Quadratic programming

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Quadratic_programming

Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a multivariate quadratic function subject to linear constraints on the variables. Quadratic programming is a type of nonlinear programming.

"Programming" in this context refers to a formal procedure for solving mathematical problems. This usage dates to the 1940s and is not specifically tied to the more recent notion of "computer programming." To avoid confusion, some practitioners prefer the term "optimization" — e.g., "quadratic optimization."

Problem formulation

The quadratic programming problem with n variables and m constraints can be formulated as follows. Given:

• a real-valued, n-dimensional vector c,
• an n×n-dimensional real symmetric matrix Q,
• an m×n-dimensional real matrix A, and
• an m-dimensional real vector b,

the objective of quadratic programming is to find an n-dimensional vector x, that will

where x^T denotes the vector transpose of x, and the notation Ax ⪯ b means that every entry of the vector Ax is less than or equal to the corresponding entry of the vector b (component-wise inequality).

Least squares

As a special case when Q is symmetric positive-definite, the cost function reduces to least squares:

where Q = R^TR follows from the Cholesky decomposition of Q and c = −R^T d. Conversely, any such constrained least squares program can be equivalently framed as a quadratic programming problem, even for a generic non-square R matrix.

Generalizations

When minimizing a function f in the neighborhood of some reference point x₀, Q is set to its Hessian matrix H(f(x₀)) and c is set to its gradient ∇f(x₀). A related programming problem, quadratically constrained quadratic programming, can be posed by adding quadratic constraints on the variables.

Solution methods

For general problems a variety of methods are commonly used, including

• interior point,
• active set,
• augmented Lagrangian,
• conjugate gradient,
• gradient projection,
• extensions of the simplex algorithm.

In the case in which Q is positive definite, the problem is a special case of the more general field of convex optimization.

Equality constraints

Quadratic programming is particularly simple when Q is positive definite and there are only equality constraints; specifically, the solution process is linear. By using Lagrange multipliers and seeking the extremum of the Lagrangian, it may be readily shown that the solution to the equality constrained problem

${\displaystyle \text{Minimize}\frac{1}{2}{\mathbf{x}}^{\mathrm{T}}Q\mathbf{x}+{\mathbf{c}}^{\mathrm{T}}\mathbf{x}}$

${\displaystyle \text{subject to}E\mathbf{x}=\mathbf{d}}$

is given by the linear system

${\displaystyle \left[\begin{array}{cc}Q& E^{\mathrm{\top }}\\ E& 0\end{array}\right]\left[\begin{array}{c}\mathbf{x}\\ \lambda \end{array}\right]=\left[\begin{array}{c}-\mathbf{c}\\ \mathbf{d}\end{array}\right]}$

where λ is a set of Lagrange multipliers which come out of the solution alongside x.

The easiest means of approaching this system is direct solution (for example, LU factorization), which for small problems is very practical. For large problems, the system poses some unusual difficulties, most notably that the problem is never positive definite (even if Q is), making it potentially very difficult to find a good numeric approach, and there are many approaches to choose from dependent on the problem.

If the constraints don't couple the variables too tightly, a relatively simple attack is to change the variables so that constraints are unconditionally satisfied. For example, suppose d = 0 (generalizing to nonzero is straightforward). Looking at the constraint equations:

${\displaystyle E\mathbf{x}=0}$

introduce a new variable y defined by

${\displaystyle Z\mathbf{y}=\mathbf{x}}$

where y has dimension of x minus the number of constraints. Then

${\displaystyle EZ\mathbf{y}=\mathbf{0}}$

and if Z is chosen so that EZ = 0 the constraint equation will be always satisfied. Finding such Z entails finding the null space of E, which is more or less simple depending on the structure of E. Substituting into the quadratic form gives an unconstrained minimization problem:

${\displaystyle \frac{1}{2}{\mathbf{x}}^{\mathrm{\top }}Q\mathbf{x}+{\mathbf{c}}^{\mathrm{\top }}\mathbf{x}⟹\frac{1}{2}{\mathbf{y}}^{\mathrm{\top }}{Z}^{\mathrm{\top }}QZ\mathbf{y}+{\left(Z^{\mathrm{\top }}\mathbf{c}\right)}^{\mathrm{\top }}\mathbf{y}}$

the solution of which is given by:

${\displaystyle Z^{\mathrm{\top }}QZ\mathbf{y}=-Z^{\mathrm{\top }}\mathbf{c}}$

Under certain conditions on Q, the reduced matrix Z^TQZ will be positive definite. It is possible to write a variation on the conjugate gradient method which avoids the explicit calculation of Z.

Lagrangian duality

See also: Dual problem

The Lagrangian dual of a quadratic programming problem is also a quadratic programming problem. To see this let us focus on the case where c = 0 and Q is positive definite. We write the Lagrangian function as

${\displaystyle L(x,\lambda )=\frac{1}{2}{x}^{\mathrm{\top }}Qx+{\lambda }^{\mathrm{\top }}(Ax-b).}$

Defining the (Lagrangian) dual function g(λ) as ${\displaystyle g(\lambda )=\underset{x}{inf}L(x,\lambda )}$, we find an infimum of L, using ${\displaystyle {\mathrm{\nabla }}_{x}L(x,\lambda )=0}$ and positive-definiteness of Q:

${\displaystyle x^{\ast }=-Q^{-1}{A}^{\mathrm{\top }}\lambda .}$

Hence the dual function is

${\displaystyle g(\lambda )=-\frac{1}{2}{\lambda }^{\mathrm{\top }}A{Q}^{-1}{A}^{\mathrm{\top }}\lambda -{\lambda }^{\mathrm{\top }}b,}$

and so the Lagrangian dual of the quadratic programming problem is

${\displaystyle {\text{maximize}}_{\lambda \ge 0}-\frac{1}{2}{\lambda }^{\mathrm{\top }}A{Q}^{-1}{A}^{\mathrm{\top }}\lambda -{\lambda }^{\mathrm{\top }}b.}$

Besides the Lagrangian duality theory, there are other duality pairings (e.g. Wolfe, etc.).

Complexity

For positive definite Q, the ellipsoid method solves the problem in (weakly) polynomial time. If, on the other hand, Q is indefinite, then the problem is NP-hard. There can be several stationary points and local minima for these non-convex problems. In fact, even if Q has only one negative eigenvalue, the problem is (strongly) NP-hard.

