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Materials for DIAS SCS Summer School 2022. Explanation of metrical form englyn

Lewis, Barry James

1 
 
The englyn 
 
Englyn, pl. englynion is the Welsh term for a stanzaic metre. Most of these metres have 
four lines in each stanza, but in early poetry forms with three lines were common. The 
Gogynfeirdd or Beirdd y Tywysogion – court poets of the 12th and 13th centuries – prefer 
four lines. 
 
There are numerous kinds of englyn. Our poem is all written in the commonest type of 
englyn metre, englyn unodl union. 
 
• Four lines (medieval Welsh grammarians count the first two as one long line, but 
it is always printed as two). 
• Length: 10 syllables, 6 syllables, 7 syllables and 7 again. 
• Rhyme: end-rhyme at the end of lines b, c and d. But in line a the rhyme occurs 
inside the line, on the seventh, eighth or ninth syllable. 
• The part of line a after the rhyme (the gair cyrch) either rhymes or alliterates 
with the first half of line b. 
• The rhyme in c d must be between an accented syllable and an unaccented one, 
though the order is free. 
• There may be further internal rhymes and alliteration, called cynghanedd. The 
rules for this are still lax in the twelfth century but quite strict by the fourteenth. 
• There may be alliteration at the beginning of each line (cymeriad). Again, this 
gets stricter with time. 
• The main rhyme changes with each stanza (not always). 
 
Here’s a really strict fourteenth-century example by Gruffudd ap Maredudd: 
 
 
 
 
 
Llyna gein goeluein vu gael – yn Lloegyr 
 Llawget greir o’r Israel; 
   Llanw a’e duc o’e dec auael, 
   Llun Crist ehun, croes Duw hael.1 
 
 
Cynghanedd:  
line a gein goeluein gael = sain anghytbwys ddyrchafedig. Normally the cynghanedd 
extends from the beginning to the gwant, as here. 
line c duc ... dec = braidd gyffwrdd. An early form of cynghanedd. 
line d llun / Crist ehun / croes Duw hael = sain gytbwys acennog, a very elaborate 
example. 
                                                          
1 ‘Here was a fine gift to be received in England, / a generously given relic from Israel; / the tide brought it 
in its fair grasp, / an image of Christ himself, the cross of noble God.’  Gruffudd ap Maredudd to the Rood 
of Chester, 14th century (GMD ii, 1.183–6). 
Gwant, main rhyme, here 
7th syllable 
Gair cyrch, here the last three syllables. 
NB Lloegyr is disyllabic here. 
Esgyll. End-rhyme, here on 
unaccented syllable in line 3 
and accented syllable in 4. 
Alliteration  
with gair cyrch 
2 
 
 
Cymeriad 
Line a llyna, b llawget, c llanw, d llun. Line b does not always participate. Here it has just 
ll where the others have a more elaborate ll ' n pattern. 
 
Connections between stanzas can be created through alliteration, and sometimes the 
final line echoes the first, like an Irish dúnad, but not in our poem. 
 
Barry Lewis 
19 July 2022 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


The englyn

Gómez-García, Clara

Bean, Christopher J.

