QUANTIFICATION OF TSUNAMIS:
A REVIEW
GERASSIMOS A.
PAPADOPOULOS
National Observatory of
Abstract
The
efforts made since 1923 to quantify tsunami size in terms of either intensity
or magnitude are critically reviewed. The existing 6point intensity scales
need a drastic revision and replacement by modern, detailed, 12point scales in
analogy to earthquake intensity scales. A new tsunami intensity scale proposed
by Papadopoulos and Imamura [1] seems to meet these requirements. Among the
existing tsunami magnitude scales even the most sophisticated ones need either
better calibration of formulas based on more wave height data or significant
improvement in the tsunami source energy calculation.
1.
Introduction
Efforts
towards a quantification of tsunamis started about seventyfive years ago by the
pioneering work of Sieberg [2, 3] who defined
the first tsunami intensity scale. However, the tsunami quantification is still
a puzzling aspect in the tsunami research since the several scales proposed to
measure tsunami size often either are confusing as for the quantity they
represent, that is intensity or magnitude, or lie under serious difficulty in
their applicability. After several attempts made by many researchers to
quantify tsunamis in terms of either intensity or magnitude it is extremely
useful to reexamine critically not only the various definitions given but also
their practical implementation. Particularly it is shown the general need for (1)
to develop detailed, pure tsunami intensity scales, established on standard
principles and on modern, well  elaborated criteria, and (2) to improve
drastically calibration of magnitude scales.
2.
Intensity and Magnitude Scales of Tsunami
The
earthquake magnitude is an objective physical parameter that measures either
energy radiated by, or moment released in, the earthquake source and does not
reflect macroseismic effects. On the contrary, the earthquake intensity is a
rather subjective estimate of the macroseismic effects. In every earthquake
event only one magnitude or moment on a particular scale corresponds. However,
every earthquake is characterized by different intensities in different
locations of the affected area.
Okal [4] showed that source depth and focal geometry
plays only a limited role in controlling the amplitude of the tsunami, and that
more important are the effects of directivity due to rupture propagation along
the fault and the possibility of enhanced tsunami excitation in material with
weaker elastic properties, such as sedimentary layers. Therefore, a tsunami can
be considered as a particular case of seismic wave and problems related to
tsunami quantification could be approached in analogy to seismology.
Sieberg [2, 3] is very likely the first to present a
6point tsunami intensity scale which, in analogy to earthquake intensity
scales, was based not on the measurement or estimation of a physical parameter,
e.g. the wave height, but it was established on the description of tsunami macroscopic
effects, like damage etc. Ambraseys [5] published a modified version of
Sieberg’s scale known as SiebergAmbraseys tsunami intensity scale. In the
Japanese tsunami literature one may find a long tradition in the effort for tsunami
quantification. Imamura [6, 7] introduced and Iida [8, 9] and Iida [10]
developed further the concept of tsunami magnitude, m, defined as
m = log_{ 2} H _{max}_{ } (1)
Where H is
the maximum tsunami wave height (in m) observed in the coast or measured in the
tide gages. Practically, the socalled Imamura – Iida scale is a 6point scale
ranging from –1 to 4 giving the impression of a rather intensity than a
magnitude scale. However, m does not
estimate effects but it measures by definition H _{max}_{ that} is a physical quantity. In this
sense it may represent magnitude in a primitive way since it does not calibrate
the wave height with the distance. In his attempt to improve the Imamura –
Iida’s definition, Soloviev [11] proposed to define tsunami intensity, i_{S,} by
i_{S}_{ }= log_{
2} √2 ( H ) (2)
where H (in
m) is the mean tsunami height in the coast. However, this is still a primitive
magnitude scale since it is also based on the physical quantity H. Tsunami magnitude M _{t} [12, 13, 14, 15] or m [16] was defined by the general form
M _{t}_{ }= a log_{10} H + b log Δ + D (3)
where H =
maximum single (crest or trough) amplitude of tsunami waves (in m) measured by
tide gages, Δ is the distance (in km) from the earthquake epicenter
to the tide station along the shortest oceanic path (in km), and a, b, D are constants. Expression (3) is
similar to the
ML = 2 ( log_{10} E – 19) (4)
where E is
the tsunami potential energy (in ergs). Definition of ML is in close analogy to the Kanamori’s [19] definition of moment
magnitude
M_{w }= 2/3 (log_{10} M_{0} – 16.1) (5)
as well as to the mantle magnitude [20]
M_{m }= log M_{0}
– 20
Where M_{0 }is
the seismic moment.