Integer constraints

There are some situations where one or more elements of the vector x will need to take on integer values. This leads to the formulation of a mixed-integer quadratic programming (MIQP) problem. Applications of MIQP include water resources and the construction of index funds.

Solvers and scripting (programming) languages

minimize	${\displaystyle \frac{1}{2}{\mathbf{x}}^{\mathrm{T}}Q\mathbf{x}+{\mathbf{c}}^{\mathrm{T}}\mathbf{x}}$
subject to	${\displaystyle A\mathbf{x}⪯\mathbf{b},}$
minimize	${\displaystyle \frac{1}{2}\Vert R\mathbf{x}-\mathbf{d}{\Vert }^2}$
subject to	${\displaystyle A\mathbf{x}⪯\mathbf{b},}$
Name	Brief info
AIMMS	A software system for modeling and solving optimization and scheduling-type problems
ALGLIB	Dual licensed (GPL/proprietary) numerical library (C++, .NET).
AMPL	A popular modeling language for large-scale mathematical optimization.
APMonitor	Modeling and optimization suite for LP, QP, NLP, MILP, MINLP, and DAE systems in MATLAB and Python.
Artelys Knitro	An Integrated Package for Nonlinear Optimization
CGAL	An open source computational geometry package which includes a quadratic programming solver.
CPLEX	Popular solver with an API (C, C++, Java, .Net, Python, Matlab and R). Free for academics.
Excel Solver Function	A nonlinear solver adjusted to spreadsheets in which function evaluations are based on the recalculating cells. Basic version available as a standard add-on for Excel.
GAMS	A high-level modeling system for mathematical optimization
GNU Octave	A free (its licence is GPLv3) general-purpose and matrix-oriented programming-language for numerical computing, similar to MATLAB. Quadratic programming in GNU Octave is available via its qp command
HiGHS	Open-source software for solving linear programming (LP), mixed-integer programming (MIP), and convex quadratic programming (QP) models
IMSL	A set of mathematical and statistical functions that programmers can embed into their software applications.
IPOPT	IPOPT (Interior Point OPTimizer) is a software package for large-scale nonlinear optimization.
Maple	General-purpose programming language for mathematics. Solving a quadratic problem in Maple is accomplished via its QPSolve command.
MATLAB	A general-purpose and matrix-oriented programming-language for numerical computing. Quadratic programming in MATLAB requires the Optimization Toolbox in addition to the base MATLAB product
Mathematica	A general-purpose programming-language for mathematics, including symbolic and numerical capabilities.
MOSEK	A solver for large scale optimization with API for several languages (C++, Java, .Net, Matlab and Python).
NAG Numerical Library	A collection of mathematical and statistical routines developed by the Numerical Algorithms Group for multiple programming languages (C, C++, Fortran, Visual Basic, Java and C#) and packages (MATLAB, Excel, R, LabVIEW). The Optimization chapter of the NAG Library includes routines for quadratic programming problems with both sparse and non-sparse linear constraint matrices, together with routines for the optimization of linear, nonlinear, sums of squares of linear or nonlinear functions with nonlinear, bounded or no constraints. The NAG Library has routines for both local and global optimization, and for continuous or integer problems.
Python	High-level programming language with bindings for most available solvers. Quadratic programming is available via the solve_qp function or by calling a specific solver directly.
R (Fortran)	GPL licensed universal cross-platform statistical computation framework.
SAS/OR	A suite of solvers for Linear, Integer, Nonlinear, Derivative-Free, Network, Combinatorial and Constraint Optimization; the Algebraic modeling language OPTMODEL; and a variety of vertical solutions aimed at specific problems/markets, all of which are fully integrated with the SAS System.
SuanShu	an open-source suite of optimization algorithms to solve LP, QP, SOCP, SDP, SQP in Java
TK Solver	Mathematical modeling and problem solving software system based on a declarative, rule-based language, commercialized by Universal Technical Systems, Inc..
TOMLAB	Supports global optimization, integer programming, all types of least squares, linear, quadratic and unconstrained programming for MATLAB. TOMLAB supports solvers like CPLEX, SNOPT and KNITRO.
XPRESS	Solver for large-scale linear programs, quadratic programs, general nonlinear and mixed-integer programs. Has API for several programming languages, also has a modelling language Mosel and works with AMPL, GAMS. Free for academic use.

 

Seismometer

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Seismometer 

Kinemetric seismograph.

A seismometer is an instrument that responds to ground noises and shaking such as caused by quakes, volcanic eruptions, and explosions. They are usually combined with a timing device and a recording device to form a seismograph. The output of such a device—formerly recorded on paper (see picture) or film, now recorded and processed digitally—is a seismogram. Such data is used to locate and characterize earthquakes, and to study the Earth's internal structure.

Basic principles

Basic horizontal-motion seismograph. The inertia of the round weight tends to hold the pen still while the base moves back and forth.

A simple seismometer, sensitive to up-down motions of the Earth, is like a weight hanging from a spring, both suspended from a frame that moves along with any motion detected. The relative motion between the weight (called the mass) and the frame provides a measurement of the vertical ground motion. A rotating drum is attached to the frame and a pen is attached to the weight, thus recording any ground motion in a seismogram.

Any movement from the ground moves the frame. The mass tends not to move because of its inertia, and by measuring the movement between the frame and the mass, the motion of the ground can be determined.

Early seismometers used optical levers or mechanical linkages to amplify the small motions involved, recording on soot-covered paper or photographic paper. Modern instruments use electronics. In some systems, the mass is held nearly motionless relative to the frame by an electronic negative feedback loop. The motion of the mass relative to the frame is measured, and the feedback loop applies a magnetic or electrostatic force to keep the mass nearly motionless. The voltage needed to produce this force is the output of the seismometer, which is recorded digitally.

In other systems the weight is allowed to move, and its motion produces an electrical charge in a coil attached to the mass which voltage moves through the magnetic field of a magnet attached to the frame. This design is often used in a geophone, which is used in exploration for oil and gas.

Seismic observatories usually have instruments measuring three axes: north-south (y-axis), east-west (x-axis), and vertical (z-axis). If only one axis is measured, it is usually the vertical because it is less noisy and gives better records of some seismic waves.

The foundation of a seismic station is critical. A professional station is sometimes mounted on bedrock. The best mountings may be in deep boreholes, which avoid thermal effects, ground noise and tilting from weather and tides. Other instruments are often mounted in insulated enclosures on small buried piers of unreinforced concrete. Reinforcing rods and aggregates would distort the pier as the temperature changes. A site is always surveyed for ground noise with a temporary installation before pouring the pier and laying conduit. Originally, European seismographs were placed in a particular area after a destructive earthquake. Today, they are spread to provide appropriate coverage (in the case of weak-motion seismology) or concentrated in high-risk regions (strong-motion seismology).