Le Pape, Florian

Title Quantification of the low-frequency seismo-acoustic soundscape in the NE Atlantic
offshore Ireland
Creators Gómez-García, Clara and Bean, Christopher J. and Le Pape, Florian
Citation Gómez-García, Clara and Bean, Christopher J. and Le Pape, Florian Quantification of
the low-frequency seismo-acoustic soundscape in the NE Atlantic offshore Ireland. In:
Irish Geological Research Meeting. (Unpublished)
URL https://dair.dias.ie/id/eprint/1364/
Quan琀椀昀椀ca琀椀on of the low-frequency
 seismo-acous琀椀c soundscape 
in the NE Atlan琀椀c o昀昀shore Ireland 
Clara Gómez-García (cgomez@cp.dias.ie), 
Christopher J. Bean and Florian Le Pape
This presenta琀椀on has emanated from research supported in 
part by a research grant from Science Founda琀椀on Ireland (SFI) 
under Grant Number 13/RC/2092_P2 and is co-funded by iCRAG 
industry partner, COMPROBE.
Project Summary
We aim, for the first time in the NE Atlantic, to accurately locate 
whales based on their vocalizations, using a new approach to 
event localisation on sparse seismo-acoustic networks. We 
will develop traditional automated and machine learning-
based (ML) detectors to quantify the marine soundscape 
over a vast area offshore Ireland. Drawing on 
methodologies in both seismology and marine 
acoustics, we will analyse the temporal and 
spatial occurrence of Baleen whales and 
References
1. Trabattoni, Alister, et al. (2020). Orienting and locating ocean-
bottom seismometers from ship noise analysis. Geophys. J. Int. 
220, 1774–1790.
2. Berrow, Simon D., et al. (2018). Acoustic Surveys of Cetaceans in the 
Irish Atlantic Margin in 2015–2016: Occurrence, distribution and 
abundance.Department of Communications, Climate Action & Environment and 
the National Parks and Wildlife Service (NPWS), Department of Culture, Heritage 
and the Gaeltacht, Dublin, Ireland, 348pp.
3. Weirathmueller, Michelle, et al. (2017). Estimating range to a vocalizing fin whale using 
the timing and amplitude of multipath arrivals. J. Acoust. Soc. Am. 142, 2101–2120.
4. You, Xiaohu, et al. "AI for 5G: research directions and paradigms." Science China Information 
Sciences 62.2 (2019): 1-13.
Acknowledgments
We acknowledge the SEA-SEIS Project and 
team (PI: Sergei Lebedev) and the operators 
involved for providing the data used in this study 
(SEA-SEIS Network, NEAMS dataset and ObSERVE 
acoustic data).
Project objectives
1. Collect synchronous baseline information on the NE 
Atlantic soundscape field over a broad
geographical area.
2. Develop an automated ML-based toolkit for separating sound sources 
into associated clusters (e.g., biological origin, ship origin).
3. Analysis and database construction of ship noise and whale call spatio-
temporal evolution.
4. Derive a methodology for determining whale locations from 
their calls, using a sparse 4-component
OBS network. 
5. Develop and make publicly available a broad 
scale ‘low frequency’ empirical noise 
propagation model for NE Atlantic offshore 
Ireland, & its associated codes and tools. 
Study Area & Data
NEAMS dataset (triangles) and vessel traffic (heatmap) obtained 
from historical automatic identification system (AIS) position data    
AIS collected trajectories
OBS collected waveforms
Modified from ref. 1. 
Sketch showing the relation between AIS trajectories and 
OBS recordings of ship noise
This project uses different data types. Ocean-
bottom seismometer (OBS) data, such as the 
NEAMS dataset (Jan – Sep 2016), located offshore 
Donegal, is analysed to quantify the occurrence of 
natural and anthropogenic acoustic sources. 
ObSERVE acoustic study area
Modified from ref. 2.
The ObSERVE 
acoustic dataset 
(different mooring points 
along the shelf between 
2015 and 2016) will be 
used to train the 
supervised deep 
learning (SDL) 
algorithm.    
Vessel AIS data is used to identify 
ship tracks recorded by OBSs with 
known sea floor locations.
 
