Nyiragongo and Nyamuragira Volcanoes, Congo

Satellite photo of adjoining volcanic fields, Goma and Lake Kivu. Photo courtesy Photovolcanica. http://www.photovolcanica.com/VolcanoInfo/Nyiragongo/Nyiragongo.html

This pair of volcanoes is responsible for 40% of Africa’s historic volcanic eruptions.  Nyiragongo hosts one of the largest lava lakes in the world.   Its immediate neighbor, Nyamuragira (Nyamulagira) no longer has a lava lake, but has had one in the past.  Both volcanoes erupt very alkaline lavas, highly liquid, from either the crater or fissures in the flanks.

The volcanoes are located on the Albertine Rift, the western branch of the East African Rift Valley system.  There are two older stratovolcanoes in the vicinity, Baruta and Shaheru.  These are partially overlapped by Nyiragongo.  The flanks of all four volcanoes have over a hundred parasitic cones mainly along radial fissures.  The grouping has been called the Virunga Volcanic Field.

Drone image of crater of Nyiragongo. Photo courtesy Bradley Ambrose, Caters News, March 2016. http://www.telegraph.co.uk/news/picturegalleries/earth/12174482/Exploring-Nyiragongo-volcano-and-worlds-largest-lava-lake-by-drone-in-pictures.html?frame=3583268

Continuing volcanic activity in the region also impacts neighboring Lake Kivu, which is charged with CO2 from vents deep in the lake and methane from decomposing vegetation on the bottom of the lake.  From time to time something will upset the chemical / thermal balance and the lake will overturn, releasing massive amounts of methane and CO2 into the atmosphere.  The methane may or may not ignite.  The CO2 is heavier than air and moves downhill into low lying areas surrounding the lake, asphyxiating local residents and wildlife.

This sort of lake overturn most recently happened in Cameroun with Lake Nyos in 1986.  A landslide into the lake upset the balance and released the dissolved CO2, killing more than 1,700 people living near the lake.  This sort of release is called a limnic eruption.  Lake Monoun also in Cameroun, most recently overturned in 1984, killing 37.  There is no historic record of Lake Kivu overturning, but there is evidence of such a release in prehistoric times perhaps every thousand years and Kivu has over 2 million people living on its shores.

Degassing fountain in Lake Nyos. Dissolved CO2 gas comes out of solution as the water column rises which in turn drives the water column upwards. Action is driven entirely by dissolved CO2 in the water turning into gas as the pressure drops. The physics behind this plume is identical to the physics driving an ashy eruption / Plinian column / pyroclastic flow all of which are driven by water and gasses in solution in the magma flashing to gas as the column ascends and depressurizes. Photo courtesy SATREPS, JP. 2010. https://www.jst.go.jp/global/english/kadai/h2214_cameroun.html

Lake Kivu has significant methane, which is described as a biogas.  There have been a series of methane extraction projects using various methods to extract, separate and process the gasses from the lakebed.  The company will also use the natural gas to produce electricity and sell it to local customers.  The most recent power plant was producing 26 MW in 2016.

Around 30,000 live within 10 km of both volcanoes.  700,000 – 1,000,000 within 30 km of both volcanoes.  And 8 – 9 million within 100 km.  Goma, a city with a population of around a million is located 18 km from Nyiragongo, downhill between the volcano and Lake Kivu.

Overhead shot of Goma looking at Nyiragongo and neighboring volcanoes. Photo courtesy Acquire Chiara Congo. http://www.acquachiaracongo.it/en/goma.php

The volcanoes are located on the eastern border of the Democratic Republic of the Congo and impact neighbors living in Rwanda.

The volcanic field is at the southern end of the Virunga National Park (Parc National des Virunga), the first national park in Africa, created by the King of Belgium in 1925 to protect the mountain gorillas living in the forests of the Virunga Mountains.  Poaching is a significant problem today, as are rolling civil wars over the last half century.  It is the civil wars that have made it difficult to study the volcanoes to the level they deserve.  British oil company SOCO is also interested in oil exploration in the park.

Map of Virunga National Park in DR Congo. Lake Kivu, Goma and the two volcanoes are at the bottom of the drawing. https://visitvirunga.org/about-virunga/

Politics in the region has been particularly bloody over the last half century.  800,000 died in Rwanda in 1994.  Since 1960, there have been at least eight civil wars, rebellions, crisis and conflicts in the Democratic Republic of the Congo killing millions.  This sort of rolling violence makes it difficult to sustain an extended scientific study of the volcanoes and the geology of the greater rift valley.