Nomenclature

The word derives from the Greek σεισμός, seismós, a shaking or quake, from the verb σείω, seíō, to shake; and μέτρον, métron, to measure, and was coined by David Milne-Home in 1841, to describe an instrument designed by Scottish physicist James David Forbes.

Seismograph is another Greek term from seismós and γράφω, gráphō, to draw. It is often used to mean seismometer, though it is more applicable to the older instruments in which the measuring and recording of ground motion were combined, than to modern systems, in which these functions are separated. Both types provide a continuous record of ground motion; this record distinguishes them from seismoscopes, which merely indicate that motion has occurred, perhaps with some simple measure of how large it was.

The technical discipline concerning such devices is called seismometry, a branch of seismology.

The concept of measuring the "shaking" of something means that the word "seismograph" might be used in a more general sense. For example, a monitoring station that tracks changes in electromagnetic noise affecting amateur radio waves presents an rf seismograph. And helioseismology studies the "quakes" on the Sun.

History

The first seismometer was made in China during the 2nd century. It was invented by Zhang Heng, a Chinese mathematician and astronomer. The first Western description of the device comes from the French physicist and priest Jean de Hautefeuille in 1703. The modern seismometer was developed in the 19th century.

Seismometers were placed on the Moon starting in 1969 as part of the Apollo Lunar Surface Experiments Package. In December 2018, a seismometer was deployed on the planet Mars by the InSight lander, the first time a seismometer was placed onto the surface of another planet.

Ancient era

Replica of Zhang Heng's seismoscope Houfeng Didong Yi

See also: List of Chinese inventions

In Ancient Egypt, Amenhotep, son of Hapu invented a precursor of seismometer, a vertical wooden poles connected with wooden gutters on the central axis functioned to fill water into a vessel until full to detect earthquakes.

In AD 132, Zhang Heng of China's Han dynasty is said to have invented the first seismoscope (by the definition above), which was called Houfeng Didong Yi (translated as, "instrument for measuring the seasonal winds and the movements of the Earth"). The description we have, from the History of the Later Han Dynasty, says that it was a large bronze vessel, about 2 meters in diameter; at eight points around the top were dragon's heads holding bronze balls. When there was an earthquake, one of the dragons' mouths would open and drop its ball into a bronze toad at the base, making a sound and supposedly showing the direction of the earthquake. On at least one occasion, probably at the time of a large earthquake in Gansu in AD 143, the seismoscope indicated an earthquake even though one was not felt. The available text says that inside the vessel was a central column that could move along eight tracks; this is thought to refer to a pendulum, though it is not known exactly how this was linked to a mechanism that would open only one dragon's mouth. The first earthquake recorded by this seismoscope was supposedly "somewhere in the east". Days later, a rider from the east reported this earthquake.

Early designs (1259–1839)

By the 13th century, seismographic devices existed in the Maragheh observatory (founded 1259) in Persia, though it is unclear whether these were constructed independently or based on the first seismoscope. French physicist and priest Jean de Hautefeuille described a seismoscope in 1703, which used a bowl filled with mercury which would spill into one of eight receivers equally spaced around the bowl, though there is no evidence that he actually constructed the device. A mercury seismoscope was constructed in 1784 or 1785 by Atanasio Cavalli, a copy of which can be found at the University Library in Bologna, and a further mercury seismoscope was constructed by Niccolò Cacciatore in 1818. James Lind also built a seismological tool of unknown design or efficacy (known as an earthquake machine) in the late 1790s.

Pendulum devices were developing at the same time. Neapolitan naturalist Nicola Cirillo set up a network of pendulum earthquake detectors following the 1731 Puglia Earthquake, where the amplitude was detected using a protractor to measure the swinging motion. Benedictine monk Andrea Bina further developed this concept in 1751, having the pendulum create trace marks in sand under the mechanism, providing both magnitude and direction of motion. Neapolitan clockmaker Domenico Salsano produced a similar pendulum which recorded using a paintbrush in 1783, labelling it a geo-sismometro, possibly the first use of a similar word to seismometer. Naturalist Nicolo Zupo devised an instrument to detect electrical disturbances and earthquakes at the same time (1784).

The first moderately successful device for detecting the time of an earthquake was devised by Ascanio Filomarino in 1796, who improved upon Salsano's pendulum instrument, using a pencil to mark, and using a hair attached to the mechanism to inhibit the motion of a clock's balance wheel. This meant that the clock would only start once an earthquake took place, allowing determination of the time of incidence.

After an earthquake taking place on October 4, 1834, Luigi Pagani observed that the mercury seismoscope held at Bologna University had completely spilled over, and did not provide useful information. He therefore devised a portable device that used lead shot to detect the direction of an earthquake, where the lead fell into four bins arranged in a circle, to determine the quadrant of earthquake incidence. He completed the instrument in 1841.

Early Modern designs (1839–1880)

In response to a series of earthquakes near Comrie in Scotland in 1839, a committee was formed in the United Kingdom in order to produce better detection devices for earthquakes. The outcome of this was an inverted pendulum seismometer constructed by James David Forbes, first presented in a report by David Milne-Home in 1842, which recorded the measurements of seismic activity through the use of a pencil placed on paper above the pendulum. The designs provided did not prove effective, according to Milne's reports. It was Milne who coined the word seismometer in 1841, to describe this instrument. In 1843, the first horizontal pendulum was used in a seismometer, reported by Milne (though it is unclear if he was the original inventor). After these inventions, Robert Mallet published an 1848 paper where he suggested ideas for seismometer design, suggesting that such a device would need to register time, record amplitudes horizontally and vertically, and ascertain direction. His suggested design was funded, and construction was attempted, but his final design did not fulfill his expectations and suffered from the same problems as the Forbes design, being inaccurate and not self-recording.

Karl Kreil constructed a seismometer in Prague between 1848 and 1850, which used a point-suspended rigid cylindrical pendulum covered in paper, drawn upon by a fixed pencil. The cylinder was rotated every 24 hours, providing an approximate time for a given quake.

Luigi Palmieri, influenced by Mallet's 1848 paper, invented a seismometer in 1856 that could record the time of an earthquake. This device used metallic pendulums which closed an electric circuit with vibration, which then powered an electromagnet to stop a clock. Palmieri seismometers were widely distributed and used for a long time.