Ship tracks recorded by 
ocean-bottom seismometers 
Vessel tracks within 30 km from ORK05 (9 May 2016)
Power spectral densities (PSD) around 
the CPA times (5-minute windows) show 
amplitude spectrum similarities based on 
the CPA distances (see legend).
Using AIS positions, 
we investigate vessel 
tracks (different colour 
lines) recorded by the 
OBS hydrophone 
channels. 
The strongest vessel signals registered in the spectrograms (colour 
rectangles) are at their closest point of approach (CPA) to OBS ORK05.
Time series and spectrogram (ORK05, 9 May 2016) 
(Top plot) Hydrophone data spectrogram recorded by OBS ORK09 for 
March, 2016. The ~ 20 Hz pulses correspond to Fin whale vocalizations.
Fin whales recorded by 
ocean-bottom seismometers
Propagation effects of fin whale calls
(Left plots) Time series and spectrograms showing 
fin whale calls recorded at ORK09 and ORK10.
(Right plot) Comparative power spectral 
densities (PSD) for 5-minute windows. 
ORK09 – ORK10 distance = 62.7 km
Combined acoustic & AIS 
vessel tracking 
The evolution of a ship’s acoustic signal spectral 
amplitude with distance (as a ship transits away from 
an OBS after its CPA) is obtained by combining the AIS 
tracking with the acoustic OBS ship noise recording. 
Below, we analyse the amplitude decay of the 
frequency spectrum of a ship transiting away ORK06. 
CPA = 3.2 km
Towards building an empirical 
noise propagation model
We combine spectral amplitude decay curves for 
narrow frequency bands from different vessels 
(each colour curve corresponds to a different ship) to 
obtain frequency-dependent empirical acoustic noise 
propagation information. All curves are normalized by 
the global maximum absolute value.
Next steps:
Event Detection and Location 
Example of a traditional detector in use
From ref. 3. Example of Fin whale vocalizations plotted as (a) a 
spectrogram and (b) as a time series. (c) Matched filter crosscorrelation 
output used for event detection
Sketch of supervised deep learning using neural networks 
From ref. 4.
We will use automated detectors (both traditional and 
ML-based methods) to identify events (e.g., Baleen 
whales) in the continuous OBS recordings.  
Underwater shot of an OBS during the SEA-SEIS 
deployment
From ref. 5.
We will locate Baleen whales identified from OBS 
recordings, by combining their distance from 
and azimuth to individual OBSs. 
Acoustic properties of
 vessel noise recordings 
The spectral characteristics of vessel track 
recordings reveal information about their associated 
ship acoustic noise signatures. We show the time 
series and spectrogram of a ship track recorded by 
ORK01 (CPA = 0.4 km). 
A Doppler effect of ~ 1 Hz 
can be observed at the CPA in 
the hydrophone spectrogram. 
The Lloyd’s mirror effect (U-shaped patterns) are observed due 
to the destructive interference varying with time. 
25-minute time series and spectrogram from ORK01 (15 Aug 2016)
CPA
Time evolution of the spectral amplitude at 12 Hz as the vessel 
transits away from ORK01
CPA
Vessel transiting away from ORK01 (CPA=0.4 km) on the 15 Aug 2016 


Quantification of the low-frequency seismo-acoustic soundscape in the NE Atlantic offshore Ireland

Weber, Maurice

Smith, Patrick J.

