Category: PALNews (page 1 of 8)

News related to the PAL

jupyter notebooks for mathematical methods in the physical sciences

A Guided Tour of Mathematical Methods for the Physical Sciences is based on a philosophy that learning mathematics for the physical sciences, requires pen and paper. Learning by doing. Three editions in, this philosophy still holds strong, but lots of things have happened since the first edition in 2001. Numerical methods play an ever-larger role in the physical sciences, for example. The Python programming language has really exploded on the scene, and more recently the jupyter notebook has been developed to facilitate learning numerical methods in python. To accompany the latest edition of our book – and your pen and paper – we wrote one jupyter notebook per chapter.

If you are new to jupyter notebooks and/or python, the online resources are virtually endless, and the installation — on any operating system — is easy with conda. We are going to assume you run python 3.

  1. Introduction
  2. Dimensional analysis (or download the notebook directly)
  3. Power series (or download the notebook directly)
  4. Spherical and cylindrical coordinates (or download the notebook directly)
  5. Gradient (or download the notebook directly)
  6. Divergence of a vector field (or download the notebook directly)
  7. Curl of a vector field (or download the notebook directly)
  8. Theorem of Gauss (or download the notebook directly)
  9. Theorem of Stokes (or download the notebook directly)
  10. The Laplacian


PORO/PAL party during the GSNZ meeting

From left to right: Steve Brennan, Sam Hitchman, Paul Freeman, Kasper van Wijk, Evert Duran, Josiah Ensing and Jonathan Simpson.

This week the annual GSNZ meeting  was on University of Auckland campus. To celebrate a successful year in research, we hosted a small get together in our labs for tours, demos, drinks and some food. Below are a few photos as proof, despite the “zapruder film” quality of these…

Sam showing Professor Martha Savage and other guests his new optical rock strain (and temperature) meter

James Clarke giving an overview of the research projects and equipment in the PORO lab to a captivated audience.

Evert Duran with guests, including Professors John Townend and David Prior.

Shreya Jagdish Kanakiya and Josiah Ensing


Jami got engaged!

Jami Johnson sent us word of her engagement to her Kiwi  boyfriend Sam! Here is a picture of the happy couple on a recent trip to Norway. We wish Sam and Jami all the best (and for them to move back to New Zealand, of course).

Apple Seismology

Today, our paper on Apple Seismology appeared in Physics Today. It was a follow up on Sam and Zoe’s experiments, highlighting the similarities between seismic waves and normal modes in the Earth, and their acoustic equivalents in a Braeburn apple.

In the panel on the left, seismic (surface) waves traverse Earth, while in the right panel laser-generated and detected surface waves circle the apple.

Joint Inversion – finer resolution checker-board

Our previous joint inversion of assessing the resolution of tomography in the Auckland Volcanic Field gives us promising results for subsurface features at the scale of ~60 km (see this post).

The latest checker-board test to improve from this finding involve using smaller sized checker-board, around half of the previous test. The same receivers configuration and local and teleseismic sources are still used here – 1330 cataloged events (681 local + 649 teleseismic) onto 25 receiver stations.

In comparison to our previous result, this recovery indicates that yes smaller scale features can plausibly be resolved, but at the cost of having the extent of the well recovered model being diminished. Some regions outside the box may also show good checker-board recovery. But these are not always nicely interconnected (ex. to the north and northwest of lake Taupo).

More specifically, this result now implies that:

  • The region where resolution is commendable, is now mostly confined around the Auckland area only. Up to about 100 km deep, EW span of 260 km, and NS extend of 167 km.
  • Within this region, ~30 km (roughly 35 in depth 30 in width and 33 in length) sized subsurface features can be resolved.

Resolution test on the AVF – Joint Inversion

Joint inversion of local and teleseismic events

Promising results are obtained from performing a joint inversion of local and teleseismic sources in a checker-board synthetic test. We proceed with using 1330 cataloged events (681 local + 649 teleseismic) onto 25 receiver stations.

The local events made up the sources coming in from the southeast of the receivers array. Whereas teleseismic sources complement this with incoming rays from other directions but most notably from the Northwest.

The extent of the model encapsulate from Northland reaching to Hawke’s Bay. The implications from this recovered patterns are:

  • Dimension of the region where resolution is most exemplary is signified by the red box (322 x 231 x 270 km). Outside of it, the smearing artefact is too prominent.
  • Within the box, the size of the features that are resolvable, corresponds to the size of each checker-board, is in the order of ~60 km (roughly 60 in depth 62 in width and 67 in length).

Comparing resolution results – Local vs Teleseismic vs Joint Inversion

We compare three sets of results of resolution test: using local sources only, teleseismic sources only, and a joint local and teleseismic. The source locations are mainly situated so that the local sources consist of earthquakes south-southeast of the receivers array, and the teleseismic sources are north-northwest of the array. The raypath plots illustrate the statement.

