Misplaced Pages

#120879

126-529: Shield volcanoes are found wherever fluid, low- silica lava reaches the surface of a rocky planet. However, they are most characteristic of ocean island volcanism associated with hot spots or with continental rift volcanism. They include the largest active volcanoes on Earth, such as Mauna Loa . Giant shield volcanoes are found on other planets of the Solar System , including Olympus Mons on Mars and Sapas Mons on Venus . The term 'shield volcano'

252-410: A + bX and Y to c + dY , where a , b , c , and d are constants ( b and d being positive). This is true of some correlation statistics as well as their population analogues. Some correlation statistics, such as the rank correlation coefficient, are also invariant to monotone transformations of the marginal distributions of X and/or Y . Most correlation measures are sensitive to

378-775: A correlation with age of the forming lava, with in the case of the Hawaiian chain, steepness increasing with age, as later lavas tend to be more alkali so are more viscous, with thicker flows, that travel less distance from the summit vents. In height they are typically about one twentieth their width. Although the general form of a "typical" shield volcano varies little worldwide, there are regional differences in their size and morphological characteristics. Typical shield volcanoes found in California and Oregon measure 3 to 4 mi (5 to 6 km) in diameter and 1,500 to 2,000 ft (500 to 600 m) in height, while shield volcanoes in

504-466: A carrier gas at 200–500 °C. Silicon dioxide is a relatively inert material (hence its widespread occurrence as a mineral). Silica is often used as inert containers for chemical reactions. At high temperatures, it is converted to silicon by reduction with carbon. Correlation In statistics , correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data . Although in

630-409: A causal relationship between the variables. This dictum should not be taken to mean that correlations cannot indicate the potential existence of causal relations. However, the causes underlying the correlation, if any, may be indirect and unknown, and high correlations also overlap with identity relations ( tautologies ), where no causal process exists. Consequently, a correlation between two variables

756-442: A correlation coefficient is not enough to define the dependence structure between random variables. The correlation coefficient completely defines the dependence structure only in very particular cases, for example when the distribution is a multivariate normal distribution . (See diagram above.) In the case of elliptical distributions it characterizes the (hyper-)ellipses of equal density; however, it does not completely characterize

882-414: A correlation matrix by a diagram where the "remarkable" correlations are represented by a solid line (positive correlation), or a dotted line (negative correlation). In some applications (e.g., building data models from only partially observed data) one wants to find the "nearest" correlation matrix to an "approximate" correlation matrix (e.g., a matrix which typically lacks semi-definite positiveness due to

1008-541: A far greater distance than those of other eruptive types before solidifying, forming extremely wide but relatively thin magmatic sheets often less than 1 m (3 ft) thick. Low volumes of such lavas layered over long periods of time are what slowly constructs the characteristically low, broad profile of a mature shield volcano. Also unlike other eruptive types, Hawaiian eruptions often occur at decentralized fissure vents , beginning with large "curtains of fire" that quickly die down and concentrate at specific locations on

1134-454: A further 13 km (8 mi) below the waterline and into the crust, approximately 80,000 km (19,000 cu mi) of rock. Kīlauea , another Hawaiian shield volcano, is one of the most active volcanoes on Earth, with its most recent eruption occurring in 2021. The Galápagos Islands are an isolated set of volcanoes, consisting of shield volcanoes and lava plateaus, about 1,100 km (680 mi) west of Ecuador. They are driven by

1260-407: A glass with no true melting point, can be used as a glass fibre for fibreglass. Silicon dioxide is mostly obtained by mining, including sand mining and purification of quartz . Quartz is suitable for many purposes, while chemical processing is required to make a purer or otherwise more suitable (e.g. more reactive or fine-grained) product. Precipitated silica or amorphous silica is produced by

1386-494: A heat capacity minimum. Its density decreases from 2.08 g/cm at 1950 °C to 2.03 g/cm at 2200 °C. The molecular SiO 2 has a linear structure like CO 2 . It has been produced by combining silicon monoxide (SiO) with oxygen in an argon matrix. The dimeric silicon dioxide, (SiO 2 ) 2 has been obtained by reacting O 2 with matrix isolated dimeric silicon monoxide, (Si 2 O 2 ). In dimeric silicon dioxide there are two oxygen atoms bridging between

SECTION 10

#1732794521121

1512-1031: A line of best fit through a dataset of two variables by essentially laying out the expected values and the resulting Pearson's correlation coefficient indicates how far away the actual dataset is from the expected values. Depending on the sign of our Pearson's correlation coefficient, we can end up with either a negative or positive correlation if there is any sort of relationship between the variables of our data set. The population correlation coefficient ρ X , Y {\displaystyle \rho _{X,Y}} between two random variables X {\displaystyle X} and Y {\displaystyle Y} with expected values μ X {\displaystyle \mu _{X}} and μ Y {\displaystyle \mu _{Y}} and standard deviations σ X {\displaystyle \sigma _{X}} and σ Y {\displaystyle \sigma _{Y}}

1638-450: A low value of 140° in α-tridymite, up to 180° in β-tridymite. In α-quartz, the Si–O–Si angle is 144°. Alpha quartz is the most stable form of solid SiO 2 at room temperature. The high-temperature minerals, cristobalite and tridymite, have both lower densities and indices of refraction than quartz. The transformation from α-quartz to beta-quartz takes place abruptly at 573 °C. Since

1764-557: A possible causal relationship, but cannot indicate what the causal relationship, if any, might be. The Pearson correlation coefficient indicates the strength of a linear relationship between two variables, but its value generally does not completely characterize their relationship. In particular, if the conditional mean of Y {\displaystyle Y} given X {\displaystyle X} , denoted E ⁡ ( Y ∣ X ) {\displaystyle \operatorname {E} (Y\mid X)} ,

