1b. Implicit surface modelling

This tutorial will demonstrate how to create an implicit surface representation of surfaces from a combination of orientation and location observations.

Implicit surface representation involves finding an unknown function where \(f(x,y,z)\) matches observations of the surface geometry. We generate a scalar field where the scalar value is the distance away from a reference horizon. The reference horizon is arbritary and can either be:

• a single geological surface where the scalar field would represent the signed distance away from this surface. (above the surface positive and below negative)

• Where multiple conformable horizons are observed the same scalar field can be used to represent these surfaces and the thickness of the layers is used to determine the relative scalar value for each surface

This tutorial will demonstrate both of these approaches for modelling a number of horizons picked from seismic data sets, by following the next steps: 1. Creation of a geological model, which includes: * Presentation and visualization of the data * Addition of a geological feature, which in this case is the stratigraphy of the model. 2. Visualization of the scalar field.

Imports

Import the required objects from LoopStructural for visualisation and model building

from LoopStructural import GeologicalModel
from LoopStructural.visualisation import Loop3DView
from LoopStructural.datasets import load_claudius  # demo data

import numpy as np

The data for this example can be imported from the example datasets module in loopstructural.

data, bb = load_claudius()

data["val"].unique()

array([250., 330.,   0.,  60.,  nan])

GeologicalModel

To create a GeologicalModel the origin (lower left) and max extent (upper right) of the model area need to be specified. In this example these are provided in the bb array.

model = GeologicalModel(bb[0, :], bb[1, :])

A pandas dataframe with appropriate columns can be used to link the data to the geological model.

• X is the x coordinate

• Y is the y # coordinate

• Z is the z coordinate

• feature_name is a name to link the data to a model object

• val is the value of the scalar field which represents the

distance from a reference horizon. It is comparable to the relative thickness

• nx is the x component of the normal vector to the surface gradient

• ny is the y component of the normal vector to the surface gradient

• nz is the z component of the normal vector to the surface gradeint

• strike is the strike angle

• dip is the dip angle

Having a look at the data for this example by looking at the top of the dataframe and then using a 3D plot

data["feature_name"].unique()

viewer = Loop3DView(background="white")
viewer.add_points(
    data[~np.isnan(data["val"])][["X", "Y", "Z"]].values,
    scalars=data[~np.isnan(data["val"])]["val"].values,
)
viewer.add_arrows(
    data[~np.isnan(data["nx"])][["X", "Y", "Z"]].values,
    direction=data[~np.isnan(data["nx"])][["nx", "ny", "nz"]].values,
)
viewer.display()

The pandas dataframe can be linked to the GeologicalModel using .set_model_data(dataframe

model.set_model_data(data)

The GeologicalModel contains an ordered list of the different geological features within a model and how these features interact. This controls the topology of the different geological features in the model. Different geological features can be added to the geological model such as: * Foliations * Faults * Unconformities * Folded foliations * Structural Frames

In this example we will only add a foliation using the function

model.create_and_add_foliation(name)

where name is the name in the feature_name field, other parameters we specified are the: * interpolatortype - we can either use a PiecewiseLinearInterpolator PLI, a FiniteDifferenceInterpolator FDI or a radial basis interpolator surfe * nelements - int is the how many elements are used to discretize the resulting solution * buffer - float buffer percentage around the model area * solver - the algorithm to solve the least squares problem e.g. lu for lower upper decomposition, cg for conjugate gradient, pyamg for an algorithmic multigrid solver * damp - bool - whether to add a small number to the diagonal of the interpolation matrix for discrete interpolators - this can help speed up the solver and makes the solution more stable for some interpolators

vals = [0, 60, 250, 330, 600]

strat_column = {"strati": {}}
for i in range(len(vals) - 1):
    strat_column["strati"]["unit_{}".format(i)] = {
        "min": vals[i],
        "max": vals[i + 1],
        "id": i,
    }


model.set_stratigraphic_column(strat_column)

strati = model.create_and_add_foliation(
    "strati",
    interpolatortype="FDI",  # try changing this to 'PLI'
    nelements=1e4,  # try changing between 1e3 and 5e4
    buffer=0.3,
    damp=True,
)

Plot the surfaces

viewer = Loop3DView(model)
viewer.plot_model_surfaces(cmap="tab20")
viewer.display()

Plot block diagram

viewer = Loop3DView(model)
viewer.plot_block_model(cmap="tab20")
viewer.display()