There are a small number of visitors who fly into Rwanda and then on into Goma for hiking trips on the volcanoes and into the park to see the mountain gorillas.  A few of the travel blogs warn that photography may be hindered by local police demanding permits and then handing out fines when no permits are produced.  Attempts to get permits are generally unsuccessful, so have some available cash.

Goma was a small town of 50,000 in 1977.  Its population swelled to over a million mostly due to the violence in the surrounding countryside on both sides of the border.

Enhanced view of Nyiragongo and Nyamuragira from the south with Goma and Lake Kivu in the foreground. Image courtesy Atlas Obscura. https://www.atlasobscura.com/places/lava-lake-nyiragongo-volcano

Nyiragongo

The Nyiragongo volcanic field is surrounded by neighboring volcanic fields of Nyamuragira to the north and west, seven volcanoes including Karisimbi and Mikeno to the east, and Lake Kivu to the south.

Nyiragongo is a steep-sided stratovolcano that has the fastest, most fluid lava known in the world.  It has the largest active lava lake known in the world.  The lake catastrophically drained via a flank eruption in 1977, flowing downhill into neighboring Goma and on into Lake Kivu.  The 2002 eruption flowed into Goma, inundating part of it.  The volcano is 3,470 m high.  It is on the list of Decade Volcanoes, particularly deadly and dangerous volcanoes.

Active lava lake in the floor of Nyiregongo crater. Photo courtesy Photovolcanica. http://www.photovolcanica.com/VolcanoInfo/Nyiragongo/Nyiragongo.html

The current lake is surrounded by an elevated ring or dike.  Lava periodically overtops it and flows into the surrounding caldera floor.

Lava is called Foidite, very fluid, low viscosity, low silica content, high content of alkali feldspar minerals.  Related to phonolites.  Alternate names are nepheline, melilite, and melilite – nepheline series based on the type of crystalline inclusions from fractionalization at depth.  Because of the combination of steep sides and fluid lavas of the volcano, flow speeds downhill approach 100 km/hr, making it difficult for local wildlife and people to escape lava flows from the flanks.

Lava overflowing rim of lava lake at night. Photo courtesy Smithsonian Global Volcanism Program. https://volcano.si.edu/volcano.cfm?vn=223030

A National Geographic video of Peter Carsten’s trip to Nyiragongno from 2010 follows.  It is quite long at 0+15 but well worth your time to view.

https://www.youtube.com/watch?v=tlIOcRycG-g

Like Kilauea, the depth of the lava lake changes based on the supply of magma from below.  Average depth is estimated at 600 m.

The main crater has several platforms created by former lake levels.  The uppermost platform, some 200 m below the top of the volcano was created by lake levels in 1972.  The next one down, some 40 m lower was created by the lava lake level in 1995 which was drained in the 2002 eruption.  Current floor of the caldera is perhaps 430 – 400 m below the top of the volcano.

Photo of crater of Nyiragongo showing benches of previous high lake levels within the crater. Current lake is at bottom right. Photo courtesy Miles Beyond blog. https://milesbeyond.it/en/location/nyragongo-into-the-inferno/

During periods of renewed activity, spatter cones are occasionally formed, which progressively fill the main crater.  This took place in 1982 and 1994 – 1995.

The magma plumbing system is not well constrained, with at least two magma chambers suspected.  The closest to the surface is 1 – 4 km below the surface and appears to be directly connected to the lava lake.  It is fed by a second chamber 10 – 14 km deep.  These are in turn fed by partial melting 80 – 150 km deep.  There are at least two dikes below the volcano.  The first some 2 km in depth is associated with the 2002 eruptive fissure.  There is a second deeper dike 40 km long that stretches southward to Lake Kivu and for an additional 20 km below it.  It sits 3 km below Goma.

Nyamuragira volcano. Photo courtesy NASA Earth Observatory. https://earthobservatory.nasa.gov/Features/VolcanoSensorWeb/

 

Nyamuragira

Nyarumagira is Africa’s most active volcano erupting 34 times since 1882.  It is a massive basaltic shield volcano with a volume of perhaps 500 km3.  Lava flows cover 1,500 km2.  Lavas are high-potassium basalt.  It is a 3,058 high mountain with a smallish 2 km caldera on top.  There was a lava lake active since 1921 which drained in 1938 during a major flank eruption.  A new lava lake formed in 2014.  It is a prodigious producer of SO2.

