Natural time analysis is a
statistical method
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
applied to analyze
complex time series and
critical phenomena
In physics, critical phenomena is the collective name associated with the
physics of critical points. Most of them stem from the divergence of the
correlation length, but also the dynamics slows down. Critical phenomena include scaling relatio ...
, based on event counts as a measure of "time" rather than the
clock time.
[Varotsos, Sarlis & Skordas 2011 (book), preface and chapter 2] Natural time concept was introduced by
P. Varotsos, N. Sarlis and E. Skordas in 2001.
Natural time analysis has been primarily applied to
earthquake prediction
Earthquake prediction is a branch of the science of seismology concerned with the specification of the time, location, and magnitude of future earthquakes within stated limits, and particularly "the determination of parameters for the ''next'' s ...
/
nowcasting and secondarily to
sudden cardiac death
Cardiac arrest is when the heart suddenly and unexpectedly stops beating. It is a medical emergency that, without immediate medical intervention, will result in sudden cardiac death within minutes. Cardiopulmonary resuscitation (CPR) and possib ...
/
heart failure
Heart failure (HF), also known as congestive heart failure (CHF), is a syndrome, a group of signs and symptoms caused by an impairment of the heart's blood pumping function. Symptoms typically include shortness of breath, excessive fatigue, a ...
and
financial market
A financial market is a market in which people trade financial securities and derivatives at low transaction costs. Some of the securities include stocks and bonds, raw materials and precious metals, which are known in the financial markets ...
s.
Natural time characteristics are considered to be unique.
Etymology
"Natural time" is a new view of time introduced in 2001
that is not continuous, in contrast to conventional time which is in the continuum of
real number
In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real ...
s, but instead its values form countable sets as
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''Cardinal n ...
s.
Definition
In natural time domain each event is characterized by two terms, the "natural time" , and the
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
. is defined as , where ''k'' is a natural number (the -th event) and is the total number of events in the time sequence of data. A related term, , is the ratio , which describes the fractional energy released. The term is the variance in natural time:
:
: where
and
Time reversal
Time reversal, in contrast to clock time, is applicable when studying the approach of a system to criticality with natural time analysis. Living systems for example are considered to operate far from
equilibrium as there is flow of energy crossing their boundaries, in contrast to deceased organisms where inner driving forces are absent. While time irreversibility is a fundamental property of a living system, the state of death is more time reversible by means of energy flow across the system's boundaries. Thus a critical state of a system can be estimated by applying natural time analysis upon calculating the
entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
upon both normal time flow and time reversal and studying the difference of the two results.
Applications
Seismology
Earthquake nowcasting
In
seismology
Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other ...
, nowcasting is the estimate of the current dynamic state of a seismological system.
It differs from forecasting which aims to estimate the probability of a future event
but it is also considered a potential base for forecasting.
Nowcasting is based on the
earthquake cycle
The earthquake cycle refers to the phenomenon that earthquakes repeatedly occur on the same fault as the result of continual stress accumulation and periodic stress release. Earthquake cycles can occur on a variety of faults including subduction ...
model, a recurring cycle between pairs of large earthquakes in a geographical area, upon which the system is evaluated using natural time.
Nowcasting calculations produce the "earthquake potential score", an estimation of the current level of seismic progress.
When applied to seismicity, natural time has the following advantages:
# Declustering of the aftershocks is not necessary as natural time count is evenly valid in any case of aftershock or backgroung seismicity.
# Natural time statistics do not depend on the level of seismicity, given that the
b value does not significantly vary.
Typical applications are: great global earthquakes and
tsunami
A tsunami ( ; from ja, 津波, lit=harbour wave, ) is a series of waves in a water body caused by the displacement of a large volume of water, generally in an ocean or a large lake. Earthquakes, volcanic eruptions and other underwater explo ...
s,
aftershocks and
induced seismicity
Induced seismicity is typically minor earthquakes and tremors that are caused by human activity that alters the stresses and strains on Earth's crust. Most induced seismicity is of a low magnitude. A few sites regularly have larger quakes, such a ...
,
induced seismicity at
gas field
A petroleum reservoir or oil and gas reservoir is a subsurface accumulation of hydrocarbons contained in porous or fractured rock formations.
Such reservoirs form when kerogen (ancient plant matter) is created in surrounding rock by the presence ...
s,
seismic risk to global megacities,
studying of
clustering of large global earthquakes,
etc.
Earthquake prediction
Natural time analysis has been initially applied to
VAN method
A van is a type of road vehicle used for transporting goods or people. Depending on the type of van, it can be bigger or smaller than a pickup truck and SUV, and bigger than a common car. There is some varying in the scope of the word across ...
in order to improve the accuracy of the estimation of the time of a forthcoming earthquake that has been indicated to occur by seismic electric signals (SES). The method deems SES valid when κ
1 = 0.070. Once the SES are deemed valid, a second NT analysis is started in which the subsequent seismic (rather than electric) events are noted, and the region is divided up as a
Venn diagram
A Venn diagram is a widely used diagram style that shows the logical relation between set (mathematics), sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple ...
with at least two seismic events per overlapping rectangle. When κ
1 approaches the value κ
1 = 0.070 for the candidate region, a critical seismic event is considered imminent, i.e. it will occur in a few days to one week or so.
[Varotsos, Sarlis & Skordas 2011 (book), chapter 7]
Cardiology
Natural time analysis has been experimentally used for the diagnosis of
heart failure
Heart failure (HF), also known as congestive heart failure (CHF), is a syndrome, a group of signs and symptoms caused by an impairment of the heart's blood pumping function. Symptoms typically include shortness of breath, excessive fatigue, a ...
syndrome
as well as identifying patients at high risk for
sudden cardiac death
Cardiac arrest is when the heart suddenly and unexpectedly stops beating. It is a medical emergency that, without immediate medical intervention, will result in sudden cardiac death within minutes. Cardiopulmonary resuscitation (CPR) and possib ...
,
even when measuring solely the heart rate, either using
electrocardiography
Electrocardiography is the process of producing an electrocardiogram (ECG or EKG), a recording of the heart's electrical activity. It is an electrogram of the heart which is a graph of voltage versus time of the electrical activity of the hear ...
or far more inexpensive and portable equipment (i.e.
oximeter
Pulse oximetry is a noninvasive method for monitoring a person's oxygen saturation. Peripheral oxygen saturation (SpO2) readings are typically within 2% accuracy (within 4% accuracy in 95% of cases) of the more accurate (and invasive) reading of ...
).
Economy
Due to similarities of the dynamic characteristics between earthquakes and financial markets, natural time analysis, which is primarily used in seismology, was chosen to assist in developing winning strategies in financial markets, with encouraging results.
References
Bibliography
*{{Cite book
, last1 = Varotsos , first1 = Panayiotis A.
, last2 = Sarlis , first2 = Nicholas V.
, last3 = Skordas , first3 = Efthimios S.
, title=Natural time analysis : the new view of time ; Precursory seismic electric signals, earthquakes and other complex time series
, date=2011
, publisher=Springer
, isbn=978-3-642-16449-1
, location=Berlin
, oclc=755081829
Statistical analysis