Lokmer, Ivan

Zuccarello, Luciano

De Angelis, Silvio

Minio, Vittorio

Title Investigation of high frequency seismic signals recorded in summit region of Mt Etna
Creators Weber, Maurice and Bean, Christopher J. and Smith, Patrick J. and Lokmer, Ivan and
Zuccarello, Luciano and De Angelis, Silvio and Minio, Vittorio
Citation Weber, Maurice ORCID: https://orcid.org/0009-0008-1845-1535, Bean, Christopher J.
ORCID: https://orcid.org/0000-0003-3285-2446, Smith, Patrick J., Lokmer, Ivan,
Zuccarello, Luciano, De Angelis, Silvio and Minio, Vittorio Investigation of high
frequency seismic signals recorded in summit region of Mt Etna. In: Deutsche
Geophysikalische Gesellschaft, March 2023, Bremen, Germany.
URL https://dair.dias.ie/id/eprint/1443/
This project has received funding from the European Horizon‘s 2020 
research and innovation programme under Grant Agreement No 858092
Maurice Weber1, Christopher J. Bean1, Patrick Smith1, Ivan Lokmer2, 
Luciano Zuccarello3,4, Silvio De Angelis4,3, Vittorio Minio5
1 Dublin Institute for Advanced Studies, Ireland; 2 University College Dublin, Ireland; 3 Instituto Nazionale di 
Geofisica e Vulcanologia, Sezione di Pisa, Italy; 4 University of Liverpool, UK; 5 University of Catania, Italy
Investigation of high frequency seismic signals 
recorded in summit region of Mt Etna
Contact: mweber@cp.dias.ie
Introduction Data
Waveform coherency
Comparison with additional data
Beamforming
Outlook
Fig. 1: Distribution of 115 deployed stations within 6 
circular array configurations and 1 profile consisting of
broadband and infrasound stations.
Fig.2: Detailed view of 2 
small arrays (30 m 
apertures) in close
proximity to one another. 
These arrays feature very
dense station spacing to
target high frequencies. Fig.3: Array response of one of the small configurations demonstrating the very high 
frequency resolution capabilities (see slowness-frequency resolution on the right.
Fig.9: Weather conditions near Etna.
Fig.10: Example of seismic-acoustic stations helping to identify
explosion signals which produce a time delayed signal on the
acoustic component (bottom) compared to seismic trace (top).
Fig.4: Examples of the huge variety of seismicity across the full spectral range recorded at different arrays and 
distances from craters. This includes countless small events (mainly explosions) covering broad frequency ranges
(top left), other interesting high frequency bands (top right), strong tremor episodes mainly between 1-10 Hz 
(bottom left) as well as rapid bursts of high amplitudes up to more than 100 Hz (bottom right).
Crater roughly
this way
Fig.5: Stacks filtered at 1-5 Hz of all stations within respective arrays
ordered with respect to distance from Bocca Nuova crater. Moveout of
signal indicates origin from Bocca Nouva with signal reaching all arrays.
Fig.8: Significant scattering effects visible at 11-15 Hz band for
stations only 20 m apart.
Fig.6: Waveforms filtered at 1-5 Hz for single stations of an 80m aperture array
showing high coherency for inner stations which are very close to eachother (green
box) but some changes are visible for outer stations which are further apart 
demonstrating scattering at local site effects. However, onset of event with decent
coherency on all stations (compare first cycles in blue circle with onset on other
stations) while waveform changes mainly effect later portion of signal indicating
propagation effects. 
Fig.7: Position of
individual nodes
relative to one
another with the
crater towards the
bottom right.
Fig.11: Top: Beamforming result for 1-5 Hz of 5 s of data including a small explosion event coming from actively degassing crater Bocca 
Nuova. Three array locations are used simultaneously as input to better constrain the origin of signal. The time evolution of the
backazimuths for each input array is given in the top subplot by the dots, circles and triangels. It can be confirmed that this signal does
indeed come from Bocca Nuova as the respective backazimuths point back in the direction of the crater. Respective Slownesses for
each computed backazimuth (using 1.5 s of computational time window with 95% overlap) are given in the second subplot while the
stacked traces of all stations in the arrays follow below. The bottom three plots show the spectral content of each array again
indicating the moveout of the incoming signal with increasing distance from Bocca Nuova. In the top right corner a polar plot provides