1890-580: A prominent feature on these volcanoes and account for their seemingly random volcanic structure. They are fueled by the movement of the Pacific Plate over the Hawaii hotspot and form a long chain of volcanoes, atolls , and seamounts 2,600 km (1,616 mi) long with a total volume of over 750,000 km (179,935 cu mi). The chain includes Mauna Loa, a shield volcano which stands 4,170 m (13,680 ft) above sea level and reaches

2016-618: A series of n {\displaystyle n} measurements of the pair ( X i , Y i ) {\displaystyle (X_{i},Y_{i})} indexed by i = 1 , … , n {\displaystyle i=1,\ldots ,n} , the sample correlation coefficient can be used to estimate the population Pearson correlation ρ X , Y {\displaystyle \rho _{X,Y}} between X {\displaystyle X} and Y {\displaystyle Y} . The sample correlation coefficient

2142-410: A silicon wafer enables it to overcome the surface states that otherwise prevent electricity from reaching the semiconducting layer. The process of silicon surface passivation by thermal oxidation (silicon dioxide) is critical to the semiconductor industry . It is commonly used to manufacture metal–oxide–semiconductor field-effect transistors (MOSFETs) and silicon integrated circuit chips (with

2268-437: A single point. The main shield then forms, burying the smaller ones formed by the early eruptions with its lava. Icelandic shields are mostly small (~15 km (4 cu mi)), symmetrical (although this can be affected by surface topography), and characterized by eruptions from summit calderas. They are composed of either tholeiitic olivine or picritic basalt . The tholeiitic shields tend to be wider and shallower than

2394-411: A straight line. Although in the extreme cases of perfect rank correlation the two coefficients are both equal (being both +1 or both −1), this is not generally the case, and so values of the two coefficients cannot meaningfully be compared. For example, for the three pairs (1, 1) (2, 3) (3, 2) Spearman's coefficient is 1/2, while Kendall's coefficient is 1/3. The information given by

2520-519: A value of zero implies independence. This led some authors to recommend their routine usage, particularly of Distance correlation . Another alternative measure is the Randomized Dependence Coefficient. The RDC is a computationally efficient, copula -based measure of dependence between multivariate random variables and is invariant with respect to non-linear scalings of random variables. One important disadvantage of

2646-477: A very shallow layer of about 1 nm or 10 Å of so-called native oxide. Higher temperatures and alternative environments are used to grow well-controlled layers of silicon dioxide on silicon, for example at temperatures between 600 and 1200 °C, using so-called dry oxidation with O 2 or wet oxidation with H 2 O. The native oxide layer is beneficial in microelectronics , where it acts as electric insulator with high chemical stability. It can protect

SECTION 20

#1732794521121

2772-524: A white powder with extremely low bulk density (0.03-0.15 g/cm ) and thus high surface area. The particles act as a thixotropic thickening agent, or as an anti-caking agent, and can be treated to make them hydrophilic or hydrophobic for either water or organic liquid applications. Silica fume is an ultrafine powder collected as a by-product of the silicon and ferrosilicon alloy production. It consists of amorphous (non-crystalline) spherical particles with an average particle diameter of 150 nm, without

2898-461: Is Nyamuragira . Eruptions at the shield volcano are generally centered within the large summit caldera or on the numerous fissures and cinder cones on the volcano's flanks. Lava flows from the most recent century extend down the flanks more than 30 km (19 mi) from the summit, reaching as far as Lake Kivu . Erta Ale in Ethiopia is another active shield volcano and one of the few places in

3024-875: Is 0. However, because the correlation coefficient detects only linear dependencies between two variables, the converse is not necessarily true. A correlation coefficient of 0 does not imply that the variables are independent . X , Y  independent ⇒ ρ X , Y = 0 ( X , Y  uncorrelated ) ρ X , Y = 0 ( X , Y  uncorrelated ) ⇏ X , Y  independent {\displaystyle {\begin{aligned}X,Y{\text{ independent}}\quad &\Rightarrow \quad \rho _{X,Y}=0\quad (X,Y{\text{ uncorrelated}})\\\rho _{X,Y}=0\quad (X,Y{\text{ uncorrelated}})\quad &\nRightarrow \quad X,Y{\text{ independent}}\end{aligned}}} For example, suppose

3150-454: Is 0.7544, indicating that the points are far from lying on a straight line. In the same way if y {\displaystyle y} always decreases when x {\displaystyle x} increases , the rank correlation coefficients will be −1, while the Pearson product-moment correlation coefficient may or may not be close to −1, depending on how close the points are to

3276-492: Is a corollary of the Cauchy–Schwarz inequality that the absolute value of the Pearson correlation coefficient is not bigger than 1. Therefore, the value of a correlation coefficient ranges between −1 and +1. The correlation coefficient is +1 in the case of a perfect direct (increasing) linear relationship (correlation), −1 in the case of a perfect inverse (decreasing) linear relationship ( anti-correlation ), and some value in

3402-602: Is a nonlinear function of the other). Other correlation coefficients – such as Spearman's rank correlation – have been developed to be more robust than Pearson's, that is, more sensitive to nonlinear relationships. Mutual information can also be applied to measure dependence between two variables. The most familiar measure of dependence between two quantities is the Pearson product-moment correlation coefficient (PPMCC), or "Pearson's correlation coefficient", commonly called simply "the correlation coefficient". It

3528-666: Is a shield volcano on the southwestern part of Isabela Island and is one of the most active in the Galapagos, with the last eruption between May and June 2008. The Geophysics Institute at the National Polytechnic School in Quito houses an international team of seismologists and volcanologists whose responsibility is to monitor Ecuador's numerous active volcanoes in the Andean Volcanic Belt and

3654-439: Is also the primary component of rice husk ash , which is used, for example, in filtration and as supplementary cementitious material (SCM) in cement and concrete manufacturing. Silicification in and by cells has been common in the biological world and it occurs in bacteria, protists, plants, and animals (invertebrates and vertebrates). Prominent examples include: About 95% of the commercial use of silicon dioxide (sand)