Historic lava flows extend as far as 30 km from the summit, all the way to Lake Kivu.

Summit caldera of Nyamuragira. Ikonos photograpy taken July 2005 showing recent lava flows. Photo courtesy NASA Earth Observatory. https://earthobservatory.nasa.gov/Features/VolcanoSensorWeb/

A strong eruption began in January 2010, the first since 2006.  It produced extensive lava flows on its flank.  Initial eruption began in the caldera from the pit crater and moved to a 600 m long fissure on the SSE flank of the shield, 1.5 km from the caldera rim.  This is not an uncommon progression of a basaltic shield eruption.  There was no noticeable increase in seismicity before the eruption.  Volcanic and tectonic earthquakes started simultaneously with the appearance of lava at the surface.  Lava from this eruption eventually traveled 15 km from the vent and covered 17.5 km2.  Satellite imagery showed a large SO2 plume downwind from the eruption.  This volcano is one of the most prolific producers of SO2 worldwide with the gas pushing lava fountaining during eruptions.

Lava flow from 2011 – 2012 flank eruption of Nyamuragira. Photo courtesy Photovolcanica. http://www.photovolcanica.com/VolcanoInfo/Nyamuragira/Nyamuragira.html

Lavas from the 1938 – 2010 eruptions cover more than 430 km2 of the Nyamuragira lava flow field.  Acid rains and tephra falls have plagued crops and urban zones in the area.

Photovolcanica writes that this volcano also has over 100 parasitic cones on its flanks.

The plumbing system beneath this volcano suggests a deep reservoir at 25 km which feeds a shallow reservoir at 4 km.  Eruptions are generally fed from the shallow reservoir, though flank eruptions can be fed directly from the deeper reservoir.  A dike-like conduit is present beneath the upper SE flank of the volcano.

Lake Kivu looking north. Volcanoes and Goma are on the north end of the lake (top). Photo courtesy NASA Goddard. http://www.geo.arizona.edu/geo5xx/geos577/projects/kayzar/index.html

 

Lake Kivu

Lake Kivu is called one of the African Great Lakes.  It sits on the border between Congo and Rwanda and straddles the western branch of the East African Rift.  It empties into the Rizizi River which in turn flows south into Lake Tanganyika.  It is the highest point of the East African Rift Valley, 1,500 in elevation.

It has a total surface area of 2,700 km2.  The greatest depth is 475 m and a mean depth of 220 m.  Because it is a lake situated on a rift valley, it is stratified, that is, layered with layers of differing CO2 content.  CO2 is pumped into the lake by hot springs on the bottom of the lake.  The hot springs also introduce heat into the cold bottom layer of the lake.

It periodically suffers a catastrophic overturn, called a limnic eruption, which simultaneously releases methane produced in the bed of the lake by organic decomposition and CO2 injected from the volcanic rocks underlying the lake.  Nobody has seen a limnic eruption driven by both methane and CO2 out of Lake Kivu yet. Speculation is that the overturn is driven by methane release which may or may not ignite as it breaches the surface, closely followed by massive release of CO2.  Sediment records suggest 5 eruptions over the last 6,000 years causing massive death of local animals.  Increasing methane levels in the lake are thought to increase the danger until the point something triggers an overturn / eruption.

Schematic of stratified Lake Kivu. Drawing courtesy Hydragas.net via Strange Sounds. https://strangesounds.org/2017/04/risk-catastrophic-explosion-lake-kivu-drc-rwanda-oil-exploration-lake-kivu-video.html

Local authorities take the threat very seriously as there are over 2 million people living on the shores of the lake.  As the bottom layer of lake water approaches saturation with methane and CO2, any disturbance in the water column (earthquake, landslide, eruption, or other external disturbance) may be sufficient to trigger an overturn.  There is no small amount of fear that such a disturbance will cause an eruption.