By 1872, a committee in the United Kingdom led by James Bryce expressed their dissatisfaction with the current available seismometers, still using the large 1842 Forbes device located in Comrie Parish Church, and requested a seismometer which was compact, easy to install and easy to read. In 1875 they settled on a large example of the Mallet device, consisting of an array of cylindrical pins of various sizes installed at right angles to each other on a sand bed, where larger earthquakes would knock down larger pins. This device was constructed in 'Earthquake House' near Comrie, which can be considered the world's first purpose-built seismological observatory. As of 2013, no earthquake has been large enough to cause any of the cylinders to fall in either the original device or replicas.

The first seismographs (1880-)

The first seismographs were invented in the 1870s and 1880s. The first seismograph was produced by Filippo Cecchi in around 1875. A seismoscope would trigger the device to begin recording, and then a recording surface would produce a graphical illustration of the tremors automatically (a seismogram). However, the instrument was not sensitive enough, and the first seismogram produced by the instrument was in 1887, by which time John Milne had already demonstrated his design in Japan.

Milne horizontal pendulum seismometer. One of the Important Cultural Properties of Japan. Exhibit in the National Museum of Nature and Science, Tokyo, Japan.

In 1880, the first horizontal pendulum seismometer was developed by the team of John Milne, James Alfred Ewing and Thomas Gray, who worked as foreign-government advisors in Japan, from 1880 to 1895. Milne, Ewing and Gray, all having been hired by the Meiji Government in the previous five years to assist Japan's modernization efforts, founded the Seismological Society of Japan in response to an Earthquake that took place on February 22, 1880, at Yokohama. Two instruments were constructed by Ewing over the next year, one being a common-pendulum seismometer and the other being the first seismometer using a damped horizontal pendulum. The innovative recording system allowed for a continuous record, the first to do so. The first seismogram was recorded on 3 November 1880 on both of Ewing's instruments. Modern seismometers would eventually descend from these designs. Milne has been referred to as the 'Father of modern seismology' and his seismograph design has been called the first modern seismometer.

This produced the first effective measurement of horizontal motion. Gray would produce the first reliable method for recording vertical motion, which produced the first effective 3-axis recordings.

An early special-purpose seismometer consisted of a large, stationary pendulum, with a stylus on the bottom. As the earth started to move, the heavy mass of the pendulum had the inertia to stay still within the frame. The result is that the stylus scratched a pattern corresponding with the Earth's movement. This type of strong-motion seismometer recorded upon a smoked glass (glass with carbon soot). While not sensitive enough to detect distant earthquakes, this instrument could indicate the direction of the pressure waves and thus help find the epicenter of a local quake. Such instruments were useful in the analysis of the 1906 San Francisco earthquake. Further analysis was performed in the 1980s, using these early recordings, enabling a more precise determination of the initial fault break location in Marin county and its subsequent progression, mostly to the south.

Later, professional suites of instruments for the worldwide standard seismographic network had one set of instruments tuned to oscillate at fifteen seconds, and the other at ninety seconds, each set measuring in three directions. Amateurs or observatories with limited means tuned their smaller, less sensitive instruments to ten seconds. The basic damped horizontal pendulum seismometer swings like the gate of a fence. A heavy weight is mounted on the point of a long (from 10 cm to several meters) triangle, hinged at its vertical edge. As the ground moves, the weight stays unmoving, swinging the "gate" on the hinge.

The advantage of a horizontal pendulum is that it achieves very low frequencies of oscillation in a compact instrument. The "gate" is slightly tilted, so the weight tends to slowly return to a central position. The pendulum is adjusted (before the damping is installed) to oscillate once per three seconds, or once per thirty seconds. The general-purpose instruments of small stations or amateurs usually oscillate once per ten seconds. A pan of oil is placed under the arm, and a small sheet of metal mounted on the underside of the arm drags in the oil to damp oscillations. The level of oil, position on the arm, and angle and size of sheet is adjusted until the damping is "critical", that is, almost having oscillation. The hinge is very low friction, often torsion wires, so the only friction is the internal friction of the wire. Small seismographs with low proof masses are placed in a vacuum to reduce disturbances from air currents.

Zollner described torsionally suspended horizontal pendulums as early as 1869, but developed them for gravimetry rather than seismometry.

Early seismometers had an arrangement of levers on jeweled bearings, to scratch smoked glass or paper. Later, mirrors reflected a light beam to a direct-recording plate or roll of photographic paper. Briefly, some designs returned to mechanical movements to save money. In mid-twentieth-century systems, the light was reflected to a pair of differential electronic photosensors called a photomultiplier. The voltage generated in the photomultiplier was used to drive galvanometers which had a small mirror mounted on the axis. The moving reflected light beam would strike the surface of the turning drum, which was covered with photo-sensitive paper. The expense of developing photo-sensitive paper caused many seismic observatories to switch to ink or thermal-sensitive paper.

After World War II, the seismometers developed by Milne, Ewing and Gray were adapted into the widely used Press-Ewing seismometer.

Modern instruments

Simplified LaCoste suspension using a zero-length spring

CMG-40T triaxial broadband seismometer

Seismometer without housing; presented during a demonstration for children about earthquakes at Alfred Wegener Institute.

Modern instruments use electronic sensors, amplifiers, and recording devices. Most are broadband covering a wide range of frequencies. Some seismometers can measure motions with frequencies from 500 Hz to 0.00118 Hz (1/500 = 0.002 seconds per cycle, to 1/0.00118 = 850 seconds per cycle). The mechanical suspension for horizontal instruments remains the garden-gate described above. Vertical instruments use some kind of constant-force suspension, such as the LaCoste suspension. The LaCoste suspension uses a zero-length spring to provide a long period (high sensitivity). Some modern instruments use a "triaxial" or "Galperin" design, in which three identical motion sensors are set at the same angle to the vertical but 120 degrees apart on the horizontal. Vertical and horizontal motions can be computed from the outputs of the three sensors.

Seismometers unavoidably introduce some distortion into the signals they measure, but professionally designed systems have carefully characterized frequency transforms.

Modern sensitivities come in three broad ranges: geophones, 50 to 750 V/m; local geologic seismographs, about 1,500 V/m; and teleseismographs, used for world survey, about 20,000 V/m. Instruments come in three main varieties: short period, long period and broadband. The short and long period measure velocity and are very sensitive, however they 'clip' the signal or go off-scale for ground motion that is strong enough to be felt by people. A 24-bit analog-to-digital conversion channel is commonplace. Practical devices are linear to roughly one part per million.