3780-399: Is an oxide of silicon with the chemical formula SiO 2 , commonly found in nature as quartz . In many parts of the world, silica is the major constituent of sand . Silica is one of the most complex and abundant families of materials , existing as a compound of several minerals and as a synthetic product. Examples include fused quartz , fumed silica , opal , and aerogels . It

3906-527: Is common in Hawaiʻi; most Hawaiian eruptions begin with a so-called "wall of fire" along a major fissure line before centralizing to a small number of points. This accounts for their asymmetrical shape, whereas Icelandic volcanoes follow a pattern of central eruptions dominated by summit calderas , causing the lava to be more evenly distributed or symmetrical. Most of what is currently known about shield volcanic eruptive character has been gleaned from studies done on

Shield volcano - Misplaced Pages Continue

4032-410: Is consideration of the copula between them, while the coefficient of determination generalizes the correlation coefficient to multiple regression . The degree of dependence between variables X and Y does not depend on the scale on which the variables are expressed. That is, if we are analyzing the relationship between X and Y , most correlation measures are unaffected by transforming X to

4158-604: Is covalently bonded in a tetrahedral manner to 4 oxygen atoms. In contrast, CO 2 is a linear molecule. The starkly different structures of the dioxides of carbon and silicon are a manifestation of the double bond rule . Based on the crystal structural differences, silicon dioxide can be divided into two categories: crystalline and non-crystalline (amorphous). In crystalline form, this substance can be found naturally occurring as quartz , tridymite (high-temperature form), cristobalite (high-temperature form), stishovite (high-pressure form), and coesite (high-pressure form). On

4284-448: Is defined as where x ¯ {\displaystyle {\overline {x}}} and y ¯ {\displaystyle {\overline {y}}} are the sample means of X {\displaystyle X} and Y {\displaystyle Y} , and s x {\displaystyle s_{x}} and s y {\displaystyle s_{y}} are

4410-845: Is defined as: ρ X , Y = corr ⁡ ( X , Y ) = cov ⁡ ( X , Y ) σ X σ Y = E ⁡ [ ( X − μ X ) ( Y − μ Y ) ] σ X σ Y , if   σ X σ Y > 0. {\displaystyle \rho _{X,Y}=\operatorname {corr} (X,Y)={\operatorname {cov} (X,Y) \over \sigma _{X}\sigma _{Y}}={\operatorname {E} [(X-\mu _{X})(Y-\mu _{Y})] \over \sigma _{X}\sigma _{Y}},\quad {\text{if}}\ \sigma _{X}\sigma _{Y}>0.} where E {\displaystyle \operatorname {E} }

4536-455: Is depicted in the so-called demand curve . Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there is a causal relationship , because extreme weather causes people to use more electricity for heating or cooling. However, in general,

4662-495: Is designed to use the sensitivity to the range in order to pick out correlations between fast components of time series . By reducing the range of values in a controlled manner, the correlations on long time scale are filtered out and only the correlations on short time scales are revealed. The correlation matrix of n {\displaystyle n} random variables X 1 , … , X n {\displaystyle X_{1},\ldots ,X_{n}}

4788-465: Is in the construction industry, e.g. in the production of concrete ( Portland cement concrete ). Certain deposits of silica sand, with desirable particle size and shape and desirable clay and other mineral content, were important for sand casting of metallic products. The high melting point of silica enables it to be used in such applications such as iron casting; modern sand casting sometimes uses other minerals for other reasons. Crystalline silica

4914-426: Is not a sufficient condition to establish a causal relationship (in either direction). A correlation between age and height in children is fairly causally transparent, but a correlation between mood and health in people is less so. Does improved mood lead to improved health, or does good health lead to good mood, or both? Or does some other factor underlie both? In other words, a correlation can be taken as evidence for

5040-460: Is not linear in X {\displaystyle X} , the correlation coefficient will not fully determine the form of E ⁡ ( Y ∣ X ) {\displaystyle \operatorname {E} (Y\mid X)} . The adjacent image shows scatter plots of Anscombe's quartet , a set of four different pairs of variables created by Francis Anscombe . The four y {\displaystyle y} variables have

5166-459: Is obtained by taking the ratio of the covariance of the two variables in question of our numerical dataset, normalized to the square root of their variances. Mathematically, one simply divides the covariance of the two variables by the product of their standard deviations . Karl Pearson developed the coefficient from a similar but slightly different idea by Francis Galton . A Pearson product-moment correlation coefficient attempts to establish

Shield volcano - Misplaced Pages Continue

5292-651: Is obtained by the dealumination of a low-sodium, ultra-stable Y zeolite with combined acid and thermal treatment. The resulting product contains over 99% silica, and has high crystallinity and specific surface area (over 800 m /g). Faujasite-silica has very high thermal and acid stability. For example, it maintains a high degree of long-range molecular order or crystallinity even after boiling in concentrated hydrochloric acid . Molten silica exhibits several peculiar physical characteristics that are similar to those observed in liquid water : negative temperature expansion, density maximum at temperatures ~5000 °C, and

5418-421: Is rapidly cooled, it does not crystallize, but solidifies as a glass. Because of this, most ceramic glazes have silica as the main ingredient. The structural geometry of silicon and oxygen in glass is similar to that in quartz and most other crystalline forms of silicon and oxygen, with silicon surrounded by regular tetrahedra of oxygen centres. The difference between the glass and crystalline forms arises from

5544-399: Is relatively smooth and flows with a ropey texture, and ʻaʻā flows which are denser, more viscous (and thus slower moving) and blockier. These lava flows can be anywhere between 2 and 20 m (10 and 70 ft) thick. ʻAʻā lava flows move through pressure— the partially solidified front of the flow steepens because of the mass of flowing lava behind it until it breaks off, after which