a visualisation of the distribution of the backazimuths which clearly form clusters representing the direction towards Bocca Nuova 
seen from each of the arrays indicated by the differently coloured circels. Compare with map in bottom right corner where the green
lines show the projection of the beam representing the backazimuth/slowness pair with maximum relative power. Two of the three
arrays seem to see a secondary direction of arrival (polar plot) but those backazimuths correspond to later parts of the signal as can be
seen in the time evolution of the backazimuths and thus might suggest propagation effects of the signal.
Bottom: The exact same signal is tested for 6-10 Hz and despite quickly increasing scattering effects a good result can still be obtained. 
We find similar clusters of backazimuths corresponding to the respective direction back to Bocca Nuova seen from each array but also 
some wider distribution of backazimuths suggesting scattering effects and thus droping waveform coherency. However, these
backazimuths can be related mainly to late parts of the signal again while the onset shows good coherency and hence indicating
beamforming capabilities at higher frequencies than usually explored on volcanic seismic data. 
Shortened references
• Smith and Bean (2020): RETREAT: A REal-Time TREmor Analysis Tool for Seismic Arrays, With Applications for Volcano Monitoring; 
Front. Earth Sci., Sec. Vulcanology, doi.org/10.3389/feart.2020.586955
• Schweitzer et al. (2011): Seismic Arrays, Chapter 9; DOI: 10.2312/GFZ.NMSOP-2_ch9 
• Soubestre et al. (2018): Network-Based Detection and Classification of Seismovolcanic Tremors: Example From the Klyuchevskoy
Volcanic Group in Kamchatka; Journal of Geophysical Research: Solid Earth, doi.org/10.1002/2017JB014726
• De Barros et al. (2011): Source mechanism of long‐period events recorded by a high‐density seismic network during the 2008 
eruption on Mount Etna; JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, B01304, doi:10.1029/2010JB007629
• Rowley et al. (2021): Deformation-controlled long-period seismicity in low-cohesion volcanic sediments; nature geoscience,
https://doi.org/10.1038/s41561-021-00844-8
Time after start [s] Time after start [s]
• Optimizing location process of different seismic signals
• Tests on several more events where origin is very sure to verify
• Depending on waveform changes on scale of array only specific stations could be used for beamforming to improve coherency of involved stations
• Determine frequency limits above which drop in coherency does not allow for beamforming
• Trying other location software (covseisnet) in comparison
• Looking at single station direction of arrival methods to explore how scattering affects direction of incoming signal between individual stations on scale of
array aperture for a given signal
Typically, high frequency seismic data (> 10 Hz) on volcanoes have been less studied as precursory seismicity to volcanic 
eruptions dominates longer periods. Because of this, a large field campaign between July and September 2022 was carried 
out in the summit region of Mt. Etna ultimately targeting high frequency signals usually overlooked. 104 nodal seismic 
sensors (250 Hz samplerate) where installed in dense array configurations as well as a profile of 11 broadband (100 Hz 
samplerate) and infrasound instruments. Inspection of this data from the high sampling rate seismic stations installed during 
the campaign reveals a variety of high frequency (10-90Hz) signals, which are poorly understood. Constraining the locations 
of different types of signals and the corresponding mechanisms might help to improve the understanding of the huge variety 
of seismicity found on volcanos across wide frequency ranges. Processing of the data reveals significant scattering effects 
causing waveform changes between stations across very little distance even on the scale of arrays posing a challenge when 
attempting to find locations of different signals. However, high frequency signals are found traveling several kilometers
across the highly heterogenous edifice of Mt Etna and initial beamforming tests suggest that focusing on onset of signals 
allows for beamforming of signal content >10 Hz while later parts of a signal are too susceptible to propagation effects. 
Signal content