Delivered seismometers come with two styles of output: analog and digital. Analog seismographs require analog recording equipment, possibly including an analog-to-digital converter. The output of a digital seismograph can be simply input to a computer. It presents the data in a standard digital format (often "SE2" over Ethernet).

Teleseismometers

A low-frequency 3-direction ocean-bottom seismometer (cover removed). Two masses for x- and y-direction can be seen, the third one for z-direction is below. This model is a CMG-40TOBS, manufactured by Güralp Systems Ltd and is part of the Monterey Accelerated Research System.

The modern broadband seismograph can record a very broad range of frequencies. It consists of a small "proof mass", confined by electrical forces, driven by sophisticated electronics. As the earth moves, the electronics attempt to hold the mass steady through a feedback circuit. The amount of force necessary to achieve this is then recorded.

In most designs the electronics holds a mass motionless relative to the frame. This device is called a "force balance accelerometer". It measures acceleration instead of velocity of ground movement. Basically, the distance between the mass and some part of the frame is measured very precisely, by a linear variable differential transformer. Some instruments use a linear variable differential capacitor.

That measurement is then amplified by electronic amplifiers attached to parts of an electronic negative feedback loop. One of the amplified currents from the negative feedback loop drives a coil very like a loudspeaker. The result is that the mass stays nearly motionless.

Most instruments measure directly the ground motion using the distance sensor. The voltage generated in a sense coil on the mass by the magnet directly measures the instantaneous velocity of the ground. The current to the drive coil provides a sensitive, accurate measurement of the force between the mass and frame, thus measuring directly the ground's acceleration (using f=ma where f=force, m=mass, a=acceleration).

One of the continuing problems with sensitive vertical seismographs is the buoyancy of their masses. The uneven changes in pressure caused by wind blowing on an open window can easily change the density of the air in a room enough to cause a vertical seismograph to show spurious signals. Therefore, most professional seismographs are sealed in rigid gas-tight enclosures. For example, this is why a common Streckeisen model has a thick glass base that must be glued to its pier without bubbles in the glue.

It might seem logical to make the heavy magnet serve as a mass, but that subjects the seismograph to errors when the Earth's magnetic field moves. This is also why seismograph's moving parts are constructed from a material that interacts minimally with magnetic fields. A seismograph is also sensitive to changes in temperature so many instruments are constructed from low expansion materials such as nonmagnetic invar.

The hinges on a seismograph are usually patented, and by the time the patent has expired, the design has been improved. The most successful public domain designs use thin foil hinges in a clamp.

Another issue is that the transfer function of a seismograph must be accurately characterized, so that its frequency response is known. This is often the crucial difference between professional and amateur instruments. Most are characterized on a variable frequency shaking table.

Strong-motion seismometers

Another type of seismometer is a digital strong-motion seismometer, or accelerograph. The data from such an instrument is essential to understand how an earthquake affects man-made structures, through earthquake engineering. The recordings of such instruments are crucial for the assessment of seismic hazard, through engineering seismology.

A strong-motion seismometer measures acceleration. This can be mathematically integrated later to give velocity and position. Strong-motion seismometers are not as sensitive to ground motions as teleseismic instruments but they stay on scale during the strongest seismic shaking.

Strong motion sensors are used for intensity meter applications.

Other forms

A Kinemetrics seismograph, formerly used by the United States Department of the Interior.

Accelerographs and geophones are often heavy cylindrical magnets with a spring-mounted coil inside. As the case moves, the coil tends to stay stationary, so the magnetic field cuts the wires, inducing current in the output wires. They receive frequencies from several hundred hertz down to 1 Hz. Some have electronic damping, a low-budget way to get some of the performance of the closed-loop wide-band geologic seismographs.

Strain-beam accelerometers constructed as integrated circuits are too insensitive for geologic seismographs (2002), but are widely used in geophones.

Some other sensitive designs measure the current generated by the flow of a non-corrosive ionic fluid through an electret sponge or a conductive fluid through a magnetic field.

Interconnected seismometers

Seismometers spaced in a seismic array can also be used to precisely locate, in three dimensions, the source of an earthquake, using the time it takes for seismic waves to propagate away from the hypocenter, the initiating point of fault rupture (See also Earthquake location). Interconnected seismometers are also used, as part of the International Monitoring System to detect underground nuclear test explosions, as well as for Earthquake early warning systems. These seismometers are often used as part of a large scale governmental or scientific project, but some organizations such as the Quake-Catcher Network, can use residential size detectors built into computers to detect earthquakes as well.

In reflection seismology, an array of seismometers image sub-surface features. The data are reduced to images using algorithms similar to tomography. The data reduction methods resemble those of computer-aided tomographic medical imaging X-ray machines (CAT-scans), or imaging sonars.

A worldwide array of seismometers can actually image the interior of the Earth in wave-speed and transmissivity. This type of system uses events such as earthquakes, impact events or nuclear explosions as wave sources. The first efforts at this method used manual data reduction from paper seismograph charts. Modern digital seismograph records are better adapted to direct computer use. With inexpensive seismometer designs and internet access, amateurs and small institutions have even formed a "public seismograph network".

Seismographic systems used for petroleum or other mineral exploration historically used an explosive and a wireline of geophones unrolled behind a truck. Now most short-range systems use "thumpers" that hit the ground, and some small commercial systems have such good digital signal processing that a few sledgehammer strikes provide enough signal for short-distance refractive surveys. Exotic cross or two-dimensional arrays of geophones are sometimes used to perform three-dimensional reflective imaging of subsurface features. Basic linear refractive geomapping software (once a black art) is available off-the-shelf, running on laptop computers, using strings as small as three geophones. Some systems now come in an 18" (0.5 m) plastic field case with a computer, display and printer in the cover.

Small seismic imaging systems are now sufficiently inexpensive to be used by civil engineers to survey foundation sites, locate bedrock, and find subsurface water.

Fiber optic cables as seismometers

A new technique for detecting earthquakes has been found, using fiber optic cables. In 2016 a team of metrologists running frequency metrology experiments in England observed noise with a wave-form resembling the seismic waves generated by earthquakes. This was found to match seismological observations of an M_w6.0 earthquake in Italy, ~1400 km away. Further experiments in England, Italy, and with a submarine fiber optic cable to Malta detected additional earthquakes, including one 4,100 km away, and an M_L3.4 earthquake 89 km away from the cable.

Seismic waves are detectable because they cause micrometer-scale changes in the length of the cable. As the length changes so does the time it takes a packet of light to traverse to the far end of the cable and back (using a second fiber). Using ultra-stable metrology-grade lasers, these extremely minute shifts of timing (on the order of femtoseconds) appear as phase-changes.

The point of the cable first disturbed by an earthquake's p-wave (essentially a sound wave in rock) can be determined by sending packets in both directions in the looped pair of optical fibers; the difference in the arrival times of the first pair of perturbed packets indicates the distance along the cable. This point is also the point closest to the earthquake's epicenter, which should be on a plane perpendicular to the cable. The difference between the p-wave/s-wave arrival times provides a distance (under ideal conditions), constraining the epicenter to a circle. A second detection on a non-parallel cable is needed to resolve the ambiguity of the resulting solution. Additional observations constrain the location of the earthquake's epicenter, and may resolve the depth.

This technique is expected to be a boon in observing earthquakes, especially the smaller ones, in vast portions of the global ocean where there are no seismometers, and at a cost much cheaper than ocean bottom seismometers.

Deep-Learning

Researchers at Stanford University created a deep-learning algorithm called UrbanDenoiser which can detect earthquakes, particularly in urban cities. The algorithm filters out the background noise from the seismic noise gathered from busy cities in urban areas to detect earthquakes.

Recording

Viewing of a Develocorder film

Matsushiro Seismological Observatory

A Seismogram graph

Further information: Seismogram

Today, the most common recorder is a computer with an analog-to-digital converter, a disk drive and an internet connection; for amateurs, a PC with a sound card and associated software is adequate. Most systems record continuously, but some record only when a signal is detected, as shown by a short-term increase in the variation of the signal, compared to its long-term average (which can vary slowly because of changes in seismic noise), also known as a STA/LTA trigger.

Prior to the availability of digital processing of seismic data in the late 1970s, the records were done in a few different forms on different types of media. A "Helicorder" drum was a device used to record data into photographic paper or in the form of paper and ink. A "Develocorder" was a machine that record data from up to 20 channels into a 16-mm film. The recorded film can be viewed by a machine. The reading and measuring from these types of media can be done by hand. After the digital processing has been used, the archives of the seismic data were recorded in magnetic tapes. Due to the deterioration of older magnetic tape medias, large number of waveforms from the archives are not recoverable.

Aging of wine

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Aging_of_wine

Bottles of wine aging in an underground cellar

The aging of wine is potentially able to improve the quality of wine. This distinguishes wine from most other consumable goods. While wine is perishable and capable of deteriorating, complex chemical reactions involving a wine's sugars, acids and phenolic compounds (such as tannins) can alter the aroma, color, mouthfeel and taste of the wine in a way that may be more pleasing to the taster. The ability of a wine to age is influenced by many factors including grape variety, vintage, viticultural practices, wine region and winemaking style. The condition that the wine is kept in after bottling can also influence how well a wine ages and may require significant time and financial investment. The quality of an aged wine varies significantly bottle-by-bottle, depending on the conditions under which it was stored, and the condition of the bottle and cork, and thus it is said that rather than good old vintages, there are good old bottles. There is a significant mystique around the aging of wine, as its chemistry was not understood for a long time, and old wines are often sold for extraordinary prices. However, the vast majority of wine is not aged, and even wine that is aged is rarely aged for long; it is estimated that 90% of wine is meant to be consumed within a year of production, and 99% of wine within 5 years.

History

During antiquity, amphorae like these were used to store wine and sealing wax made it possible to age the wine.

The Ancient Greeks and Romans were aware of the potential of aged wines. In Greece, early examples of dried "straw wines" were noted for their ability to age due to their high sugar contents. These wines were stored in sealed earthenware amphorae and kept for many years. In Rome, the most sought after wines – Falernian and Surrentine – were prized for their ability to age for decades. In the Book of Luke, it is noted that "old wine" was valued over "new wine" (Luke 5:39). The Greek physician Galen wrote that the "taste" of aged wine was desirable and that this could be accomplished by heating or smoking the wine, though, in Galen's opinion, these artificially aged wines were not as healthy to consume as naturally aged wines.

Bottles with cork closure reinvented the process of wine aging.

Following the Fall of the Roman Empire, appreciation for aged wine was virtually non-existent. Most of the wines produced in northern Europe were light bodied, pale in color and with low alcohol. These wines did not have much aging potential and barely lasted a few months before they rapidly deteriorated into vinegar. The older a wine got the cheaper its price became as merchants eagerly sought to rid themselves of aging wine. By the 16th century, sweeter and more alcoholic wines (like Malmsey and Sack) were being made in the Mediterranean and gaining attention for their aging ability. Similarly, Riesling from Germany with its combination of acidity and sugar were also demonstrating their ability to age. In the 17th century, two innovations occurred that radically changed the wine industry's view on aging. One was the development of the cork and bottle which again allowed producers to package and store wine in a virtually air-tight environment. The second was the growing popularity of fortified wines such as Port, Madeira and Sherries. The added alcohol was found to act as a preservative, allowing wines to survive long sea voyages to England, The Americas and the East Indies. The English, in particular, were growing in their appreciation of aged wines like Port and Claret from Bordeaux. Demand for matured wines had a pronounced effect on the wine trade. For producers, the cost and space of storing barrels or bottles of wine was prohibitive so a merchant class evolved with warehouses and the finances to facilitate aging wines for a longer period of time. In regions like Bordeaux, Oporto and Burgundy, this situation dramatically increased the balance of power towards the merchant classes.

Aging potential

The Italian wine Tignanello is a blend of Sangiovese, Cabernet Sauvignon and Cabernet franc – varieties which usually have aging potential.

There is a widespread misconception that wine always improves with age, or that wine improves with extended aging, or that aging potential is an indicator of good wine. Some authorities state that more wine is consumed too old than too young. Aging changes wine, but does not categorically improve it or worsen it. Fruitiness deteriorates rapidly, decreasing markedly after only 6 months in the bottle. Due to the cost of storage, it is not economical to age cheap wines, but many varieties of wine do not benefit from aging, regardless of the quality. Experts vary on precise numbers, but typically state that only 5–10% of wine improves after 1 year, and only 1% improves after 5–10 years.

