More ways to make models

A few weeks ago I wrote about a new feature in bruges for making wedge models. This new feature makes it really easy to make wedge models, for example:

import bruges as bg
import matplotlib.pyplot as plt

strat = [(0, 1, 0), (2, 3, 2, 3, 2), (4, 5, 4)]
wedge, *_ = bg.models.wedge(strat=strat, conformance=’top’)
plt.imshow(wedge)

And here are some examples of what this will produce, depending on the conformance argument:

What’s new

I thought it might be interesting to be able to add another dimension to the wedge model — in and out of the screen in the models shown above. In that new dimension — as long as there are only two rock types in there — we could vary the “net:gross” of the wedge.

So if we have two rock types in the wedge, let’s say 2 and 3 as in the wedges shown above, we’ll end up with a lot of different wedges. At one end of the new dimension, we’ll have a wedge that is all 2. At the other end, it’ll be all 3. And in between, there’ll be a mixture of 2 and 3, with the layers interfingering in a geometrically symmetric way.

Let’s look at those 3 slices in the central model shown above:

We can also see slices in that other dimension, to visualize the net:gross variance across the model. These slices are near the thin end of the wedge, the middle, and the thick end:

To get 3D wedge models like this, just make a binary (2-component) wedge and add breadth=100 (the number of slices in the new dimension).

These models are admittedly a little mind-bending. Here’s what slices in all 3 orthogonal directions look like, along with (very badly) simulated seismic through this 3D wedge model:

New wedge shapes!

As well as the net-to-gross thing, I added some new wedge shapes, so now you can have some steep-sided alternatives to the linear and sigmoidal ramps I had in there originally. In fact, you can pass in a wedge shape function of your own, so there’s no end to what you could implement.

You can read about these new features in this notebook. Please note that you will need the latest version of bruges to use these new features, so run pip install —upgrade bruges in your environment, then you’ll be all set. Share your models, I’d love to see what you make!

All the wedges

Wedges are a staple of the seismic interpreter’s diet. These simple little models show at a glance how two seismic reflections interact with each other when a rock layer thins down to — and below — the resolution limit of the data. We can also easily study how the interaction changes as we vary the wavelet’s properties, especially its frequency content.

Here’s how to make and plot a basic wedge model with Python in the latest version of bruges, v0.4.2:

import bruges as bg
import matplotlib.pyplot as plt

wedge, *_ = bg.models.wedge()

plt.imshow(wedge)

It really is that simple! This model is rather simplistic though: it contains no stratigraphy, and the numerical content of the 2D array is just a bunch of integers. Let’s instead make a P-wave velocity model, with an internal bed of faster rock inside the wedge:

strat = [2.35, (2.40, 2.50, 2.40), 2.65]
wedge, *_ = bg.models.wedge(strat=strat)

plt.imshow(wedge)
plt.colorbar()

We can also choose to make the internal geometry top- or bottom-conformant, mimicking onlap or an unconformity, respectively.

strat = strat=[0, 7*[1,2], 3]
wedge, *_ = bg.models.wedge(strat=strat,
                            conformance='base'
                           )

plt.imshow(wedge)

The killer feature of this new function might be using a log to make the stratigraphy, rather than just a few beds. This is straightforward to do with welly, because it makes selecting depth intervals and resampling a bit easier:

import welly

gr = welly.Well.from_las('R-39.las').data['GR']
log_above = gr.to_basis(stop=2620, step=1.0)
log_wedge = gr.to_basis(start=2620, stop=2720, step=1.0)
log_below = gr.to_basis(start=2720, step=1.0)

strat = (log_above, log_wedge, log_below)
depth, width = (100, 400, 100), (40, 200, 40)
wedge, top, base, ref = bg.models.wedge(depth=depth,
                                        width=width,
                                        strat=strat,
                                        thickness=(0, 1.5)
                                       )

plt.figure(figsize=(15, 6))
plt.imshow(wedge, aspect='auto')
plt.axvline(ref, color='k', ls='--')
plt.plot(top, 'r', lw=2)
plt.plot(base, 'r', lw=2)

Notice that the function returns to you the top and base of the wedgy part, as well as the position of the ‘reference’, in this case the well.

I’m not sure if anyone wanted this feature… but you can make clinoform models too:

Lastly, the whole point of all this was to make a synthetic — the forward model of the seismic experiment. We can make a convolutional model with just a few more lines of code:

strat = np.array([2.32 * 2.65,  # Layer 1
                  2.35 * 2.60,  # Layer 2
                  2.35 * 2.62,  # Layer 3
                 ])

# Fancy indexing into the rocks with the model.
wedge, top, base, ref = bg.models.wedge(strat=strat)

# Make reflectivity.
rc = (wedge[1:] - wedge[:-1]) / (wedge[1:] + wedge[:-1])

# Get a wavelet.
ricker = bg.filters.ricker(0.064, 0.001, 40)

# Repeated 1D convolution for a synthetic.
syn = np.apply_along_axis(np.convolve, arr=rc, axis=0, v=ricker, mode='same')

That covers most of what the tool can do — for now. I’m working on extending the models to three dimensions, so you will be able to vary layers or rock properties in the 3rd dimension. In the meantime, take these wedges for a spin and see what you can make! Do share your models on Twitter or LinkedIn, and have fun!