A particular scale measuring tsunami size is that
proposed by Shuto [21] who considered it as an intensity scale:
i = log _{2} H (6)
Where H is
the local tsunami height (in m). Obviously by definition it is still a
magnitude scale. However, in order to use it as an intensity scale for the tsunami
damage description, Shuto [21] proposed to define H according to its possible impact. A 6point classification of
tsunami effects ranging from 0 to 5 is tabulated for the description of the
expected damage or destruction as a function of H.
3. Possibilities
and Limitations of the Tsunami Size Scales
All the tsunami magnitude scales that are based on
measurements of tsunami wave heights at coastlines, from the primitive ones,
like those of Imamura  Iida and Soloviev, to the more recent and more
sophisticated scales of Abe and Hatori are very sensitive to local effects like
coastal topography, nearshore bathymetry, refraction, diffraction and
resonance. However, better calibration of formulas, based on more tidegage and
measured in the field wave heights, may drastically improve the applicability
of such scales for the tsunami magnitude determination in the future.
TABLE 1. Time
evolution of tsunami size scales proposed.
Tsunami Scale 
Type of Tsunami 
Analogy to Earthquake Scales 
Intensity
Scales 


Sieberg [2, 3] 
primitive 6point
intensity scale 
early intensity scales 
Ambraseys
[5] 
improved 6point intensity
scale 
improved intensity scales 
Shuto [21] 
developed 6point
intensity scale 
developed intensity scales 
Papadopoulos and Imamura [1] 
new 12point intensity
scale 
new 12point intensity scale 
Magnitude
Scales 


Imamura –Iida
(40’s, 50’s and 60’s) 
primitive magnitude scale 
local Richter magnitude scale 
Soloviev
[11] 
primitive magnitude scale 
local Richter magnitude 
Abe [12, 13,
14, 15] 
magnitude scale 
surfacewave magnitude scale 
Murty –Loomis [18] 
magnitude scale 
moment – magnitude scale 
On the other hand, the MurtyLoomis tsunami magnitude,
which is directly based on the total tsunami energy, E, at the source, provides a wider magnitude range but is not
easily applicable at the moment because of serious difficulties involved in the
calculation of energy E . Better
esimates of tsunami energy in the future certainly will result in the magnitude
determination of a more and more increasing number of tsunamis. Table 1
summarizes a classification of the several tsunami size scales proposed and
their analogy to earthquake size scales.
The tsunami intensity scale proposed by Sieberg [2, 3]
and modified by Ambraseys [5] is a 6point scale constructed in such a way that
its divisions are not detailed enough and certainly do not incorporate the
experience gained from the impact of large destructive tsunamis occurring in
the last decades. Shuto’s [21] tsunami scale is by definition a magnitude scale
because H is simply a physical
parameter. On the other hand, its description of tsunami impact is a 6point
tsunami intensity scale, ranging from 0 to 5, the division of which, however,
is a function of H. Therefore, the
scale under discussion is a mixture of magnitude and intensity. Apparently,
Shuto [21] tried rather to produce a predictive tool that describes expected
tsunami impact as a function of H, than
to create a new tsunami intensity scale describing tsunami effects
independently from physical parameters that control the type and extent of the
effects. The overall approach is a useful tool for the tsunami size
quantification.
The lack of a pure tsunami intensity scale with a
detailed description of its divisions that incorporate recent experience from
large, catastrophic tsunamis of the Pacific Ocean, creates serious problems in
the standardization of the estimation of the tsunami effects, as well as in the
comparisons of the effects from site to site for a given tsunami and from case
to case for different tsunami events. Following the long seismological experience,
Papadopoulos and Imamura [1] proposed the establishment of a new tsunami
intensity scale based on the next principles: ( a ) independency from any
physical parameter ; ( b ) sensitivity,
that is incorporation of an adequate number of divisions (or points) in order
to describe even small differences in tsunami effects; (c) detailed description of each intensity division by taking
into account all possible tsunami impact on the human and natural environment,
the vulnerability of buildings and other engineered structures on the basis of
recent experiences gained from large, catastrophic tsunamis of the Pacific
Ocean. The new tsunami intensity scale incorporates twelve divisions and is
consistent with the several 12point seismic intensity scales established and
extensively used in
4. Conclusions
The
present review implies that the time evolution of the tsunami quantification
follows the steps made for the earthquake quantification with a time shift of about
30 years. For a drastic improvement of the tsunami quantification some further,
drastic developments are needed. In the field of tsunami intensity scaling, new,
detailed and sensitive scales are needed with the intensity to be estimated independently
from the wave heights or any other physical parameter observed. The intensity
scale proposed recently by Papadopoulos and Imamura [1] seems to meet these
requirements. As for the tsunami magnitude scales that are based on
measurements of wave heights in tidegages, there is a general need for better
calibration of the formulas in use which strongly depends on the improvement of
both the quality and quantity of instrumental data collected. Tsunami magnitude
scales based on the energy at the source need improvement of the methods in use
for the energy calculation that is improvement of our understanding of the
tsunami generation mechanisms.