5670-532: Is taken from the German term Schildvulkan , coined by the Austrian geologist Eduard Suess in 1888 and which had been calqued into English by 1910. Shield volcanoes are distinguished from the three other major volcanic types— stratovolcanoes , lava domes , and cinder cones —by their structural form, a consequence of their particular magmatic composition. Of these four forms, shield volcanoes erupt

5796-406: Is the n × n {\displaystyle n\times n} matrix C {\displaystyle C} whose ( i , j ) {\displaystyle (i,j)} entry is Thus the diagonal entries are all identically one . If the measures of correlation used are product-moment coefficients, the correlation matrix is the same as the covariance matrix of

5922-1087: Is the expected value operator, cov {\displaystyle \operatorname {cov} } means covariance , and corr {\displaystyle \operatorname {corr} } is a widely used alternative notation for the correlation coefficient. The Pearson correlation is defined only if both standard deviations are finite and positive. An alternative formula purely in terms of moments is: ρ X , Y = E ⁡ ( X Y ) − E ⁡ ( X ) E ⁡ ( Y ) E ⁡ ( X 2 ) − E ⁡ ( X ) 2 ⋅ E ⁡ ( Y 2 ) − E ⁡ ( Y ) 2 {\displaystyle \rho _{X,Y}={\operatorname {E} (XY)-\operatorname {E} (X)\operatorname {E} (Y) \over {\sqrt {\operatorname {E} (X^{2})-\operatorname {E} (X)^{2}}}\cdot {\sqrt {\operatorname {E} (Y^{2})-\operatorname {E} (Y)^{2}}}}} It

6048-426: Is the major constituent of sand . Even though it is poorly soluble, silica occurs in many plants such as rice . Plant materials with high silica phytolith content appear to be of importance to grazing animals, from chewing insects to ungulates . Silica accelerates tooth wear, and high levels of silica in plants frequently eaten by herbivores may have developed as a defense mechanism against predation. Silica

6174-516: Is the measure of how two or more variables are related to one another. There are several correlation coefficients , often denoted ρ {\displaystyle \rho } or r {\displaystyle r} , measuring the degree of correlation. The most common of these is the Pearson correlation coefficient , which is sensitive only to a linear relationship between two variables (which may be present even when one variable

6300-457: Is the only polymorph of silica stable at the Earth's surface. Metastable occurrences of the high-pressure forms coesite and stishovite have been found around impact structures and associated with eclogites formed during ultra-high-pressure metamorphism . The high-temperature forms of tridymite and cristobalite are known from silica-rich volcanic rocks . In many parts of the world, silica

6426-504: Is the process by which a semiconductor surface is rendered inert, and does not change semiconductor properties as a result of interaction with air or other materials in contact with the surface or edge of the crystal. The formation of a thermally grown silicon dioxide layer greatly reduces the concentration of electronic states at the silicon surface . SiO 2 films preserve the electrical characteristics of p–n junctions and prevent these electrical characteristics from deteriorating by

SECTION 50

#1732794521121

6552-436: Is used as a fining agent for wine, beer, and juice, with the E number reference E551 . In cosmetics, silica is useful for its light-diffusing properties and natural absorbency. Diatomaceous earth , a mined product, has been used in food and cosmetics for centuries. It consists of the silica shells of microscopic diatoms ; in a less processed form it was sold as "tooth powder". Manufactured or mined hydrated silica

6678-489: Is used as the hard abrasive in toothpaste . Silicon dioxide is widely used in the semiconductor technology: Because silicon dioxide is a native oxide of silicon it is more widely used compared to other semiconductors like gallium arsenide or indium phosphide . Silicon dioxide could be grown on a silicon semiconductor surface. Silicon oxide layers could protect silicon surfaces during diffusion processes , and could be used for diffusion masking. Surface passivation

6804-418: Is used in hydraulic fracturing of formations which contain tight oil and shale gas . Silica is the primary ingredient in the production of most glass . As other minerals are melted with silica, the principle of freezing point depression lowers the melting point of the mixture and increases fluidity. The glass transition temperature of pure SiO 2 is about 1475 K. When molten silicon dioxide SiO 2

6930-498: Is used in structural materials , microelectronics , and as components in the food and pharmaceutical industries. All forms are white or colorless, although impure samples can be colored. Silicon dioxide is a common fundamental constituent of glass . In the majority of silicon dioxides, the silicon atom shows tetrahedral coordination , with four oxygen atoms surrounding a central Si atom ( see 3-D Unit Cell ). Thus, SiO 2 forms 3-dimensional network solids in which each silicon atom

7056-538: Is used to produce elemental silicon . The process involves carbothermic reduction in an electric arc furnace : Fumed silica , also known as pyrogenic silica, is prepared by burning SiCl 4 in an oxygen-rich hydrogen flame to produce a "smoke" of SiO 2 . It can also be produced by vaporizing quartz sand in a 3000 °C electric arc. Both processes result in microscopic droplets of amorphous silica fused into branched, chainlike, three-dimensional secondary particles which then agglomerate into tertiary particles,

7182-405: Is zero; they are uncorrelated . However, in the special case when X {\displaystyle X} and Y {\displaystyle Y} are jointly normal , uncorrelatedness is equivalent to independence. Even though uncorrelated data does not necessarily imply independence, one can check if random variables are independent if their mutual information is 0. Given

7308-402: The uncorrected sample standard deviations of X {\displaystyle X} and Y {\displaystyle Y} . If x {\displaystyle x} and y {\displaystyle y} are results of measurements that contain measurement error, the realistic limits on the correlation coefficient are not −1 to +1 but a smaller range. For

