D               ['vp']                                                              yes            yes
+  AcousticSEM3DDeformed       hex27 3-D, topography  ['vp']                                                              yes            yes
+  BiotAnisoPermSEM2DDeformed  quad9 2-D, topography  ['H', 'mu', 'C', 'M', 'rho', 'rho_f', 'm', 'b_xx', 'b_xz', 'b_zz']  no             no
+  BiotVSSEM2DDeformed         quad9 2-D, topography  ['H', 'mu', 'C', 'M', 'rho', 'rho_f', 'm', 'b']                     no             no
+  ElasticSEM2D                quad4 2-D              ['vp', 'vs', 'rho']                                                 no             no
+  ElasticSEM2DDeformed        quad9 2-D, topography  ['vp', 'vs', 'rho']                                                 yes            yes
+  ElasticSEM3D                hex8 3-D               ['vp', 'vs', 'rho']                                                 yes            yes
+  ElasticSEM3DDeformed        hex27 3-D, topography  ['vp', 'vs', 'rho']                                                 yes            yes
+  ElasticVSSEM2DDeformed      quad9 2-D, topography  ['vp', 'vs', 'rho']                                                 no             no
+  ElasticVSSEM3D              hex8 3-D               ['vp', 'vs', 'rho']                                                 yes            yes
+  ElasticVSSEM3DDeformed      hex27 3-D, topography  ['vp', 'vs', 'rho']                                                 no             no
+  ElasticVTISEM2DDeformed     quad9 2-D, topography  ['vp', 'vs', 'rho', 'epsilon', 'delta']                             no             no
 ```
 
 The unified facades `DAS` (formerly `DASModeler`) and `AcousticAniso` are
@@ -172,8 +174,16 @@ sweep show AcousticPotentialSEM2D
 
 On the elastic SEM classes `source_type` also takes `PropTorch`'s names: `vx`,
 `vz` (and `vy`) for a force and, in 2-D, `sxx`, `szz`, `sxz` for a moment
-tensor (see [SEM · Source types](sem.md#source-types)). A class without an
-absorbing layer says so, as `ElasticSEM2D` does:
+tensor (see [SEM · Source types](sem.md#source-types)). The Biot classes
+name the `source_type` values `PropSEM` takes for them (a force, a moment, a
+pore-pressure or flux injection), so `show` prints those instead of their
+source fields:
+
+```text
+  Source types: ['vx', 'vz', 'qx', 'qz', 'v_x', 'v_z', 'q_x', 'q_z', 'fx', 'fz', 'p', 'sxx', 'szz', 'sxz']
+```
+
+A class without an absorbing layer says so, as `ElasticSEM2D` does:
 
 ```text
   C-PML: no -- a reflecting box, abcn=0 only
@@ -193,7 +203,7 @@ sweep show Acoustic3d ; echo "exit=$?"
 ```text
 No such wave equation: Acoustic3d
   Did you mean: Acoustic3D, Acoustic, AcousticVRZ3D?
-  `sweep list equations` names all 43 finite-difference and 14 spectral-element equations.
+  `sweep list equations` names all 43 finite-difference and 16 spectral-element equations.
 exit=1
 ```
 

diff --git a/docs/user-guide/equations.md b/docs/user-guide/equations.md
@@ -86,8 +86,8 @@ The `impl="c"` column says whether `PropSEM(impl='c')` can route the class to
 the CUDA kernels; every class runs on `impl="eager"`. The
 `BoundarySaving()` column is the CUDA-side coverage of
 [boundary saving](sem.md#boundary-saving) -- on `impl="eager"` it works for
-every class; ✅ = both backends, "eager" = eager only, and the C-PML is
-required wherever the ring IS the C-PML band.
+every class but the dissipative Biot one; ✅ = both backends, "eager" = eager
+only, and the C-PML is required wherever the ring IS the C-PML band.
 
 | Equation | Models | Mesh | Dim | Notes | `impl="c"` | `BoundarySaving()` |
 | --- | --- | --- | --- | --- | --- | --- |
@@ -105,6 +105,8 @@ required wherever the ring IS the C-PML band.
 | `ElasticVSSEM3DDeformed` | `['vp', 'vs', 'rho']` | hex27 | 3D | 3-D elastic with **both** topography and absorbing boundaries (the velocity–stress family is where 3-D C-PML exists) | ❌ | eager |
 | `ElasticVTISEM2DDeformed` | `['vp', 'vs', 'rho', 'epsilon', 'delta']` | quad9 | 2D | VTI anisotropic velocity–stress: topography + C-PML | ❌ | eager |
 | `AcousticElasticSEM2D` | `['vp', 'vs', 'rho']` | quad9 | 2D | Coupled fluid–solid (ocean over seabed): split acoustic + elastic C-PML, records `chi, u_x, u_z` (+ derived `p, vx, vz`) | ✅ | ✅ (C-PML; fp32; +anchors) |
+| `BiotVSSEM2DDeformed` | `['H', 'mu', 'C', 'M', 'rho', 'rho_f', 'm', 'b']` | quad9 | 2D | [Biot poroelastic](sem.md#poroelastic-waves-biot) velocity–stress with Darcy flux, the FD `Biot`'s equations and names (pore pressure continuous, flux element-local): topography + C-PML, open-pore surface, fluid (`rho = 0`) and dry elastic (`M = 0`) regions, viscous attenuation (`viscous_q`), records `vx, vz, p, qx, qz, sxx, szz, sxz` | ❌ | ❌ (dissipative) |
+| `BiotAnisoPermSEM2DDeformed` | `['H', 'mu', 'C', 'M', 'rho', 'rho_f', 'm', 'b_xx', 'b_xz', 'b_zz']` | quad9 | 2D | `BiotVSSEM2DDeformed` with an [anisotropic permeability](sem.md#anisotropic-permeability-and-viscous-attenuation) (drag tensor) | ❌ | ❌ (dissipative) |
 
 For the authoritative list of equations exported by your installation,
 with their models and compiled-binding support, use the CLI: