Superpowers for striplogs

In between recent courses and hackathons, I’ve been chipping away at some new features in striplog. An open-source Python package, striplog handles irregularly sampled data, like lithologic intervals, chronostratigraphic zones, or anything that isn’t regularly sampled like, say, a well log. Instead of defining what is present at every depth location, you define intervals with a top and a base. The interval can contain whatever you like: names of rocks, images, or special core analyses, or anything at all.

You can read about all of the newer features in the changelog, but let’s look at a couple of the more interesting ones…

Binary morphology filters

Sometimes we’d like to simplify a striplog a bit, for example by ‘weeding out’ the thin beds. The tool has long had a method prune to systematically remove all intervals (e.g. beds) thinner than some cutoff; one can then optionally anneal the gaps, and merge the resulting striplog to combine similar neighbours. The result of this sequence of operations (prune, anneal, merge, or ‘PAM’) is shown below on the left.

striplog_binary_ops.png

If the intervals of a striplog have at least one property of a binary nature — with only two states, like sand and shale, or pay and non-pay — one can also use binary morphological operations. This well-known image processing technique aims to simplify data by eliminating small things. The result of opening vs closing operations is shown above.

Markov chains

I wrote about Markov chains earlier this year; they offer a way to identify bias in the order of units in a stratigraphic column. I’ve now put all the code into striplog — albeit not in a very fancy way. You can import the Markov_chain class from striplog.markov, then use it in exactly the same way as in the notebook I shared in that Markov chain post:

I started with some pseudorandom data (top) representing a known succession of Mudstone (M), Siltstone (S), Fine Sandstone (F) and coarse sandstone (C). Then I generate a Markov chain model of the succession. The chi-squared test indicates that the succession is highly unlikely to be unordered. We can look at the normalized difference matrix, generate a synthetic sequence of lithologies, or plot the difference matrix as a heatmap or a directed graph. The graph illustrates the order we originally imposed: M-S-F-C.

There is one additional feature compared to the original implementation: multi-step Markov chains. Previously, I was only looking at immediately adjacent intervals (beds or whatever). Now you can look at actual vs expected transition frequencies for next-but-one interval, or next-but-two. Don’t ask me how to interpret that information though…

Other new things

  • New ways to anneal. Now the user can choose whether the gaps in the log are filled in by flooding upwards (that is, by extending the interval below the gap upwards), flooding downwards (extending the upper interval), or flooding symmetrically into the middle from both above and below, meeting in the middle. (Note, you can also fill gaps with another component, using the fill() method.)

  • New merging strategies. Now you can merge overlapping intervals by precedence, rather than by blending the contents of the intervals. Precedence is defined however you like; for example, you can choose to keep the thickest interval in all overlaps, or if intervals have a date, you could keep the latest interval.

  • Improved bar charts. The histogram is easier to use, and there is a new bar chart summary of intervals. The bars can be sorted by any property you like.

Try it out and help add new stuff

You can install the latest version of striplog using pip. It’s as easy as:

pip install striplog

Start by checking out the tutorial notebooks in the repo, especially Striplog_basics.ipynb. Let me know how you get on, or jump on the Software Underground Slack to ask for help.

Here are some things I’d like striplog to support in the future:

  • Stratigraphic prediction.

  • Well-to-well correlation.

  • More interactions with well logs.

What ideas do you have? Or maybe you can help define how these things should work? Either way, do get in touch or check out the Striplog repository on GitHub.

x lines of Python: Loading images

Difficulty rating: Beginner

We'd often like to load images into Python. Once loaded, we might want to treat them as images, for example cropping them, saving in another format, or adjusting brightness and contrast. Or we might want to treat a greyscale image as a two-dimensional NumPy array, perhaps so that we can apply a custom filter, or because the image is actually seismic data.

This image-or-array duality is entirely semantic — there is really no difference between images and arrays. An image is a regular array of numbers, or, in the case of multi-channel rasters like full-colour images, a regular array of several numbers: one for each channel. So each pixel location in an RGB image contains 3 numbers:

raster_with_RGB_triples.png

In general, you can go one of two ways with images:

  1. Load the image using a library that 'knows about' (i.e. uses language related to) images. The preeminent tool here is pillow (which is a fork of the grandparent of all Python imaging solutions, PIL).
  2. Load the image using a library that knows about arrays, like matplotlib or scipy. These wrap PIL, making it a bit easier to use, but potentially losing some options on the way.

The Jupyter Notebook accompanying this post shows you how to do both of these things. I recommend learning to use some of PIL's power, but knowing about the easier options too.