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96.
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N.N. (1962). Data for the investigation of seismic sea waves in the
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Appendix: A New Tsunami Intensity
Scale
The new tsunami intensity scale proposed by Papadopoulos and Imamura [1]
incorporates twelve divisions and is consistent with the several 12grade seismic
intensity scales established and extensively used in
I. Not felt
Not felt even under the most favourable
circumstances.
No effect. No damage.
II. Scarcely felt
Felt by few people on board in small vessels. Not observed in the coast.
No effect. No damage.
III. Weak
Felt by most people on board in small vessels. Observed
by few people in the coast. No effect. No damage.
IV. Largely observed
Felt by all on board in small vessels and by few people on board in large
vessels. Observed by most people in the coast. Few
small vessels move slightly onshore. No damage.
V. Strong
Felt by all on board in large vessels and observed by all in the coast.
Few people are frightened and run to higher ground.
Many small vessels move stronlgy onshore, few
of them crash each other or overturn. Traces of sand layer are left behind in
grounds of favourable conditions. Limited
flooding of cultivated land.
Limited flooding of outdoors facilities (e.g.
gardens) of nearshore structures.
VI. Slightly damaging
Many people are frightened and run to higher ground.
Most small vessels move violently onshore, or crash stronly
each other, or overturn.
Damage and flooding in a few wooden
structures. Most masonry
buildings withstand.
VII. Damaging
Most people are frightened and try to run in higher ground.
Many small vessels damaged. Few large vessels oscillate violently.
Objects of variable size and stability overturn and drift. Sand layer and
accumulations of pebbles are left behind. Few aquaculture rafts washed away.
Many wooden structures damaged, few are demolished or washed away. Damage of grade 1 and flooding in a few masonry buildings.
VIII. Heavily damaging
All people escape to higher ground, a few are
washed away.
Most of the small vessels are damaged, many are washed away. Few large
vessels are moved ashore or crashed each other. Big objects are drifted away. Errosion and
littering in the beach. Extensive flooding . Slight damage in tsunami control forest, stop drifts. Many
aquaculture rafts washed away, few partially damaged.
Most wooden structures are washed away or demolished. Damage
of grade 2 in a few masonry buildings. Most RC buildings sustain damage,
in a few damage of grade 1 and flooding is observed.
IX. Destructive
Many people are washed away.
Most small vessels are destructed or washed away. Many large vessels are
moved violently ashore, few are destructed. Extensive errosion and littering of the beach. Local ground subsidence. Partial destruction in tsunami
control forest, stop drifts. Most aquaculture rafts washed away, many partially
damaged.
Damage of grade 3 in many masonry buildings, few RC buildings suffer from
damage grade 2.
X. Very destructive
General panic. Most people are washed away.
Most large vessels are moved violently ashore, many are destructed or
collided with buildings. Small bolders from the sea
bottom are moved inland. Cars overturned and drifted. Oil spill, fires start. Extensive
ground subsidence.
Damage of grade 4 in many masonry buildings, few RC buildings suffer from
damage grade 3. Artificial embankments collapse, port water breaks damaged.
XI .
Devastating
Lifelines interrupted. Extensive fires. Water
backwash drifts cars and other objects in the sea. Big bolders
from the sea bottom are moved inland.
Damage of grade 5 in many masonry buildings. Few RC buildings suffer from damage grade 4, many suffer from damage grade 3.
XII. Completely devastating
Practically all masonry buildings
demolished. Most RC buildings
suffer
from at least damage grade 3.
Table
2. Possible correlation between the intensity domains, I, proposed here and the quantities H and i introduced in formula (5) by Shuto [21].
IV <1.0 0
VI 2.0 1
VIIVIII 4.0 2
IXX 8.0 3
XI 16.0 4
XII 32.0 5