7434-475: The Galápagos hotspot , and are between approximately 4.2 million and 700,000 years of age. The largest island, Isabela , consists of six coalesced shield volcanoes, each delineated by a large summit caldera. Española , the oldest island, and Fernandina , the youngest, are also shield volcanoes, as are most of the other islands in the chain. The Galápagos Islands are perched on a large lava plateau known as

7560-684: The Mid-Atlantic Ridge , a divergent tectonic plate boundary in the middle of the Atlantic Ocean, Iceland is the site of about 130 volcanoes of various types. Icelandic shield volcanoes are generally of Holocene age, between 5,000 and 10,000 years old. The volcanoes are also very narrow in distribution, occurring in two bands in the West and North Volcanic Zones. Like Hawaiian volcanoes, their formation initially begins with several eruptive centers before centralizing and concentrating at

7686-833: The Newton's method for computing the nearest correlation matrix ) results obtained in the subsequent years. Similarly for two stochastic processes { X t } t ∈ T {\displaystyle \left\{X_{t}\right\}_{t\in {\mathcal {T}}}} and { Y t } t ∈ T {\displaystyle \left\{Y_{t}\right\}_{t\in {\mathcal {T}}}} : If they are independent, then they are uncorrelated. The opposite of this statement might not be true. Even if two variables are uncorrelated, they might not be independent to each other. The conventional dictum that " correlation does not imply causation " means that correlation cannot be used by itself to infer

SECTION 60

#1732794521121

7812-439: The Pearson product-moment correlation coefficient , and are best seen as measures of a different type of association, rather than as an alternative measure of the population correlation coefficient. To illustrate the nature of rank correlation, and its difference from linear correlation, consider the following four pairs of numbers ( x , y ) {\displaystyle (x,y)} : As we go from each pair to

7938-448: The coefficient of multiple determination , a measure of goodness of fit in multiple regression . In statistical modelling , correlation matrices representing the relationships between variables are categorized into different correlation structures, which are distinguished by factors such as the number of parameters required to estimate them. For example, in an exchangeable correlation matrix, all pairs of variables are modeled as having

8064-412: The corrected sample standard deviations of X {\displaystyle X} and Y {\displaystyle Y} . Equivalent expressions for r x y {\displaystyle r_{xy}} are where s x ′ {\displaystyle s'_{x}} and s y ′ {\displaystyle s'_{y}} are

8190-444: The open interval ( − 1 , 1 ) {\displaystyle (-1,1)} in all other cases, indicating the degree of linear dependence between the variables. As it approaches zero there is less of a relationship (closer to uncorrelated). The closer the coefficient is to either −1 or 1, the stronger the correlation between the variables. If the variables are independent , Pearson's correlation coefficient

8316-555: The planar process ). Hydrophobic silica is used as a defoamer component . In its capacity as a refractory , it is useful in fiber form as a high-temperature thermal protection fabric. Silica is used in the extraction of DNA and RNA due to its ability to bind to the nucleic acids under the presence of chaotropes . Silica aerogel was used in the Stardust spacecraft to collect extraterrestrial particles. Pure silica (silicon dioxide), when cooled as fused quartz into

8442-401: The standardized random variables X i / σ ( X i ) {\displaystyle X_{i}/\sigma (X_{i})} for i = 1 , … , n {\displaystyle i=1,\dots ,n} . This applies both to the matrix of population correlations (in which case σ {\displaystyle \sigma } is

8568-418: The 1976–1979 Viking mission . The principal difference between the volcanoes of Mars and those on Earth is in terms of size; Martian volcanoes range in size up to 14 mi (23 km) high and 370 mi (595 km) in diameter, far larger than the 6 mi (10 km) high, 74 mi (119 km) wide Hawaiian shields. The highest of these, Olympus Mons , is the tallest known mountain on any planet in

8694-567: The Galapagos Islands. La Cumbre is an active shield volcano on Fernandina Island that has been erupting since April 11, 2009. The Galápagos islands are geologically young for such a big chain, and the pattern of their rift zones follows one of two trends, one north-northwest, and one east–west. The composition of the lavas of the Galápagos shields are strikingly similar to those of the Hawaiian volcanoes. Curiously, they do not form

8820-531: The Galápagos Platform. This platform creates a shallow water depth of 360 to 900 m (1,181 to 2,953 ft) at the base of the islands, which stretch over a 174 mi (280 km) diameter. Since Charles Darwin 's visit to the islands in 1835 during the second voyage of HMS Beagle , there have been over 60 recorded eruptions in the islands, from six different shield volcanoes. Of the 21 emergent volcanoes, 13 are considered active. Cerro Azul

8946-779: The accumulation of fragmentary material from particularly powerful explosive eruptions, and rarer felsic lava shields formed by unusually fluid felsic magmas. Examples of pyroclastic shields include Billy Mitchell volcano in Papua New Guinea and the Purico complex in Chile ; an example of a felsic shield is the Ilgachuz Range in British Columbia , Canada. Shield volcanoes are similar in origin to vast lava plateaus and flood basalts present in various parts of

9072-496: The acidification of solutions of sodium silicate . The gelatinous precipitate or silica gel , is first washed and then dehydrated to produce colorless microporous silica. The idealized equation involving a trisilicate and sulfuric acid is: Approximately one billion kilograms/year (1999) of silica were produced in this manner, mainly for use for polymer composites – tires and shoe soles. Thin films of silica grow spontaneously on silicon wafers via thermal oxidation , producing

9198-453: The alternative, more general measures is that, when used to test whether two variables are associated, they tend to have lower power compared to Pearson's correlation when the data follow a multivariate normal distribution. This is an implication of the No free lunch theorem theorem. To detect all kinds of relationships, these measures have to sacrifice power on other relationships, particularly for

9324-412: The assumption of normality. The second one (top right) is not distributed normally; while an obvious relationship between the two variables can be observed, it is not linear. In this case the Pearson correlation coefficient does not indicate that there is an exact functional relationship: only the extent to which that relationship can be approximated by a linear relationship. In the third case (bottom left),