Here's the way I generally load an image:

 
from PIL import Image
im = Image.open("my_image.png")

(One strange thing about pillow is that, while you install it with pip install pillow, you still actually import and use PIL in your code.) This im is an instance of PIL's Image class, which is a data structure especially for images. It has some handy methods, like im.crop(), im.rotate(), im.resize(), im.filter(), im.quantize(), and lots more. Doing some of these operations with NumPy arrays is fiddly — hence PIL's popularity.

But if you just want your image as a NumPy array:

 
import numpy as np
arr = np.array(im)

Note that arr is a 3-dimensional array, the dimensions being row, column, channel. You can go off with arr and do whatever you need, then cast back to an Image with Image.fromarray(arr).

All this stuff is demonstrated in the Notebook accompanying this post, or you can use one of these links to run it right now in your browser:

Binder   Run the accompanying notebook in MyBinder


x lines of Python: Physical units

Difficulty rating: Intermediate

Have you ever wished you could carry units around with your quantities — and have the computer figure out the best units and multipliers to use?

pint is a nice, compact library for doing just this, handling all your dimensional analysis needs. It can also detect units from strings. We can define our own units, it knows about multipliers (kilo, mega, etc), and it even works with numpy and pandas.

To use it in its typical mode, we import the library then instantiate a UnitRegistry object. The registry contains lots of physical units:

 
import pint
units = pint.UnitRegistry()
thickness = 68 * units.m

Now thickness is a Quantity object with the value <Quantity(68, 'meter')>, but in Jupyter we see a nice 68 meter (as far as I know, you're stuck with US spelling).

Let's make another quantity and multiply the two:

 
area = 60 * units.km**2
volume = thickness * area

This results in volume having the value <Quantity(4080, 'kilometer ** 2 * meter')>, which pint can convert to any units you like, as long as they are compatible:

 
>>> volume.to('pint')
8622575788969.967 pint

More conveniently still, you can ask for 'compact' units. For example, volume.to_compact('pint') returns 8.622575788969966 terapint. (I guess that's why we don't use pints for field volumes!)

There are lots and lots of other things you can do with pint; some of them — dealing with specialist units, NumPy arrays, and Pandas dataframes — are demonstrated in the Notebook accompanying this post. You can use one of these links to run this right now in your browser if you like:

Binder   Run the accompanying notebook in MyBinder

Open In Colab   Run the notebook in Google Colaboratory (note the install cell at the beginning)

That's it for pint. I hope you enjoy using it in your scientific computing projects. If you have your own tips for handling units in Python, let us know in the comments!


There are some other options for handling units in Python:

  • quantities, which handles uncertainties without also needing the uncertainties package.
  • astropy.units, part of the large astropy project, is popular among physicists.

Training digital scientists

Gulp. My first post in… a while. Life, work, chaos, ideas — it all caught up with me recently. I’ve missed the blog greatly, and felt a regular pang of guilt at letting it gather dust. But I’m back! The 200+ draft posts in my backlog ain’t gonna write themselves. Thank you for returning and reading this one.


Recently I wrote about our continuing adventures in training; since I wrote that post in April, we’ve taught another 166 people. It occurred to me that while teaching scientists to code, we’ve also learned a bit about how to teach, and I wanted to share that too. Perhaps you will be inspired to share your skills, and together we can have exponential impact.

Wanting to get better

As usual, it all started with not knowing how to do something, doing it anyway, then wanting to get better.

We started teaching in 2014 as rank amateurs, both as coders and as teachers. But we soon discovered the ‘teaching tech’ subculture among computational scientists. In particular, we found Greg Wilson and the Software Carpentry movement he started. By that point, it had been around for many, many years. Incredibly, Software Carpentry has helped more than 34,000 researchers ‘go digital’. The impact on science can’t be measured.

Eager as ever, we signed up for the instructor’s course. It was fantastic. The course, taught by Greg Wilson himself, perfectly modeled the thing it was offering to teach you: “Do what I say, and what I do”. This is, of course, critically important in all things, especially teaching. We accepted the content so completely that I’m not even sure we graduated. We just absorbed it and ran with it, no doubt corrupting it on the way. But it works for us.

What to read

TTT_rules.png

I should preface what follows by telling you that I haven’t taken any other courses on the subject of teaching. For all I know, there’s nothing new here. That said, I have never experienced a course like Greg Wilson’s, so either the methods he promotes are not widely known, or they’re widely ignored, or I’ve been really unlucky.

The easiest way to get Greg Wilson’s wisdom is probably to read his book-slash-website, Teaching Tech Together. (It’s free, but you can get a hard copy if you prefer.) It’s really good. You can get the vibe — and much of the most important advice — from the ten Teaching Tech Together rules laid out on the main page of that site (box, right).

As you can probably tell, most of it is about parking your ego, plus most of your knowledge (for now), and orientating everything — every single thing — around the learner.

If you want to go deeper, I also recommend reading the excellent, if rather academic, How Learning Works, by Susan Ambrose (Northeastern University) and others. It’s strongly research-driven, and contains a lot of great advice. In particular, it does a great job of listing the factors that motivate students to learn (and those that demotivate them), and spelling out the various ways in which students acquire mastery of a subject.

How to practice

It goes without saying that you’ll need to teach. A lot. Not surprisingly, we find we get much better if we teach several courses in a short period. If you’re diligent, take a lot of notes and study them before the next class, maybe it’s okay if a few weeks or months go by. But I highly doubt you can teach once or twice a year and get good at it.

Something it took us a while to get comfortable with is what Evan calls ‘mistaking’. If you’re a master coder, you might not make too many mistakes (but your expertise means you will have other problems). If you’re not a master (join the club), you will make a lot of mistakes. Embracing everything as a learning opportunity is less awkward for you, and for the students — dealing with mistakes is a core competency for all programmers.

Reflective practice means asking for, and then acting on, student feedback — every day. We ask students to write it on sticky notes. Reading these back to the class the next morning is a good way to really read it. One of the many benefits of ‘never teach alone’ is always having someone to give you feedback from another teacher’s perspective too. Multi-day courses let us improve in real time, which is good for us and for the students.

Some other advice:

  • Keep the student:instructor ratio to no more than ten; seven or eight is better.

  • Take a packet of orange and a packet of green Post-It notes. Use them for names, as ‘help me’ flags, and for feedback.

  • When teaching programming, the more live coding — from scratch — you can do, the better. While you code, narrate your thought process. This way, students are able to make conections between ideas, code, and mistakes.

  • To explain concepts, draw on a whiteboard. Avoid slides whenever possible.

  • Our co-teacher John Leeman likes to say, “I just showed you something new, what questions do you have?” This beats “Any questions?” for opening the door to engagement.

  • “No-one left behind” is a nice idea, but it’s not always practical. If students can’t devote 100% to the class and then struggle because of it, you owe it to the the others to politely suggest they pick the class up again next time.

  • Devote some time to the practical application of the skills you’re teaching, preferably in areas of the participants’ own choosing. In our 5-day class, we devote a whole day to getting students started on their own projects.

  • Don’t underestimate the importance of a nice space, natural light, good food, and frequent breaks.

  • Recognize everyone’s achievement with a small gift at the end of the class.

  • Learning is hard work. Finish early every day.

Give it a try

If you’re interested in help people learn to code, the most obvious way to start is to offer to assist or co-teach in someone else’s class. Or simply start small, offering a half-day session to a few co-workers. Even if you only recently got started yourself, they’ll appreciate the helping hand. If you’re feeling really confident, or have been coding for a year or two at least, try something bolder — maybe offer a one-day class at a meeting or conference. You will find plenty of interest.

There are few better ways to improve your own skills than to teach. And the feeling of helping people develop a valuable skill is addictive. If you give it a try, let us know how you get on!

Feel superhuman: learning and teaching geocomputing

Diego teaching in Houston in 2018.

Diego teaching in Houston in 2018.

It’s five years since we started teaching Python to geoscientists. To be honest, it might have been premature. At the time, Evan and I were maybe only two years into serious, daily use of Python. But the first class, at the Atlantic Geological Society’s annual meeting in February 2014, was free so the pressure was not too high. And it turns out that only being a step or two ahead of your students can be an advantage. Your ‘expert blind spot’ is partially sighted not completely blind, because you can clearly remember being a noob.

Being a noob is a weird, sometimes very uncomfortable, even scary, feeling for some people. Many of us are used to feeling like experts, at least some of the time. Happy, feeling like a noob is a core competency in programming. Learning new things is a more or less hourly experience for coders. Even a mature language like Python evolves fast enough that it’s hard to keep up. Instead of feeling threatened or exhausted by this, I think the best strategy is to enjoy it. You’ll never be done, there are (way) more questions than answers, and you can learn forever!

One of the bootcamp groups at the Copenhagen hackathon in 2018

One of the bootcamp groups at the Copenhagen hackathon in 2018

This week we’re teaching our 40th course. Last year alone we gave digital superpowers to 325 people, mostly geoscientists, Not all of them learned to code, as such — some people already could, and some found out theydidn’t like it… coding really isn’t for everyone. But I think all of them learned something new about technology, and how it can serve them and their science. I hope all of them look at spreadsheets, and Petrel, and websites differently now. I think most of them want, at some point, to learn more. And everyone is excited about machine learning.

The expanding community of quantitative earth scientists

This year we’ve already spent 50 days teaching, and taught 174 people. Imagine that! I get emotional when I think about what these hundreds of new digital geoscientists and engineers will go and do with their new skills. I get really excited when I see what they are already doing — when they come to hackathons, send us screenshots, or write papers with beautiful figures. If the joy of sharing code and collaborating with peers has also rubbed off on them, there’s no telling where it could lead.

Matt teaching in Aberdeen in October 2018

Matt teaching in Aberdeen in October 2018

The last nine months or so have been an adventure. Teaching is not supposed to be what Agile is about. We’re a consulting company, a technology company. But for now we’re mostly a training company — it’s where we’re needed. And it makes sense... Programming is fundamentally about knowledge sharing. Teaching is about helping, collaborating. It’s perfect for us.

Besides, it’s a privilege and a thrill to meet all these fantastically smart, motivated people and to hear about their projects and their plans. Sometimes I wish it didn’t mean leaving my family in Nova Scotia and flying to Houston and London and Kuala Lumpur and Kalamazoo… but mostly I wish we could do more of it. Especially when we get comments like these:

Given how ‘dry’ programming can be, it was DYNAMIC.”
”Excellent teachers with geoscience background.”
”Great instructors, so so approachable, even for newbies like me.”
”Great course [...] Made me realize what could be done in a short time.”
”My only regret was not taking a class like this sooner.”
”Very positive, feel superhuman.

How many times have you felt superhuman at work recently?

The courses we teach are evolving and expanding in scope. But they all come back to the same thing: growing digital skills in our profession. This is critical because using computers for earth science is really hard. Why? The earth is weird. We’ve spent hundreds of years honing conceptual models, understanding deep time, and figuring out complex spatial relationships.

If data science eats the subsurface without us, we’re all going to get indigestion. Society needs to better understand the earth — for all sorts of reasons — and it’s our duty to build and adopt the most powerful analytical tools available so that we can help.


Learning resources

If you can’t wait to get started, here are some suggestions:

Classroom courses are a big investment in dollars and time, but they can get you a long way really quickly. Our courses are built especially for subsurface scientists and engineers. As far as I know, they are the only ones of their kind. If you think you’d like to take one, talk to us, or look out for a public course. You can find out more or sign up for email alerts here >> https://agilescientific.com/training/

Last thing: I suggest avoiding DataCamp, because of sexual misconduct by an executive, compounded by total inaction, dishonest obfuscation, and basically failing spectacularly. Even their own trainers have boycotted them. Steer clear.

The order of stratigraphic sequences

Much of stratigraphic interpretation depends on a simple idea:

Depositional environments that are adjacent in a geographic sense (like the shoreface and the beach, or a tidal channel and tidal mudflats) are adjacent in a stratigraphic sense, unless separated by an unconformity.

Usually, geologists are faced with only the stratigraphic picture, and are challenged with reconstructing the geographic picture.

One interpretation strategy might be to look at which rocks tend to occur together in the stratigraphy. The idea is that rock types tend to be associated with geographic environments — maybe fine sand on the shoreface, coarse sand on the beach; massive silt in the tidal channel, rhythmically laminated mud in the mud-flats. Since if two rocks tend to occur together, their environments were probably adjacent, we can start to understand associations between the rock types, and thus piece together the geographic picture.

So which rock types tend to occur together, and which juxtapositions are spurious — perhaps the result of allocyclic mechanisms like changes in relative sea-level, or sediment supply? To get at this question, some stratigraphers turn to Markov chain analysis.

What is a Markov chain?

Markov chains are sequences of events, or states, resulting from a Markov process. Here’s how Wikipedia describes a Markov process:

A stochastic process that satisfies the Markov property (sometimes characterized as “memorylessness”). Roughly speaking, a process satisfies the Markov property if one can make predictions for the future of the process based solely on its present state just as well as one could knowing the process’s full history, hence independently from such history; i.e., conditional on the present state of the system, its future and past states are independent.

So if we believe that a stratigraphic sequence (I’m using ‘sequence’ here in the most general sense) can be modeled by a process like this — i.e. that its next state depends substantially on its present state — then perhaps we can model it as a Markov chain.