In general, wines with a low pH (such as pinot noir and Sangiovese) have a greater capability of aging. With red wines, a high level of flavor compounds, such as phenolics (most notably tannins), will increase the likelihood that a wine will be able to age. Wines with high levels of phenols include Cabernet Sauvignon, Nebbiolo and Syrah. The white wines with the longest aging potential tend to be those with a high amount of extract and acidity (such as Riesling). The acidity in white wines, acting as a preservative, has a role similar to that of tannins in red wines. The process of making white wines, which includes little to no skin contact, means that white wines have a significantly lower amount of phenolic compounds, though barrel fermentation and oak aging can impart some phenols. Similarly, the minimal skin contact with rosé wine limits their aging potential.

After aging at the winery most wood-aged ports, sherries, vins doux naturels, vins de liqueur, basic level ice wines, and sparkling wines are bottled when the producer feels that they are ready to be consumed. These wines are ready to drink upon release and will not benefit much from aging. Vintage ports and other bottled-aged ports and sherries will benefit from some additional aging.

Champagne and other sparkling wines are infrequently aged, and frequently have no vintage year (no vintage, NV), but vintage champagne may be aged. Aged champagne has traditionally been a peculiarly British affectation, and thus has been referred to as le goût anglais "the English taste", though this term also refers to a level of champagne sweetness. In principle champagne has aging potential, due to the acidity, and aged champagne has increased in popularity in the United States since the 1996 vintage. A few French winemakers have advocated aging champagne, most notably René Collard (1921–2009). In 2009, a 184-year-old bottle of Perrier-Jouët was opened and tasted, still drinkable, with notes of "truffles and caramel", according to the experts.

Little to no aging potential

A guideline provided by Master of Wine Jancis Robinson

• German QBAs (Qualitätswein bestimmter Anbaugebiete)
• Asti and Moscato Spumante
• Rosé and blush wines like White Zinfandel
• Branded wines like Yellow Tail, Mouton Cadet, etc.
• European table wine
• American jug & box wine
• Inexpensive varietals (with the possible exception of Cabernet Sauvignon)
• The majority of Vin de pays
• All Nouveau wines
• Vermouth
• Basic Sherry
• Tawny Ports
• Kit wines made from mostly concentrated grape juice

Good aging potential

Master of Wine Jancis Robinson provides the following general guidelines on aging wines. Note that vintage, wine region and winemaking style can influence a wine's aging potential, so Robinson's guidelines are general estimates for the most common examples of these wines.

• Botrytized wines (5–25 yrs)
• Chardonnay (2–6 yrs)
• Riesling (2–30 yrs)
• Hungarian Furmint (3–25 yrs)
• Loire Valley Chenin blanc (4–30 yrs)
• Hunter Valley Semillon (6–15 yrs)
• Cabernet Sauvignon (4–20 yrs)
• Merlot (2–10 yrs)
• Nebbiolo (4–20 yrs)
• Pinot noir (2–8 yrs)
• Sangiovese (2–8 yrs)
• Syrah (4–16 yrs)
• Zinfandel (2–6 yrs)
• Classified Bordeaux (8–25 yrs)
• Grand Cru Burgundy (8–25 yrs)
• Aglianico from Taurasi (4–15 yrs)
• Baga from Bairrada (4–8 yrs)
• Hungarian Kadarka (3–7 yrs)
• Bulgarian Melnik (3–7 yrs)
• Croatian Plavac Mali (4–8 yrs)
• Georgian Saperavi (3–10 yrs)
• Madiran Tannat (4–12 yrs)
• Spanish Tempranillo (2–8 yrs)
• Greek Xynomavro (4–10 yrs)
• Vintage Ports (20–50 yrs)

Factors and influences

Wine constituents

The ratio of sugars, acids and phenolics to water is a key determination of how well a wine can age. The less water in the grapes prior to harvest, the more likely the resulting wine will have some aging potential. Grape variety, climate, vintage and viticultural practice come into play here. Grape varieties with thicker skins, from a dry growing season where little irrigation was used and yields were kept low will have less water and a higher ratio of sugar, acids and phenolics. The process of making Eisweins, where water is removed from the grape during pressing as frozen ice crystals, has a similar effect of decreasing the amount of water and increasing aging potential.

In winemaking, the duration of maceration or skin contact will influence how much phenolic compounds are leached from skins into the wine. Pigmented tannins, anthocyanins, colloids, tannin-polysaccharides and tannin-proteins not only influence a wine's resulting color but also act as preservatives. During fermentation adjustment to a wine's acid levels can be made with wines with lower pH having more aging potential. Exposure to oak either during fermentation or after (during barrel aging) will introduce more phenolic compounds to the wines. Prior to bottling, excessive fining or filtering of the wine could strip the wine of some phenolic solids and may lessen a wine's ability to age.

Storage conditions can influence a wine's aging ability.

Storage factors

Main article: Storage of wine

The storage condition of the bottled wine will influence a wine's aging. Vibrations and heat fluctuations can hasten a wine's deterioration and cause adverse effect on the wines. In general, a wine has a greater potential to develop complexity and more aromatic bouquet if it is allowed to age slowly in a relatively cool environment. The lower the temperature, the more slowly a wine develops. On average, the rate of chemical reactions in wine double with each 18 °F (10 °C) increase in temperature. Wine expert Karen MacNeil recommends keeping wine intended for aging in a cool area with a constant temperature around 55 °F (13 °C). Wine can be stored at temperatures as high as 69 °F (20 °C) without long term negative effect. Professor Cornelius Ough of the University of California, Davis believes that wine could be exposed to temperatures as high as 120 °F (49 °C) for a few hours and not be damaged. However, most experts believe that extreme temperature fluctuations (such as repeated transferring of a wine from a warm room to a cool refrigerator) would be detrimental to the wine. The ultra-violet rays of direct sunlight should also be avoided because of the free radicals that can develop in the wine and result in premature oxidation.

Wines packaged in large format bottles, such as magnums and 3 liter Jeroboams, seem to age more slowly than wines packaged in regular 750 ml bottles or half bottles. This may be because of the greater proportion of oxygen exposed to the wine during the bottle process. The advent of alternative wine closures to cork, such as screw caps and synthetic corks have opened up recent discussions on the aging potential of wines sealed with these alternative closures. Currently there are no conclusive results and the topic is the subject of ongoing research.