9450-552: The branching of the pyrogenic product. The main use is as pozzolanic material for high performance concrete. Fumed silica nanoparticles can be successfully used as an anti-aging agent in asphalt binders. Silica, either colloidal, precipitated, or pyrogenic fumed, is a common additive in food production. It is used primarily as a flow or anti- caking agent in powdered foods such as spices and non-dairy coffee creamer, or powders to be formed into pharmaceutical tablets. It can adsorb water in hygroscopic applications. Colloidal silica

9576-402: The broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it

9702-402: The case of a linear model with a single independent variable, the coefficient of determination (R squared) is the square of r x y {\displaystyle r_{xy}} , Pearson's product-moment coefficient. Consider the joint probability distribution of X and Y given in the table below. For this joint distribution, the marginal distributions are: This yields

9828-505: The central Mexican Michoacán–Guanajuato volcanic field average 340 m (1,100 ft) in height and 4,100 m (13,500 ft) in width, with an average slope angle of 9.4° and an average volume of 1.7 km (0.4 cu mi). Rift zones are a prevalent feature on shield volcanoes that is rare on other volcanic types. The large, decentralized shape of Hawaiian volcanoes as compared to their smaller, symmetrical Icelandic cousins can be attributed to rift eruptions. Fissure venting

9954-474: The conditional expectation of one variable given the other is not constant as the conditioning variable changes ; broadly correlation in this specific sense is used when E ( Y | X = x ) {\displaystyle E(Y|X=x)} is related to x {\displaystyle x} in some manner (such as linearly, monotonically, or perhaps according to some particular functional form such as logarithmic). Essentially, correlation

10080-509: The connectivity of the tetrahedral units: Although there is no long-range periodicity in the glassy network, ordering remains at length scales well beyond the SiO bond length. One example of this ordering is the preference to form rings of 6-tetrahedra. The majority of optical fibers for telecommunications are also made from silica. It is a primary raw material for many ceramics such as earthenware , stoneware , and porcelain . Silicon dioxide

10206-495: The correlation-like range ⁠ [ − 1 , 1 ] {\displaystyle [-1,1]} ⁠ . The odds ratio is generalized by the logistic model to model cases where the dependent variables are discrete and there may be one or more independent variables. The correlation ratio , entropy -based mutual information , total correlation , dual total correlation and polychoric correlation are all also capable of detecting more general dependencies, as

10332-488: The densest of the low-pressure forms, which has a density of 2.648 g/cm . The difference in density can be ascribed to the increase in coordination as the six shortest Si–O bond lengths in stishovite (four Si–O bond lengths of 176 pm and two others of 181 pm) are greater than the Si–O bond length (161 pm) in α-quartz. The change in the coordination increases the ionicity of the Si–O bond. Faujasite silica, another polymorph,

10458-424: The dependence structure (for example, a multivariate t-distribution 's degrees of freedom determine the level of tail dependence). For continuous variables, multiple alternative measures of dependence were introduced to address the deficiency of Pearson's correlation that it can be zero for dependent random variables (see and reference references therein for an overview). They all share the important property that

10584-449: The extents of the volcano have not been confirmed. Although Tamu Massif was initially believed to be a shield volcano, Sanger and his colleagues acknowledged in 2019 that Tamu Massif is not a shield volcano. Shield volcanoes feature a gentle (usually 2° to 3°) slope that gradually steepens with elevation (reaching approximately 10°) before flattening near the summit, forming an overall upwardly convex shape. These slope characteristics have

10710-416: The following expectations and variances: Therefore: Rank correlation coefficients, such as Spearman's rank correlation coefficient and Kendall's rank correlation coefficient (τ) measure the extent to which, as one variable increases, the other variable tends to increase, without requiring that increase to be represented by a linear relationship. If, as the one variable increases, the other decreases ,

10836-411: The gaseous ambient environment. Silicon oxide layers could be used to electrically stabilize silicon surfaces. The surface passivation process is an important method of semiconductor device fabrication that involves coating a silicon wafer with an insulating layer of silicon oxide so that electricity could reliably penetrate to the conducting silicon below. Growing a layer of silicon dioxide on top of

10962-410: The general mass behind it moves forward. Though the top of the flow quickly cools down, the molten underbelly of the flow is buffered by the solidifying rock above it, and by this mechanism, ʻaʻā flows can sustain movement for long periods of time. Pāhoehoe flows, in contrast, move in more conventional sheets, or by the advancement of lava "toes" in snaking lava columns. Increasing viscosity on the part of

11088-571: The height of the volcano above the sea floor , the "true" height of Mauna Loa from the start of its eruptive history is about 17,170 m (56,000 ft). Mount Everest , by comparison, is 8,848 m (29,029 ft) in height. In 2013, a team led by the University of Houston 's William Sager announced the discovery of Tamu Massif , an enormous extinct submarine volcano, approximately 450 by 650 km (280 by 400 mi) in area, which dwarfs all previously known volcanoes on Earth. However,

11214-626: The important special case of a linear relationship with Gaussian marginals, for which Pearson's correlation is optimal. Another problem concerns interpretation. While Person's correlation can be interpreted for all values, the alternative measures can generally only be interpreted meaningfully at the extremes. For two binary variables , the odds ratio measures their dependence, and takes range non-negative numbers, possibly infinity: ⁠ [ 0 , + ∞ ] {\displaystyle [0,+\infty ]} ⁠ . Related statistics such as Yule's Y and Yule's Q normalize this to

11340-463: The largest volcanic features on Earth. The summit of the largest subaerial volcano in the world, Mauna Loa , lies 4,169 m (13,678 ft) above sea level , and the volcano, over 60 mi (100 km) wide at its base, is estimated to contain about 80,000 km (19,000 cu mi) of basalt. The mass of the volcano is so great that it has slumped the crust beneath it a further 8 km (5 mi). Accounting for this subsidence and for