Lake Kivu methane extraction unit. Photo courtesy MIT Technology Review. April 2015. https://www.technologyreview.com/s/536656/lake-kivus-great-gas-gamble/

The lake is estimated to hold 60 billion m3 of methane and 300 billion m3 of CO2.  There is an ongoing effort to extract methane and use it to produce electrical power for eastern Congo and Rwanda.  The first phase of the project will produce 25 MW.  There is another extraction / generation plant on the Rwandan side of the lake that should add another 50 MW of electrical output.  The Rwandan government has operated a gas-fired pilot plant since 2008.

There is sufficient gas to power up to 100 MW in perpetuity, perhaps 50% of Rwanda’s total electrical generation capacity today.

Schematic of 2002 fissure eruption from Nyiragongo. Photo courtesy Smithsonian GVP April 2002. https://volcano.si.edu/showreport.cfm?doi=10.5479/si.GVP.BGVN200204-223030

Nyiragongo Eruptions

Nyiragongo is currently active.  The lava lake is some 250 m below the level of the 1994 lava lake.  One of the ongoing problems is localized CO2 toxic gas releases.  The deadly releases are locally referred to as “mazuku.”  The gas seeps from fumaroles and cracks in the flanks of the volcano.  A new vent opened on the flank in March 2016.  It was accompanied with reports of rumbling leading to fears of an impending flank eruption.

The most recent large eruption was in 2002.  It killed 147 people.  Lava flows traveled through the neighboring city of Goma, destroying 13% of it.  The eruption displaced 12 – 15,000 homes and hundreds of thousands of people.  The lava flows entered the lake, and posed a threat to release CO2 and methane gas stored in the lake.  Lava from the 2002 eruption is thought to be residual lava from the lava lake activity in the mid-1990s.  It was followed by a fresh batch erupted from fissure vents.  The eruption was followed by unusual tectonic activity with over 100 earthquakes greater than 3.5 Richter during the 5 days following the eruption.  There was also land subsidence at Goma and up to 10 km south along the northern lake shore.

Nyiragongo lava flow through Goma 2002 eruption. Photo courtesy Pedro Ugarte, Getty Images. http://www.gettyimages.com/detail/news-photo/goma-resident-watches-lava-flowing-at-goma-airport-18-news-photo/51351257#goma-resident-watches-lava-flowing-at-goma-airport-18-january-2002-picture-id513512

The days following the 2002 eruption in Goma and along the northern shore of Lake Kivu had several post-eruption events.  There were measurable hydrocarbon odors in areas up to 800 m from lava flows.  Levels of CO2 and methane were elevated.  Methane concentrations in the air of a few percent were found in open air.  In some cases, the gas discharge was violent with gas explosions that destroyed concrete pavements.  The burst sites suggest a subsurface methane source that may have been from Lake Kivu or underground reservoirs cracked open by post-eruption earthquakes under the volcanic layers.    Local residents of Himbi reported ccrawfish jumping out of the lake, dead fish, and rotten egg smells (H2S), discolored water, bubbling water, and breathing difficulties.  Geologists suggest fractures beneath Goma dangerously close to Lake Kivu.

Even after the lavas have cooled, they are still dangerous as they degas CO2 which tends to pool up in low spots, asphyxiating the occasional passing child.

Schematic of plumbing system for Nyiragongo and 2002 eruption. Note that the lava chambers and dikes are not properly depicted. Image courtesy The Extinction Protocol, March 2011. https://theextinctionprotocol.wordpress.com/2011/03/16/nyiragongo-volcano-ticking-closer-to-catastrophe/

The 1977 eruption drained the lava lake in perhaps 30 minutes.  Death toll downhill was officially listed at 70, though there are many reports of much higher numbers, perhaps in the thousands.  At the time of the eruption, the lava lake was at the maximum depth recorded, 3,260 m.  The breach in the crater wall released an estimated 3 – 5 million m3 (.003 – .005 km3).  Lava poured to the north, west and south of the volcano, reaching neighboring Goma within 20 minutes.  Most of the volume of the lava drained into the surrounding forests.  The 1977 eruption was preceded by formation of a new cone, Maurara on the flanks of Nyamuragira.

The lava lake was first confirmed in 1948, though it was suspected for a time before confirmation.  It has emptied and refilled multiple times since.

There have been 84 eruptions from Nyiragongo since the 1882.