For example, we might have a hunch that we can model a shallow marine system as a sequence like:

offshore mudstone > lower shoreface siltstone > upper shoreface sandstone > foreshore sandstone

Then we might expect to see these transitions occur more often than other, non-successive transitions. In other words — if we compare the transition frequencies we observe to the transition frquencies we would expect from a random sequence of the same beds in the same proportions, then autocyclic or genetic transitions might happen unusually frequently.

The Powers & Easterling method

Several workers have gone down this path. The standard approach seems to be that of Powers & Easterling (1982). Here are the steps they describe:

  • Count the upwards transitions for each rock type. This results in a matrix of counts. Here’s the transition frequency matrix for the example used in the Powers & Easterling paper, in turn take from Gingerich (1969):

 
data = [[ 0, 37,  3,  2],
        [21,  0, 41, 14],
        [20, 25,  0,  0],
        [ 1, 14,  1,  0]]
  • Compute the expected counts by an iterative process, which usually converges in a few steps. The expected counts represent what Goodman (1968) called a ‘quasi-independence’ model — a random sequence:

 
array([[ 0. , 31.3,  8.2,  2.6],
       [31.3,  0. , 34.1, 10.7],
       [ 8.2, 34. ,  0. ,  2.8],
       [ 2.6, 10.7,  2.8,  0. ]])
  • Now we can compare our observed frequencies with the expected ones in two ways. First, we can inspect the \(\chi^2\) statistic, and compare it with the \(\chi^2\) distribution, given the degrees of freedom (5 in this case). In this example, it’s 35.7, which is beyond the 99.999th percentile of the chi-squared distribution. This rejects the hypothesis of quasi-independence. In other words: the succession appears to be organized. Phew!

  • Secondly, we can compute a matrix of so-called normalized differences. This lets us compare the observed and expected data. By calculating Z-scores, which are approximately normally distributed; since 95% of the distribution falls between −2 and +2, any value greater in magnitude than 2 is ‘fairly unusual’, in the words of Powers & Easterling. In the example, we can see that the large number of transitions from C (third row) to A (first column) is anomalous:

 
 
array([[ 0. ,  1. , -1.8, -0.3],
       [-1.8,  0. ,  1.2,  1. ],
       [ 4.1, -1.6,  0. , -1.7],
       [-1. ,  1. , -1.1,  0. ]])
powers_easterling_normdiff.png
  • The normalized difference matrix can also be interpreted as a directed graph, indicating the ‘strengths’ of the connections (edges) between rock types (nodes):

powers_easterling_graph.png

It would be all too easy to over-interpret this graph — B and D seem to go together, as do A and C, and C tends to pass into A, which tends to pass into a B/D system before passing back into C — and one could get carried away. But as a complement to sedimentological interpretation, knowledge of processes and the succession in hand, perhaps inspecting Markov chains can help understand the stratigraphic story.

One last thing… there is another use for Markov chains. We can also use the model to produce stochastic realizations of stratigraphy. These will share the same statistics as the original data, but are otherwise quite random. Here are 20 random beds generated from our model:

 
'ABABCBABABCABDABABCA'

The code to build your own Markov chains is all in this notebook. It’s very much a work in progress. Eventually I hope to merge it into the striplog library, but for now it’s a ‘minimum viable product’. Stay tuned for more on striplog.

Open In Colab   ⇐   Launch the notebook right here in your browser!


References

Gingerich, PD (1969). Markov analysis of cyclic alluvial sediments. Journal of Sedimentary Petrology, 39, p. 330-332. https://doi.org/10.1306/74D71C4E-2B21-11D7-8648000102C1865D

Goodman, LA (1968), The analysis of cross-classified data: independence, quasi-independence, and interactions in contingency tables with or without missing entries. Journal of American Statistical Association 63, p. 1091-1131. https://doi.org/10.2307/2285873

Powers, DW and RG Easterling (1982). Improved methodology for using embedded Markov chains to describe cyclical sediments. Journal of Sedimentary Petrology 52 (3), p. 0913-0923. https://doi.org/10.1306/212F808F-2B24-11D7-8648000102C1865D

x lines of Python: Ternary diagrams

Difficulty rating: beginner-friendly

(I just realized that calling the more approachable tutorials ‘easy’ is perhaps not the most sympathetic way to put it. But I think this one is fairly approachable.)

If you’re new to Python, plotting is a great way to get used to data structures, and even syntax, because you get immediate visual feedback. Plots are just fun.