11466-450: The latter case. Several techniques have been developed that attempt to correct for range restriction in one or both variables, and are commonly used in meta-analysis; the most common are Thorndike's case II and case III equations. Various correlation measures in use may be undefined for certain joint distributions of X and Y . For example, the Pearson correlation coefficient is defined in terms of moments , and hence will be undefined if

11592-640: The lava or shear stress on the part of local topography can morph a pāhoehoe flow into an ʻaʻā one, but the reverse never occurs. Although most shield volcanoes are by volume almost entirely Hawaiian and basaltic in origin, they are rarely exclusively so. Some volcanoes, such as Mount Wrangell in Alaska and Cofre de Perote in Mexico, exhibit large enough swings in their historical magmatic eruptive characteristics to cast strict categorical assignment in doubt; one geological study of de Perote went so far as to suggest

11718-541: The least viscous lavas. Whereas stratovolcanoes and lava domes are the product of highly viscous flows, and cinder cones are constructed of explosively eruptive tephra , shield volcanoes are the product of gentle effusive eruptions of highly fluid lavas that produce, over time, a broad, gently sloped eponymous "shield". Although the term is generally applied to basaltic shields, it has also at times been applied to rarer scutiform volcanoes of differing magmatic composition—principally pyroclastic shields , formed by

11844-404: The manner in which X and Y are sampled. Dependencies tend to be stronger if viewed over a wider range of values. Thus, if we consider the correlation coefficient between the heights of fathers and their sons over all adult males, and compare it to the same correlation coefficient calculated when the fathers are selected to be between 165 cm and 170 cm in height, the correlation will be weaker in

11970-466: The moments are undefined. Measures of dependence based on quantiles are always defined. Sample-based statistics intended to estimate population measures of dependence may or may not have desirable statistical properties such as being unbiased , or asymptotically consistent , based on the spatial structure of the population from which the data were sampled. Sensitivity to the data distribution can be used to an advantage. For example, scaled correlation

12096-777: The most prominent ones are situated along the Snake River in Idaho and the Columbia River in Washington and Oregon, where they have been measured to be over 1 mi (2 km) in thickness. Calderas are a common feature on shield volcanoes. They are formed and reformed over the volcano's lifespan. Long eruptive periods form cinder cones, which then collapse over time to form calderas. The calderas are often filled up by progressive eruptions, or formed elsewhere, and this cycle of collapse and regeneration takes place throughout

12222-516: The next pair x {\displaystyle x} increases, and so does y {\displaystyle y} . This relationship is perfect, in the sense that an increase in x {\displaystyle x} is always accompanied by an increase in y {\displaystyle y} . This means that we have a perfect rank correlation, and both Spearman's and Kendall's correlation coefficients are 1, whereas in this example Pearson product-moment correlation coefficient

12348-400: The other hand, amorphous silica can be found in nature as opal and diatomaceous earth . Quartz glass is a form of intermediate state between these structures. All of these distinct crystalline forms always have the same local structure around Si and O. In α-quartz the Si–O bond length is 161 pm, whereas in α-tridymite it is in the range 154–171 pm. The Si–O–Si angle also varies between

12474-546: The picritic shields. They do not follow the pattern of caldera growth and destruction that other shield volcanoes do; caldera may form, but they generally do not disappear. Bingöl Mountains are one of the shield volcanoes in Turkey . In East Africa, volcanic activity is generated by the development of the East African Rift and from nearby hotspots. Some volcanoes interact with both. Shield volcanoes are found near

12600-405: The population standard deviation), and to the matrix of sample correlations (in which case σ {\displaystyle \sigma } denotes the sample standard deviation). Consequently, each is necessarily a positive-semidefinite matrix . Moreover, the correlation matrix is strictly positive definite if no variable can have all its values exactly generated as a linear function of

12726-467: The presence of a correlation is not sufficient to infer the presence of a causal relationship (i.e., correlation does not imply causation ). Formally, random variables are dependent if they do not satisfy a mathematical property of probabilistic independence . In informal parlance, correlation is synonymous with dependence . However, when used in a technical sense, correlation refers to any of several specific types of mathematical relationship between

12852-463: The random variable X {\displaystyle X} is symmetrically distributed about zero, and Y = X 2 {\displaystyle Y=X^{2}} . Then Y {\displaystyle Y} is completely determined by X {\displaystyle X} , so that X {\displaystyle X} and Y {\displaystyle Y} are perfectly dependent, but their correlation

12978-406: The rank correlation coefficients will be negative. It is common to regard these rank correlation coefficients as alternatives to Pearson's coefficient, used either to reduce the amount of calculation or to make the coefficient less sensitive to non-normality in distributions. However, this view has little mathematical basis, as rank correlation coefficients measure a different type of relationship than

13104-505: The rift and off the coast of Africa, although stratovolcanoes are more common. Although sparsely studied, the fact that all of its volcanoes are of Holocene age reflects how young the volcanic center is. One interesting characteristic of East African volcanism is a penchant for the formation of lava lakes ; these semi-permanent lava bodies, extremely rare elsewhere, form in about 9% of African eruptions. The most active shield volcano in Africa

13230-440: The same correlation, so all non-diagonal elements of the matrix are equal to each other. On the other hand, an autoregressive matrix is often used when variables represent a time series, since correlations are likely to be greater when measurements are closer in time. Other examples include independent, unstructured, M-dependent, and Toeplitz . In exploratory data analysis , the iconography of correlations consists in replacing

13356-404: The same mean (7.5), variance (4.12), correlation (0.816) and regression line ( y = 3 + 0.5 x {\textstyle y=3+0.5x} ). However, as can be seen on the plots, the distribution of the variables is very different. The first one (top left) seems to be distributed normally, and corresponds to what one would expect when considering two variables correlated and following