Pyroclastic cone source of 2011 – 2012 Nyamuragira flank eruption. Lava flows are to the left off the photo. Photo courtesy Volcano Discovery. https://www.volcanodiscovery.com/photos/nyamuragira/22-25jan12-activity/image14.html

Nyamuragira Eruptions

Most of the eruptions from Nyamuragira are from fissures on the flanks.  It is not uncommon for a typical basaltic shield eruption start in the crater / caldera on top of the volcano and progress to fissures on the flanks.  Most eruptions release clouds of SO2 which damage surrounding plant and wildlife.  The gasses also

The most recent eruption was detected via satellite thermal imagery in early 2017.

Nyamuragira had a lava lake that was active 2014 – 2016.  The depth of the lake was estimated at 500 m.

The last major eruption was in 2011 – 2012.  Lava fountains up to 400 m high started along a 1 km long fissure.  This was described as the largest eruption in 100 years.

SO2 emissions from Nyamuragira eruption 2006. Satellite image courtesy NASA Earth Observatory. https://earthobservatory.nasa.gov/IOTD/view.php?id=7189

The 2010 eruption produced extensive lava flows that traveled 25 km SW to Lake Kivu, 22 km N, and 35 km to the NNE.  The lava flows traveled through relatively uninhabited forests and jungle.

The July 1994 eruption was on the west flank and generated ash, Pele’s hair, lava fountains and flows.  Pele’s hair fell 12 km from the volcano.

There were at least 20 eruptions between the 1912 and 1994 eruptions.

The 1912 – 1913 eruption is the only one that caused fatalities.

The majority of eruptions are in the VEI 1 – 2 range with 7 VEI 3 eruptions in the 20^th Century.

East Africa Rift System schematic. Region labeled Kenya Dome is actually Tanzania Craton. http://slideplayer.com/slide/10533026/

Tectonics

Nyiragongo and its neighboring volcanoes are located along the western arm of the East African Rift, active since 22 – 25 Ma.  Africa is separating into two plates, tentatively called the Somali (east) and Nubian (west) Plates.  The new oceanic basin is expected to form along the line of lithospheric rupture in perhaps 10 Ma.

The rupture of east Africa by the East African Rift System (EARS) started roughly 35 Ma in Kenya.  It proceeded in two phases, the first from 35 – 12 Ma, centered mostly in Ethiopia and extending as far south as Kenya.  The second created the east and west branches, the Kenya Dome, and reactivated failed continental rifts in central and southern Africa as old as 300 Ma.

As the rifts propagated north to the Afar triple junction, a large volume of trap basalts erupted 28 – 25 Ma in Ethiopia.  This is thought to be related to a plume under the Afar which started rifting 25 Ma.  Rifting and uplift progressed in Ethiopia 25 – 21 Ma.

Current configuration of East African Rift System. Image courtesy Structural Geology Blog. http://structuralgeologyof.weebly.com/extensional/the-east-african-rift-system

By 15 Ma, volcanism filled up rift valleys in northern Kenya.  This was the earliest start of rifting on the western branch.  Eastern branch rifting continues.  Rifting offshore east Africa is assumed based on seismic coverage.

Around 12 Ma, there was another round of flood basalt activity in Ethiopia and Kenya.  The Kenya Dome uplift started.  Subsidence in various rift basins began.

8 Ma rifting progressed on the western arm and the Virunga Volcanic Complex began activity.  Block faulting on the eastern arm around Lake Tanganyika began.  Offshore rifting began.  There is little volcanic activity in the western branch older than 10 Ma.  The branches of the rift stretch around the Tanzanian craton which has been uplifted over the last 8 Ma.

5 Ma years ago, the main phase of EARS phase 2 rift subsidence began.  Major subsidence took place in in Ethiopia and the Afar.  The east and west branches of the rift system met north and south around the uplift section of the East African Plateau (Tanzanian Craton) centered on Lake Victoria in northern Tanzania, western Kenya, Southern Uganda, Rwanda and Burundi.

Most of the current rifting activity south of Kenya and offshore is relatively recent, not older than the last 8 Ma.  Major rifting activity is propagating southward over the last 5 Ma, accelerating over the last couple million years.

The region around the volcanoes is uplifted over 1.6 km above sea level, leading to no small amount of speculation that the rifting and volcanic activity, particularly the highly fluid magma, is driven by a mantle plume beneath the region.  The plume is over 500 km wide.  The difference between lavas from Nyiragongo and Nyamuragira is explained by location of the plume, with Nyiragongo tapping materials directly from the main body of the plume while the other volcanoes are fed with mixed magmas from the edge of the plume.