Investigation of high frequency seismic signals

recorded in summit region of Mt Etna

Title Characterisation and locations of volcanic high frequency tremor above 10 Hz on
Mount Etna
Creators Weber, Maurice and Bean, Christopher J. and Smith, Patrick J. and Lokmer, Ivan and
Zuccarello, Luciano and De Angelis, Silvio and Minio, Vittorio
Citation Weber, Maurice ORCID: https://orcid.org/0009-0008-1845-1535, Bean, Christopher J.
ORCID: https://orcid.org/0000-0003-3285-2446, Smith, Patrick J., Lokmer, Ivan,
Zuccarello, Luciano, De Angelis, Silvio and Minio, Vittorio Characterisation and
locations of volcanic high frequency tremor above 10 Hz on Mount Etna. In: European
Geosciences Union (EGU) General Assembly, 14th - 19th April, 2024, Austria Centre,
Vienna.
URL https://dair.dias.ie/id/eprint/1447/
• Previous work suggests tremor-like 
signals may be generated by brittle
failure of weak volcanic material
• Seen in numerical simulations (top left)
• The events are closely spaced in time 
merging into a tremor-like signal
• Also seen in laboratory experiments
where Napolitan Tuff has been deformed
producing a train of tremor-like signals
(top right)
• The volcanic sample was oven-dried (no
fluids involved in generating the tremor-
like signals)
• This opens up the question: Can volcanic
tremor only originate from gas 
fluctuations or is brittle failure of
volcanic material another source of
volcanic tremor?
This project has received funding from the European Horizon‘s 2020 
research and innovation programme under Grant Agreement No 858092
Maurice Weber1, Christopher J. Bean1, Patrick Smith1, Ivan Lokmer2, 
Luciano Zuccarello3,4, Silvio De Angelis4,3, Vittorio Minio5
1 Dublin Institute for Advanced Studies, Ireland; 2 University College Dublin, Ireland; 3 Instituto Nazionale di 
Geofisica e Vulcanologia, Sezione di Pisa, Italy; 4 University of Liverpool, UK; 5 University of Catania, Italy
Characterisation and locations of volcanic high 
frequency tremor above 10 Hz on Mount Etna
Contact: mweber@cp.dias.ie
1.Deployments on Mount Etna 2.Motivation and Aims
4.Tremor Detection and Characterisation
3.Tremor Localisation
Outlook
Shortened references
• Bean et al. (2013): Long-period seismicity in the shallow volcanic edifice formed from slow-rupture earthquakes; nature geoscience, DOI: 
10.1038/NGEO2027
• Rowley et al. (2021): Deformation-controlled long-period seismicity in low-cohesion volcanic sediments; nature geoscience, 
https://doi.org/10.1038/s41561-021-00844-8
• Soubestre et al. (2018): Network-Based Detection and Classification of Seismovolcanic Tremors: Example From the Klyuchevskoy Volcanic Group 
in Kamchatka; Journal of Geophysical Research: Solid Earth, doi.org/10.1002/2017JB014726
• De Barros et al. (2011): Source mechanism of long‐period events recorded by a high‐density seismic network during the 2008 eruption on 
Mount Etna; JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, B01304, doi:10.1029/2010JB007629
• Two field campaigns were
undertaken in summer 2022 
and summer 2023 
• Installing arrays and profiles of
about 100 short period
seismometers around the
summit craters
• Additionally, broadband
stations,  microphones and 
timelapse cameras were utilised
Bean et al., 2013
Rowley et al., 2021
60 minutes
Below: Mean Spectral
content from 16 stations
stacked Clearly shows a 
tremor episode between 13-
15 Hz varying in intensity
over time
Localisation of two examples of volcanic tremor using COVSEISNET (Soubestre et al.). Note that the distribution of
stations is far from ideal in terms of a good azimuthal coverage.
What is different as the seismic tremor
is generated in both incidences?
Is Degassing involved here? Is Degassing not relevant here?
• Optimise localisation by deriving shallow velocity structure underneath arrays deployed and use permanent INGV 
stations in addition to improve azimuthal coverage
• How robust are the localisation results? Are diffusive looking distributions of tremor sources real or just due to the
station configuration?
• Do we find changes in seismicity (tremor) in 2023 data that relate to variations in degassing by comparing with
envelopes of optical and thermal data (INGV Rome) recording from crater
• Numerical modelling: Utilising displacement over time records from analogue modelling of surface edifice deformation
as input for seismic wavefield propagation modelling. 
• How do the displacement records from the lab compare to seismic records from the field?
Sumup
• Two incidences of high frequency seismic tremor (13-15 Hz)
• Seismic energy and spectral contents are quite similar
• Example on the left is matched in time by acoustic signal at different 
frequency (3-5 Hz)
• Two different but linked processes?
• Example to the right is not accompanied by acoustic signal (or at least 
much weaker given the similar seismic energy in both cases)
• What processes are causing the high frequency tremor?
• Is it gas fluctuations only or could it be brittle failure of weak material? 
• Does the acoustic signal (Degassing?) trigger the seismic tremor (when
both acoustic and seismic signal is present)
• It seems as though the seismic tremor can also be triggered „itself“ 
when the acoustic signal is missing – are there no gases involved in the
tremor generation then?
• What role could slow deformation of the edifice play?
Unshifted Envelopes of CCFs Unshifted Envelopes of CCFs Shifted Envelopes of CCFs Shifted Envelopes of CCFs 
Left:
• Correlating seismic (13-15Hz) and acoustic (3-5Hz) 
mean amplitudes during all tremor episodes found
• Clearly some correlation is visible
• However episodes of very similar seismic energy
show strongly varying acoustic amplitudes
Right:
• Attempt to account for wind contamination in 
acoustic data – some epsiodes with high acoustic
amplitudes these are likely contributed to by wind 
as strong broadband noise is found (7-15Hz)