Data loading

The first thing is to load the data, which is contained in a Google Sheets spreadsheet. If you make a sheet public, it’s easy to make a URL that provides a CSV. Happily, the Python data management library pandas can read URLs directly, so loading the data is quite easy — the only slightly ugly thing is the long URL:

    import pandas as pd
    uid = "1r7AYOFEw9RgU0QaagxkHuECvfoegQWp9spQtMV8XJGI"
    url = f"https://docs.google.com/spreadsheets/d//export?format=csv"
    df = pd.read_csv(url) 

This dataset contains results from point-counting 51 shallow marine sandstones from the Eocene Sobrarbe Formation. We’re going to plot normalized volume percentages of quartz grains, detrital carbonate grains, and undifferentiated matrix. Three parameters? Two degrees of freedom? Let’s make a ternary plot!

Data exploration

Once you have the data in pandas, and before getting to the triangular stuff, we should have a look at it. Seaborn, a popular statistical plotting library, has a nifty ‘pairplot’ which plots the numerical parameters against each other to help reveal patterns in the data. On the diagonal, it shows kernel density estimations to reveal the distribution of each property:

    import seaborn as sns
    vars = ['Matrix', 'Quartz', 'Carbonate', 'Bioclasts', 'Authigenic']
    sns.pairplot(df, vars=vars, hue='Facies Association')
ternary_data_pairplot.png

Normalization is fairly straightforward. For each column, e.g. df['Carbonate'], we make a new column, e.g. df['C'], which is normalized to the sum of the three components, given by df[cols].sum(axis=1):

cols = ['Carbonate', 'Quartz', 'Matrix']
for col in cols:
    df[col[0]] = df[col] * 100 / df[cols].sum(axis=1)

The ternary plot

For the ternary plot itself I’m using the python-ternary library, which is pretty hands-on in that most plots take quite a bit of code. But the upside of this is that you can do almost anything you want. (Theres one other option for Python, the ever-reliable plotly, and there’s a solid-looking package for R too in ggtern.)

We just need a few lines of plotting code (left) to pull a ternary diagram (right) together.

    fig, tax = ternary.figure(scale=100)
    fig.set_size_inches(5, 4.5)

    tax.scatter(df[['M', 'Q', 'C']].values)
    tax.gridlines(multiple=20)
    tax.get_axes().axis('off')
ternary_tiny.png

But here you see what I mean about this being quite a low-level library: each element of the plot has to be added explicitly. So if we want axis labels, titles, and other annotations, we need more code… all of which is laid out in the accompanying notebook. You can download this from GitHub, or run in right now, right in your browser, with these links:

Binder   Run the accompanying notebook in MyBinder

Open In Colab   Run the notebook in Google Colaboratory (note you need to install python-ternary)

Give it a go, and have fun making your own ternary plots in Python! Share them on LinkedIn or Twitter.

Quartz, carbonate and matrix quantities (normalized to 100%) for 51 calcareous sandstones from the Eocene Sobrarbe Formation. The ternary plot was made with python-ternary library for Python and matplotlib.

Quartz, carbonate and matrix quantities (normalized to 100%) for 51 calcareous sandstones from the Eocene Sobrarbe Formation. The ternary plot was made with python-ternary library for Python and matplotlib.

x lines of Python: Gridding map data

Difficulty rating: moderate.

Welcome to the latest in the X lines of Python series. You probably thought it had died, gawn to ‘eaven, was an x-series. Well, it’s back!

Today we’re going to fit a regularly sampled surface — a grid — to an irregular set of points in (x, y) space. The points represent porosity, measured in volume percent.

Here’s what we’re going to do; it all comes to only 9 lines of code!

  1. Load the data from a text file (needs 1 line of code).

  2. Compute the extents and then the coordinates of the new grid (2 lines).

  3. Make a radial basis function interpolator using SciPy (1 line).

  4. Perform the interpolation (1 line).

  5. Make a plot (4 lines).

As usual, there’s a Jupyter Notebook accompanying this blog post, and you can run it right now without installing anything.

 

Binder Run the accompanying notebook in MyBinder

Open In Colab Run the notebook in Google Colaboratory

Just the juicy bits

The notebook goes over the workflow in a bit more detail — with more plots and a few different ways of doing the interpolation. For example, we try out triangulation and demonstrate using scikit-learn’s Gaussian process model to show how we might use kriging (turns out kriging was machine learning all along!).