Virunga volcanic field. Volcanoes to the east of Nyiragongo are from west to east: Mikeno, Karisimbi, Visoke, Muside, Sabinyo, Gahinga and Muhabura. Image courtesy Satellite Image Corp. https://news.satimagingcorp.com/2010/01/1277/

If this speculation is correct, it is not beyond the realm of possibility that the region around Nyiragongo is ripe for a large igneous province outbreak as the rifting progresses.  The Deccan Traps are constructed of nepheline basalts similar to oceanic island basalts and thought to be tied to the action of a mantle plume.

Spreading rate of this portion of the rift is 2.8 mm/yr.  The rift here is marked by a half-graben with a normal fault on the west and no clear bounding fault on the eastern side.

Lava flow field for Nyamuragira. Photo courtesy Lyell Special Publications Collection. http://sp.lyellcollection.org/content/380/1/39

Conclusions

Nyiragongo, Nyamuragira, Lake Kivu and the western portion of the East Africa Rift System (EARS) appear to be one of the more dangerous geologic locations in Africa.  We have two massive active volcanoes that produce large amounts of highly fluid lavas and volcanic gasses.  We have a 2,700 km2 stratified lake that periodically overturns, releasing methane and CO2 on the surrounding countryside.  We have a million people living between the lake and the volcano, and another million living along the lake shore.  Vents and other hot springs are busily pumping heat and CO2 into the bottom layer of the lake while the decay of biological matter produces large amounts of methane which dissolve into the water column.

There is uplift of the region along the growing, rift with speculation that a mantle plume may be responsible for the uplift.  This speculation is supported by the difference in lava composition between Nyiragongo and Nyamuragira, and the similarity of Nyiragongo lavas to other flood basalt lavas (Deccan Traps).  And the rift system has been quite active over the last couple of years.

Add to all that, the unstable political situation on both sides of the border, and you have a recipe for a real dangerous and deadly situation.

Yet the East African Rift System is the birthplace of humanity a few million years ago.  We appear to have survived millennia of flood basalts, volcanic action, uplift, and rifting quite well.  Perhaps we will continue to do so in the future.

False color image of Nyiragongo and Nyamuragira showing lava lake and flank eruption from Nyamuragira in 2011. Photo courtesy NASA Earth Observatory. https://earthobservatory.nasa.gov/IOTD/view.php?id=76862

Additional Information

https://volcano.si.edu/volcano.cfm?vn=223030

https://volcano.si.edu/volcano.cfm?vn=223020

https://www.atlasobscura.com/places/lava-lake-nyiragongo-volcano

http://volcano.oregonstate.edu/most-dangerous-volcano-world-tale-nyiragongo

https://www.volcanodiscovery.com/nyiragongo.html

http://www.virunga-volcanoes.org/volcanoes/nyiragongo/

https://volcano.si.edu/showreport.cfm?doi=10.5479/si.GVP.BGVN201008-223020

https://www.unops.org/english/News/UNOPS-in-action/Pages/UNOPS20-Monitoring-volcanoes-in-the-Democratic-Republic-of-the-Congo.aspx

http://www.science20.com/news_releases/why_nyiragongo_volcano_lava_different_others

https://www.nationalgeographic.com/adventure/destinations/africa/democratic-republic-congo/nyiragongo-volcano-hike/

http://www.photovolcanica.com/VolcanoInfo/Nyiragongo/Nyiragongo.html

https://www.technologyreview.com/s/536656/lake-kivus-great-gas-gamble/

http://www.uta.edu/ees/faculty/basu/assets/publications/earlyandlatealkaliplumes.pdf

http://www.photovolcanica.com/VolcanoInfo/Nyamuragira/Nyamuragira.html

http://onlinelibrary.wiley.com/doi/10.1029/2006JB004762/full

http://onlinelibrary.wiley.com/doi/10.1029/2011GC003699/full

http://sp.lyellcollection.org/content/380/1/39.short

http://onlinelibrary.wiley.com/doi/10.1029/2011JB008257/full

http://www.mantleplumes.org/WebDocuments/Macgregor2015.pdf

http://www.univie.ac.at/ajes/archive/volume_107_1/ring_ajes_107_1.pdf

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