Characterisation and locations of volcanic high

frequency tremor above 10 Hz on Mount Etna

Molodtsov, Dmitry

Kiyan, Duygu

Title Investigation of a multiphysics joint inversion framework
Creators Molodtsov, Dmitry and Kiyan, Duygu and Bean, Christopher J.
Citation Molodtsov, Dmitry, Kiyan, Duygu ORCID: https://orcid.org/0000-0001-6024-5366 and
Bean, Christopher J. ORCID: https://orcid.org/0000-0003-3285-2446 Investigation of a
multiphysics joint inversion framework. In: European Geosciences Union (EGU)
General Assembly, 19–30 April 2021, Online. (Unpublished)
URL https://dair.dias.ie/id/eprint/1455/
Investigation of a multiphysics joint inversion framework
 
Dmitry Molodtsov1,2, Duygu Kiyan1, and Christopher J. Bean1,2
1Dublin Institute for Advanced Studies, Ireland; 2Irish Centre for Research in Applied Geosciences
EGU21-13265
EGU21-13265
update m 
u fixed
update u 
m fixed
Multiphysics joint inversion of MT, first-arrival traveltimes (FATT), gravity and other data
Alternating minimization approach based on introducing auxiliary 
variable u and splitting (1) into two subproblems: 
(2) converges to (1) with 
Advantages of this formulation:
- fully independent inversion grids
- independent optimization methods tailored for each subproblem
- using existing inverse solvers without modification (we use ModEM for MT) 
- scalability  
Joint regularization-coupling: 
1) mixed-norm term – regularization and coupling by aligning edges (for p ≤ 1)
2) cross-gradient terms – coupling by aligning gradient directions
multiparameter model
regularization 
and coupling
data misfits
(2)
'inversion'
'regularization'
(1)
EGU21-13265
In the following examples, we show relative 
performance of different joint regularization / 
coupling functionals
Magnetotellurics:
(modified from Egbert and Kelbert, 2012)
impedance tensor and tipper at 12 periods 
in 10-103 s range + 3% / 0.03 noise
225 stations
66 x 66 x 59 cells
First-Arrival Traveltime Tomography:
background (= initial-model) velocity:
linearly increazing with depth from 5 km/s 
to 8.5 km/s
225 x 64 traveltimes 
+ 0.1 s noise
140x140x40 model cells
Gravity:
vertical component of gravity field
@ 225 stations
+ 1 mGal noise
64x64x64 model cells
MT FATT Gravity
EGU21-13265
Separate inversions with Total Variation:
MT FATT Gravity
EGU21-13265
MT FATT Gravity
Joint inversion with Joint Total Variation:
EGU21-13265
MT
fixed res. from 
separate inversion
FATT
(Δv=±0.5 km/s)
Gravity
Joint inversion with Total Variation + cross-
gardient:
EGU21-13265
MT 
fixed res. from 
separate inversion
FATT
(Δv=±0.5 km/s)
Gravity
Joint inversion with Joint Total Variation + cross-
gardient:
EGU21-13265
MT 
fixed res. from 
separate inversion
FATT
(Δv=±0.5 km/s)
Gravity
Joint inversion with (2, 0.1) - mixed-norm of the 
gradient + cross-gardient:


Investigation of a multiphysics joint inversion framework

Kobel, Chantal

1. Use of a suprascript dot (punctum delens) over f for nasalised f:  
 
/hi\ fhil leptha lán becca, BL Harl. MS 1802, f. 9v40 
do fhir na faicti i fhagabar he, TCD MS H 2.15a (1316), p. 25a11 [Plate XXI]. 
 