If you don’t have time for all that, and just want the meat of the notebook, here it is:

 
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.interpolate import Rbf

# Load the data.
df = pd.read_csv('../data/ZoneA.dat',
                 sep=' ',
                 header=9,
                 usecols=[0, 1, 2, 3],
                 names=['x', 'y', 'thick', 'por']
                )

# Build a regular grid with 500-metre cells.
extent = x_min, x_max, y_min, y_max = [df.x.min()-1000, df.x.max()+1000,
                                       df.y.min()-1000, df.y.max()+1000]
grid_x, grid_y = np.mgrid[x_min:x_max:500, y_min:y_max:500]

# Make the interpolator and do the interpolation.
rbfi = Rbf(df.x, df.y, df.por)
di = rbfi(grid_x, grid_y)

# Make the plot.
plt.figure(figsize=(15, 15))
plt.imshow(di.T, origin="lower", extent=extent)
cb = plt.scatter(df.x, df.y, s=60, c=df.por, edgecolor='#ffffff66')
plt.colorbar(cb, shrink=0.67)
plt.show()

This results in the following plot, in which the points are the original data, plotted with the same colourmap as the surface itself (so they should be the same colour, more or less, as their background).

rbf_interpolation.png

What is the fastest axis of an array?

One of the participants in our geocomputing course asked us a tricky question earlier this year. She was a C++ and Java programmer — we often teach experienced programmers who want to learn about Python and/or machine learning — and she worked mostly with seismic data. She had a question related to the performance of n-dimensional arrays: what is the fastest axis of a NumPy array?

I’ve written before about how computational geoscience is not ‘software engineering’ and not ‘computer science’, but something else. And there’s a well established principle in programming, first expressed by Michael Jackson:

We follow two rules in the matter of optimization:
Rule 1: Don’t do it.
Rule 2 (for experts only). Don’t do it yet — that is, not until you have a perfectly clear and unoptimized solution.

Most of the time the computer is much faster than we need it to be, so we don’t spend too much time thinking about making our programs faster. We’re mostly concerned with making them work, then making them correct. But sometimes we have to think about speed. And sometimes that means writing smarter code. (Other times it means buying another GPU.) If your computer spends its days looping over seismic volumes extracting slices for processing, you should probably know whether you want to put time in the first dimension or the last dimension of your array.

The 2D case

Let’s think about a two-dimensional case first — imagine a small 2D array, also known as a matrix in some contexts. I’ve coloured in the elements of the matrix to make the next bit easier to understand.

matrix-memory-a.png

When we store a matrix in a computer (or an image, or any array), we have a decision to make. In simple terms, the computer’s memory is like a long row of boxes, each with a unique address — shown here as a 3-digit hexadecimal number:

We can only store one number in each box, so we’re going to have to flatten the 2D array. The question is, do we put the rows in together, effectively splitting up the columns, or do we put the columns in together? These two options are commonly known as ‘row major’, or C-style, and ‘column major’, or Fortran-style:

matrix-memory-b.png

Let’s see what this looks like in terms of the indices of the elements. We can plot the index number on each axis vs. the position of the element in memory. Notice that the C-ordered elements are contiguous in axis 0:

If you spend a lot of time loading seismic data, you probably recognize this issue — it’s analgous to how traces are stored in a SEG-Y file. Of couse, with seismic data, two dimensions aren’t always enough…

Higher dimensions

The problem multiplies at higher dimensions. If we have a cube of data, then C-style ordering results in the first dimension having large contiguous chunks, and the last dimension being broken up. The middle dimension is somewhere in between. As before, we can illustrating this by plotting the indices of the data. This time I’m highlighting the positions of the elements with index 2 (i.e. the third element) in each dimension:

So if this was a seismic volume, we might organize inlines in the first dimension, and travel-time in the last dimension. That way, we can access inlines very quickly, but timeslices will take longer.

In Fortran order, which we can optionally specify in NumPy, the situation is reversed. Now the fast axis is the last axis:

3d-array-forder.png

Lots of programming languages and libraries use row-major memory layout, including C, C++, Torch and NumPy. Most others use column-major ordering, including MATLAB, R, Julia, and Fortran. (Some other languages, such as Java and .NET, use a variant of row-major order called Iliffe vectors). NumPy calls row-major order ‘C’ (for C, not for column), and column-major ‘F’ for Fortran (thankfully they didn’t use R, for R not for row).

I expect it’s related to their heritage, but the Fortran-style languages also start counting at 1, whereas the C-style languages, including Python, start at 0.

What difference does it make?

The main practical difference is in the time it takes to access elements in different orientations. It’s faster for the computer to take a contiguous chunk of neighbours from the memory ‘boxes’ than it is to have to ‘stride’ across the memory taking elements from here and there.