Bottling factors

Bottle shock

Main article: Bottle-shock

One of the short-term aging needs of wine is a period where the wine is considered "sick" due to the trauma and volatility of the bottling experience. During bottling the wine is exposed to some oxygen which causes a domino effect of chemical reactions with various components of the wine. The time it takes for the wine to settle down and have the oxygen fully dissolve and integrate with the wine is considered its period of "bottle shock". During this time the wine could taste drastically different from how it did prior to bottling or how it will taste after the wine has settled. While many modern bottling lines try to treat the wine as gently as possible and utilize inert gases to minimize the amount of oxygen exposure, all wine goes through some period of bottle shock. The length of this period will vary with each individual wine.

Cork taint

Main article: Cork taint

The transfer of off-flavours in the cork used to bottle a wine during prolonged aging can be detrimental to the quality of the bottle. The formation of cork taint is a complex process which may result from a wide range of factors ranging from the growing conditions of the cork oak, the processing of the cork into stoppers, or the molds growing on the cork itself.

Dumb phase

During the course of aging, a wine may slip into a "dumb phase" where its aromas and flavors are very muted. In Bordeaux this phase is called the age ingrat or "difficult age" and is likened to a teenager going through adolescence. The cause or length of time that this "dumb phase" will last is not yet fully understood and seems to vary from bottle to bottle.

Effects on wine

As vintage Port matures, sediments develop in the wine that are often left in the bottle when the wine is decanted.

As red wine ages, the harsh tannins of its youth gradually give way to a softer mouthfeel. An inky dark color will eventually lose its depth of color and begin to appear orange at the edges, and eventually turn brown. These changes occur due to the complex chemical reactions of the phenolic compounds of the wine. In processes that begin during fermentation and continue after bottling, these compounds bind together and aggregate. Eventually these particles reach a certain size where they are too large to stay suspended in the solution and precipitate out. The presence of visible sediment in a bottle will usually indicate a mature wine. The resulting wine, with this loss of tannins and pigment, will have a paler color and taste softer, less astringent. The sediment, while harmless, can have an unpleasant taste and is often separated from the wine by decanting.

During the aging process, the perception of a wine's acidity may change even though the total measurable amount of acidity is more or less constant throughout a wine's life. This is due to the esterification of the acids, combining with alcohols in complex array to form esters. In addition to making a wine taste less acidic, these esters introduce a range of possible aromas. Eventually the wine may age to a point where other components of the wine (such as a tannins and fruit) are less noticeable themselves, which will then bring back a heightened perception of wine acidity. Other chemical processes that occur during aging include the hydrolysis of flavor precursors which detach themselves from glucose molecules and introduce new flavor notes in the older wine and aldehydes become oxidized. The interaction of certain phenolics develops what is known as tertiary aromas which are different from the primary aromas that are derived from the grape and during fermentation.

An aged Malmsey Madeira shows the color change that white wines go through as they age.

As a wine starts to mature, its bouquet will become more developed and multi-layered. While a taster may be able to pick out a few fruit notes in a young wine, a more complex wine will have several distinct fruit, floral, earthy, mineral and oak derived notes. The lingering finish of a wine will lengthen. Eventually the wine will reach a point of maturity, when it is said to be at its "peak". This is the point when the wine has the maximum amount of complexity, most pleasing mouthfeel and softening of tannins and has not yet started to decay. When this point will occur is not yet predictable and can vary from bottle to bottle. If a wine is aged for too long, it will start to descend into decrepitude where the fruit tastes hollow and weak while the wine's acidity becomes dominant.

The natural esterification that takes place in wines and other alcoholic beverages during the aging process is an example of acid-catalysed esterification. Over time, the acidity of the acetic acid and tannins in an aging wine will catalytically protonate other organic acids (including acetic acid itself), encouraging ethanol to react as a nucleophile. As a result, ethyl acetate – the ester of ethanol and acetic acid – is the most abundant ester in wines. Other combinations of organic alcohols (such as phenol-containing compounds) and organic acids lead to a variety of different esters in wines, contributing to their different flavours, smells and tastes. Of course, when compared to sulfuric acid conditions, the acid conditions in a wine are mild, so yield is low (often in tenths or hundredths of a percentage point by volume) and take years for ester to accumulate.

Coates’ Law of Maturity

Coates’ Law of Maturity is a principle used in wine tasting relating to the aging ability of wine. Developed by the British Master of Wine, Clive Coates, the principle states that a wine will remain at its peak (or optimal) drinking quality for a duration of time that is equal to the time of maturation required to reach its optimal quality. During the aging of a wine certain flavors, aromas and textures appear and fade. Rather than developing and fading in unison, these traits each operate on a unique path and time line. The principle allows for the subjectivity of individual tastes because it follows the logic that positive traits that appeal to one particular wine taster will continue to persist along the principle's guideline while for another taster these traits might not be positive and therefore not applicable to the guideline. Wine expert Tom Stevenson has noted that there is logic in Coates' principle and that he has yet to encounter an anomaly or wine that debunks it.

Example

An example of the principle in practice would be a wine that someone acquires when it is 9 years of age, but finds dull. A year later the drinker finds this wine very pleasing in texture, aroma and mouthfeel. Under the Coates Law of Maturity the wine will continue to be drunk at an optimal maturation for that drinker until it has reached 20 years of age at which time those positive traits that the drinker perceives will start to fade.

Artificial aging

There is a long history of using artificial means to try to accelerate the natural aging process. In Ancient Rome a smoke chamber known as a fumarium was used to enhance the flavor of wine through artificial aging. Amphorae were placed in the chamber, which was built on top of a heated hearth, in order to impart a smoky flavor in the wine that also seemed to sharpen the acidity. The wine would sometimes come out of the fumarium with a paler color just like aged wine. Modern winemaking techniques like micro-oxygenation can have the side effect of artificially aging the wine. In the production of Madeira and rancio wines, the wines are deliberately exposed to excessive temperatures to accelerate the maturation of the wine. Other techniques used to artificially age wine (with inconclusive results on their effectiveness) include shaking the wine, exposing it to radiation, magnetism or ultra-sonic waves. More recently, experiments with artificial aging through high-voltage electricity have produced results above the remaining techniques, as assessed by a panel of wine tasters. Some artificial wine-aging gadgets include the "Clef du Vin", which is a metallic object that is dipped into wine and purportedly ages the wine one year for every second of dipping. The product has received mixed reviews from wine commentators. Several wineries have begun aging finished wine bottles undersea; ocean aging is thought to accelerate natural aging reactions as a function of depth (pressure).