For further examples, see:  
James Carney, Regimen na Sláinte: Regimen Sanitates Magnini Mediolanensis (Baile Átha 
Cliath, 1942–4), xxxiii 
Mícheál Hoyne, Fuidheall Áir: Bardic Poems on the Meic Dhiarmada of Magh Luirg, c. 
1377 – c. 1637 (2018), 121. 
 
Note also the orthographical practice of writing a punctum delens above a nasalised b, e.g. 
mBhealltaini, f. 45va6 (rather than above the m). 
 
2. The letter k  
‣ K + l + medial stroke for kaland (Lat. kalandae) 
 
It can also stand for ca or cat(h) 
‣ An elongated k to represent the noun cath ‘battle’, i.e. cath, NLS 72.1.40 (15th/ 16th ?), p. 
1.15, 20 (with punctum delens); catt (written ktt),  BL Additional 30512, 33Ra marg. inf. 
‣ To represent the syllable cath in cathir, TCD MS H 3.18 (1337), p. 467; Conchobar mac 
Cathbad, RIA MS D iv 2, fol. 46va33 
 
3. Variant acht-compendium 
‣ The letter s + what appears to be something similar to the us-compendium (here standing 
for ed < Lat. sed) for (a)cht in:  
 rechtarea, RIA MS 23 N 10 (c. 1575), p. 16.6 
 Connachtaibh, TCD MS H 3.18 (1337), p. 755.11 (c. 1616) 
 co becht, Brussels, KBR, MS 20978–79, f. 57v8 (c. 1645) 


Palaeographical notes for lecture 6

Materials for DIAS SCS Summer School 2022. Paradigm of kael, kaffael

1 
 
kael, kaffael 
 
‘to get, obtain; find; have (condition, experience)’. 
 
This verb is irregular in having two stems, kaf- and kaff-. The latter is from the 
subjunctive originally and has spread into other parts of the verb. In addition there is a 
reduced stem ka-. Once these three stems are clear, the actual forms are regular. 
 
The preterite is formed from the old stem kaf- and regular but for f/v > w (GMW §10): 
 
keveis 
keveist 
cavas 
cawssam, -om 
cawssawch 
cawssant, -ont 
 
The pluperfect similarly: cawsswn, cawssut, etc. 
 
The present is formed from kaff- or reduced ka-: 
 
caffaf, caf 
keffy, key 
keiff 
caffwn, cawn 
keffwch, kewch 
caffant, cant 
keffir, keir 
 
You will meet with old forms from reduced ka- which have not become monosyllables: 
cahaf, kehy, etc. The h grew in hiatus. 
 
The imperfect similarly: caffwn or cawn, caffut or kaut, caei > cai, etc. 
 
The preterite impersonal is caffat from kaff-, or kat from ka-. 
 
The subjunctive is from kaff- (< kaf-h-) and regular: kaffwyf, keffych, kaffo etc. (kaho 
etc. < ka- is rare and early). 
 
The imperative is lacking. 
 
The verbal noun is kael, kaffael. 
 
An alternative pluperfect kawssoedwn etc. consists of kawss- and the imperfect of the 
verb ‘to be’ stuck on the end. You will find such compound pluperfects formed from 
certain other irregular verbs too. 
 
 
 
2 
 
For the etymology: 
 
GMW §161. 
Eric P. Hamp, ‘OIr. gaib-, Welsh gafael, caffael, cael, cahel’, ZCP 24 (1954), 229–33. 
Schumacher, Historical Morphology of the Welsh Verbal Noun, Chapter 8 (pp. 203–6). 
 
Barry Lewis 
19 July 2022 


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Palaeographical notes for lecture 6

Extra handout kael kaffael

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