How much faster? To find out, I made datasets full of random numbers, then selected slices and added 1 to them. This was the simplest operation I could think of that actually forces NumPy to do something with the data. Here are some statistics — the absolute times are pretty irrelevant as the data volumes I used are all different sizes, and the speeds will vary on different machines and architectures:

  • 2D data: 3.6× faster. Axis 0: 24.4 µs, axis 1: 88.1 µs (times relative to first axis: 1, 3.6).

  • 3D data: 43× faster. 229 µs, 714 µs, 9750 µs (relatively 1, 3.1, 43).

  • 4D data: 24× faster. 1.27 ms, 1.36 ms, 4.77 ms, 30 ms (relatively 1, 1.07, 3.75, 23.6).

  • 5D data: 20× faster. 3.02 ms, 3.07 ms, 5.42 ms, 11.1 ms, 61.3 ms (relatively 1, 1.02, 1.79, 3.67, 20.3).

  • 6D data: 5.5× faster. 24.4 ms, 23.9 ms, 24.1 ms, 37.8 ms, 55.3 ms, 136 ms (relatively 1, 0.98, 0.99, 1.55, 2.27, 5.57).

These figures are more or less simply reversed for Fortran-ordered arrays (see the notebook for datails).

Clearly, the biggest difference is with 3D data, so if you are manipulating seismic data a lot and need to access the data in that last dimension, usually travel-time, you might want to think about ways to reduce this overhead.

What difference does it really make?

The good news is that, for most of us most of the time, we don’t have to worry about any of this. For one thing, NumPy’s internal workings (in particular, its universal functions, or ufuncs) know which directions are fastest and take advantage of this when possible. For another thing, we generally try to avoid looping over arrays at all, leaving the iterative components of our algorithms to the ufuncs — so the slicing speed isn’t a factor. Even when it is a factor, or if we can’t avoid looping, it’s often not the bottleneck in the code. Usually the guts of our algorithm are what are slowing the computer down, not the access to memory. The net result of all this is that we don’t often have to think about the memory layout of our arrays.

So when does it matter? The following situations merit a bit of thought:

  • When you’re doing a very large number of accesses to memory or disk. Saving a few microseconds might add up to a lot if you’re doing it a billion times.

  • When the objects you’re accessing are very large. Reading and writing elements of a 200GB array in memory brings new challenges compared to handling a few gigabytes.

  • Reading and writing data files — really just another kind of memory — brings all the same issues. Reading a chunk of contiguous data is much faster than reading bytes from here and there. Landmark’s BRI seismic data format, Schlumberger’s ZGY files, and HDF5 files, all implement strategies to help make reading arbitrary data faster.

  • Converting code from other languages, especially MATLAB, although do realize that other languages may have their own indexing rules, as well as differing in how they store n-dimensional arrays.

If you determine that you do need to think about this stuff, then you’re going to need to read this essay about NumPy’s internal representations, and I recommend checking out this blog post by Eli Bendersky too.

There you have it. Very occasionally we scientists also need to think a bit about how computers work… but most of the time someone has done that thinking for us.

Some of the figures and all of the timings for this post came from this notebook — please have a look. If you have anything to add, or (better yet) correct, please get in touch. I’d love to hear from you.

Reproduce this!

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There’s a saying in programming: untested code is broken code. Is unreproducible science broken science?

I hope not, because geophysical research is — in general — not reproducible. In other words, we have no way of checking the results. Some of it, hopefully not a lot of it, could be broken. We have no way of knowing.

Next week, at the SEG Annual Meeting, we plan to change that. Well, start changing it… it’s going to take a while to get to all of it. For now we’ll be content with starting.

We’re going to make geophysical research reproducible again!

Welcome to the Repro Zoo!

If you’re coming to SEG in Anaheim next week, you are hereby invited to join us in Exposition Hall A, Booth #749.

We’ll be finding papers and figures to reproduce, equations to implement, and data tables to digitize. We’ll be hunting down datasets, recreating plots, and dissecting derivations. All of it will be done in the open, and all the results will be public and free for the community to use.

You can help

There are thousands of unreproducible papers in the geophysical literature, so we are going to need your help. If you’ll be in Anaheim, and even if you’re not, here some things you can do:

That’s all there is to it! Whether you’re a coder or an interpreter, whether you have half an hour or half a day, come along to the Repro Zoo and we’ll get you started.

Figure 1 from Connolly’s classic paper on elastic impedance. This is the kind of thing we’ll be reproducing.

Figure 1 from Connolly’s classic paper on elastic impedance. This is the kind of thing we’ll be reproducing.