Initial model is the same in all three tests. Comparing the recovered checker-board for the horizontal slices, we expected to see recovery mainly in the Southeast for local sources and to the Northwest for teleseismic sources. Therefore we see a success in joint inversion, as in the joint model, we can see an improved coverage width extending from Northland to Waikato.

In vertical slices, local sources provide better depth recovery as the results from the teleseismic sources are more smeared. However a joint inversion albeit with added smearing can resolve more feature, for example the shallow positive anomaly at 175.8 E.

The next step is to add the remainder of the sources both local and teleseismic, to be inverted jointly. Once cleared, we need to assess the extent of the resolution i.e. how small of a feature we can resolve in the inversion, which is linked to the size of our checker-board.

Joint Inversion – Preliminary

To improve the results for the tomography resolution test, we attempt to do a joint inversion using local (within model) and global teleseismic activities.

The early attempts make use of the SE Australia example in FMTOMO and translate this for the AVF. Some of the parameters specified in the example are kept unchanged. This includes having a two layered model split at the approximate moho depth. Though to try and keep this test as similar to the previous synthetic tests, we make the geometry of the two checker-board layers equal, so we cannot see the interface boundary at the initial model.

Ultimately, we want to use the full number of local and teleseismic sources in a single joint inversion. But as a test-run, we use small samples from the sources used in the previous tests: 5 local sources and 5 teleseismic sources.

This shows that joint inversion is applicable with reasonable outcome for a relatively small number of sample sources. At 30 km deep is the defined interface between the two layers of the model, clearly shown as a discontinuity in the recovered model.

Having a middle interface at 30 km is important if we want to use for example reflected phases in our inversion. For a direct first arrival though, one layer model is sufficient. Our trials of redefining initial model into one checker-board layer is met with an interpolation error. We note though that this is only an issue when we try to implement the teleseismic sources.

finished reading sources
interpolate_interface : interpolation outside range :ilong
1 -2147483647 -2147483648
3.0513999021530127 -0.63879440704080281
if this happens during initialization your interface parameter
grid may not cover the entire propagation grid
Note: The following floating-point exceptions are signalling: IEEE_INVALID_FLAG IEEE_OVERFLOW_FLAG IEEE_DENORMAL

One plan to bypass this error is to define the interface at very deep location and not having the checker-board pattern imposed onto the second layer. This makes the second layer virtually the background ak135 velocity model. And our checker-board model only really start into the first layer. This strategy produce a smoother results essentially removing the discontinuity.

A final note is that all the teleseismic sources are required to have a P phase arrival as oppose to p phase. Which imply that the epicentre of the teleseismic source has to be significantly far away from our receivers array, as it allows the wave to travel down before ascending towards the receivers. Therefore, our other attempts of using teleseismic sources that are regional and close to our array have yet to yield any successful results. This assumes that those close telesseismic sources don’t have the chance and space to travel downward priorly as defined by P arrival. We have yet find the way to utilize this direct upward p arrival.

Congratulations, Dr. Jami Johnson!

It’s the end of an era… Jami Johnson successfully completed her PhD thesis in photoacoustic imaging.  She is now off to The University Pierre and Marie Curie, in Paris (France) to pursue postdoctoral research in medical imaging. We wish Jami all the best, and we will follow her in what will undoubtedly be a very exciting career. The PALs want to thank Jami for all her efforts and the wonderful memories she leaves behind.


Postgraduate opportunities in our lab

Below are short descriptions of research projects available for postgraduate students in our group at the University of Auckland. If you are interested in any of these, please contact us for technical questions. For questions around enrollment at the University of Auckland, please go here. Scholarships may be available for the best applications through the University of Auckland, or the Dodd Walls Centre.

ResonanT Ultrasound Spectroscopy

Resonant ultrasonic spectroscopy fills an important gap between our ultrasonic and seismic research. Together with the PORO lab, we have rock samples to complement laser ultrasound and a host of other petrophysical data with new RUS results.

Laser ultrasonic rock physics under high pressure and/or temperature

The PAL and PORO lab join forces by combining our respective strengths in laser ultrasound and rock physics to improve data quality and quantity. In this project, we are building the expertise to do laser ultrasound in a pressure vessel with optical windows. Source/receiver locations are varied under computer control with an arduino-controlled servo rotational stage.

unraveling the mysteries of the Auckland volcanic field

Part of an active volcanic field, questions surround the nature of Auckland’s past, present and future. Using a suite of seismic techniques that range from ambient seismic noise tomography, to receiver functions and body wave tomography, we aim to build a representative model that helps us explain the geodynamics of the Auckland Volcanic Field.

quality control of timber and fruit products with laser ultrasound

Laser ultrasound can be applied to products of interest to a wide community. Current methods of testing the quality of fruit and timber, for example, can often be described by one or more of the following terms: sparse, contacting, expensive, and often destructive. In this project, we aim to explore the opportunities for laser ultrasound in estimating the quality of  fruit and timber in a non-contacting and non-destructive matter.

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