3a. Modelling faults using structural frames

from LoopStructural import GeologicalModel
from LoopStructural.visualisation import LavaVuModelViewer
from LoopStructural.datasets import load_intrusion
import numpy as np
import matplotlib.pyplot as plt

data, bb = load_intrusion()

Modelling faults using structural frames

Standard implicit modelling techniques either treat faults as domain boundaries or use a step function in the implicit function to capture the displacement in the faulted surface.

Adding faults into the implicit function using step functions is limited because this does not capture the kinematics of the fault. It effectively defines the fault displacement by adding a value to the scalar field on the hanging wall of the fault. In the example below a 2-D ellipsoidal function is combined with a step function to show how the resulting geometry results in a shrinking shape. This would be representative of modelling an intrusion.

intrusion = lambda x, y: (x * 2) ** 2 + (y**2)
x = np.linspace(-10, 10, 100)
y = np.linspace(-10, 10, 100)
xx, yy = np.meshgrid(x, y)
fault = np.zeros(xx.shape)
fault[yy > 0] = 50
val = intrusion(xx, yy) + fault


plt.contourf(val)

<matplotlib.contour.QuadContourSet object at 0x7faa2bbf1150>

LoopStructural applies structural frames to the fault geometry to capture the geometry and kinematics of the fault. A fault frame consisting of the fault surface, fault slip direction and fault extent are built from observations. The geometry of the deformed surface is then interpolated by first restoring the observations by combining the fault frame and an expected displacement model.

model = GeologicalModel(bb[0, :], bb[1, :])
model.set_model_data(data)
fault = model.create_and_add_fault(
    "fault", 500, nelements=10000, steps=4, interpolatortype="FDI", buffer=0.3
)

viewer = LavaVuModelViewer(model)
viewer.add_isosurface(
    fault,
    isovalue=0,
    #                       slices=[0,1]#nslices=10
)
xyz = model.data[model.data["feature_name"] == "strati"][["X", "Y", "Z"]].to_numpy()
xyz = xyz[fault.evaluate(xyz).astype(bool), :]
viewer.add_vector_field(fault, locations=xyz)
viewer.add_points(
    model.rescale(
        model.data[model.data["feature_name"] == "strati"][["X", "Y", "Z"]],
        inplace=False,
    ),
    name="prefault",
)
viewer.rotation = [-73.24819946289062, -86.82220458984375, -13.912878036499023]
viewer.display()


displacement = 400  # INSERT YOUR DISPLACEMENT NUMBER HERE BEFORE #

model = GeologicalModel(bb[0, :], bb[1, :])
model.set_model_data(data)
fault = model.create_and_add_fault(
    "fault", displacement, nelements=2000, steps=4, interpolatortype="PLI", buffer=2
)
strati = model.create_and_add_foliation("strati", nelements=30000, interpolatortype="PLI", cgw=0.03)
model.update()
viewer = LavaVuModelViewer(model)
viewer.add_isosurface(strati, isovalue=0)
# viewer.add_data(model.features[0][0])
viewer.add_data(strati)
viewer.add_isosurface(
    fault,
    isovalue=0,
    #                       slices=[0,1]#nslices=10
)
viewer.add_points(
    model.rescale(
        model.data[model.data["feature_name"] == "strati"][["X", "Y", "Z"]],
        inplace=False,
    ),
    name="prefault",
)
viewer.rotation = [-73.24819946289062, -86.82220458984375, -13.912878036499023]
viewer.display()

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adding fault trace anisotropy
adding fault dip anisotropy fault_dip_anisotropy
adding fault trace anisotropy
adding fault dip anisotropy fault_dip_anisotropy

  0%|          | 0/4 [00:00<?, ?it/s]
Interpolating fault:   0%|          | 0/4 [00:00<?, ?it/s]
Interpolating fault:  25%|██▌       | 1/4 [00:00<00:00,  3.88it/s]
Interpolating fault:  50%|█████     | 2/4 [00:00<00:00,  2.50it/s]
Interpolating strati:  75%|███████▌  | 3/4 [00:00<00:00,  2.50it/s]/LoopStructural/LoopStructural/interpolators/supports/_3d_base_structured.py:236: RuntimeWarning: invalid value encountered in cast
  cell_indexes[:, 0] = x // self.step_vector[None, 0]
/LoopStructural/LoopStructural/interpolators/supports/_3d_base_structured.py:237: RuntimeWarning: invalid value encountered in cast
  cell_indexes[:, 1] = y // self.step_vector[None, 1]
/LoopStructural/LoopStructural/interpolators/supports/_3d_base_structured.py:238: RuntimeWarning: invalid value encountered in cast
  cell_indexes[:, 2] = z // self.step_vector[None, 2]
/LoopStructural/LoopStructural/interpolators/supports/_3d_base_structured.py:236: RuntimeWarning: invalid value encountered in cast
  cell_indexes[:, 0] = x // self.step_vector[None, 0]
/LoopStructural/LoopStructural/interpolators/supports/_3d_base_structured.py:237: RuntimeWarning: invalid value encountered in cast
  cell_indexes[:, 1] = y // self.step_vector[None, 1]
/LoopStructural/LoopStructural/interpolators/supports/_3d_base_structured.py:238: RuntimeWarning: invalid value encountered in cast
  cell_indexes[:, 2] = z // self.step_vector[None, 2]

Interpolating strati: : 7it [00:41,  6.73s/it]
Interpolating strati: : 7it [00:41,  5.99s/it]