13482-569: The same volcanic "line" associated with most hotspots. They are not alone in this regard; the Cobb–Eickelberg Seamount chain in the North Pacific is another example of such a delineated chain. In addition, there is no clear pattern of age between the volcanoes, suggesting a complicated, irregular pattern of creation. How the islands were formed remains a geological mystery, although several theories have been proposed. Located over

13608-422: The seafloor. The Hawaiian and Galápagos shields, and other hotspot shields like them, are constructed of oceanic island basalt. Their lavas are characterized by high levels of sodium , potassium , and aluminium . Features common in shield volcanism include lava tubes . Lava tubes are cave-like volcanic straights formed by the hardening of overlaying lava. These structures help further the propagation of lava, as

13734-401: The silicon atoms with an Si–O–Si angle of 94° and bond length of 164.6 pm and the terminal Si–O bond length is 150.2 pm. The Si–O bond length is 148.3 pm, which compares with the length of 161 pm in α-quartz. The bond energy is estimated at 621.7 kJ/mol. SiO 2 is most commonly encountered in nature as quartz , which comprises more than 10% by mass of the Earth's crust. Quartz

13860-418: The silicon, store charge, block current, and even act as a controlled pathway to limit current flow. Many routes to silicon dioxide start with an organosilicon compound, e.g., HMDSO, TEOS. Synthesis of silica is illustrated below using tetraethyl orthosilicate (TEOS). Simply heating TEOS at 680–730 °C results in the oxide: Similarly TEOS combusts around 400 °C: TEOS undergoes hydrolysis via

13986-401: The site of one of the longest-lasting rift eruptions in known history. The Hawaiian shield volcanoes are not located near any plate boundaries ; the volcanic activity of this island chain is distributed by the movement of the oceanic plate over an upwelling of magma known as a hotspot . Over millions of years, the tectonic movement that moves continents also creates long volcanic trails across

14112-492: The so-called sol-gel process . The course of the reaction and nature of the product are affected by catalysts, but the idealized equation is: Being highly stable, silicon dioxide arises from many methods. Conceptually simple, but of little practical value, combustion of silane gives silicon dioxide. This reaction is analogous to the combustion of methane: However the chemical vapor deposition of silicon dioxide onto crystal surface from silane had been used using nitrogen as

14238-480: The solar system. Venus has over 150 shield volcanoes which are much flatter, with a larger surface area than those found on Earth, some having a diameter of more than 700 km (430 mi). Although the majority of these are long extinct it has been suggested, from observations by the Venus Express spacecraft , that many may still be active. Silica Silicon dioxide , also known as silica ,

14364-1081: The surface wells up), such as the Hawaiian–Emperor seamount chain and the Galápagos Islands , or over more conventional rift zones, such as the Icelandic shields and the shield volcanoes of East Africa. Although shield volcanoes are not usually associated with subduction , they can occur over subduction zones. Many examples are found in California and Oregon, including Prospect Peak in Lassen Volcanic National Park , as well as Pelican Butte and Belknap Crater in Oregon. Many shield volcanoes are found in ocean basins , such as Kīlauea in Hawaii, although they can be found inland as well—East Africa being one example of this. The largest and most prominent shield volcano chain in

14490-439: The surrounding heat, and hit the ground still hot, accumulating into spatter cones . If eruptive rates are high enough, they may even form splatter-fed lava flows. Hawaiian eruptions are often extremely long-lived; Puʻu ʻŌʻō , a cinder cone of Kīlauea , erupted continuously from January 3, 1983, until April 2018. Flows from Hawaiian eruptions can be divided into two types by their structural characteristics: pāhoehoe lava which

14616-416: The term "compound shield-like volcano" instead. Most mature shield volcanoes have multiple cinder cones on their flanks, the results of tephra ejections common during incessant activity and markers of currently and formerly active sites on the volcano. An example of these parasitic cones is at Puʻu ʻŌʻō on Kīlauea—continuous activity ongoing since 1983 has built up a 2,290 ft (698 m) tall cone at

14742-446: The transformation is accompanied by a significant change in volume, it can easily induce fracturing of ceramics or rocks passing through this temperature limit. The high-pressure minerals, seifertite , stishovite, and coesite, though, have higher densities and indices of refraction than quartz. Stishovite has a rutile -like structure where silicon is 6-coordinate. The density of stishovite is 4.287 g/cm , which compares to α-quartz,

14868-459: The values of the others. The correlation matrix is symmetric because the correlation between X i {\displaystyle X_{i}} and X j {\displaystyle X_{j}} is the same as the correlation between X j {\displaystyle X_{j}} and X i {\displaystyle X_{i}} . A correlation matrix appears, for example, in one formula for

14994-469: The volcano's lifespan. Interactions between water and lava at shield volcanoes can cause some eruptions to become hydrovolcanic . These explosive eruptions are drastically different from the usual shield volcanic activity and are especially prevalent at the waterbound volcanoes of the Hawaiian Isles . Shield volcanoes are found worldwide. They can form over hotspots (points where magma from below

15120-442: The volcano's rift zones. Central-vent eruptions, meanwhile, often take the form of large lava fountains (both continuous and sporadic), which can reach heights of hundreds of meters or more. The particles from lava fountains usually cool in the air before hitting the ground, resulting in the accumulation of cindery scoria fragments; however, when the air is especially thick with pyroclasts , they cannot cool off fast enough because of

15246-431: The volcanoes of Hawaiʻi Island , by far the most intensively studied of all shields because of their scientific accessibility; the island lends its name to the slow-moving, effusive eruptions typical of shield volcanism, known as Hawaiian eruptions . These eruptions, the least explosive of volcanic events, are characterized by the effusive emission of highly fluid basaltic lavas with low gaseous content . These lavas travel

15372-532: The walls of the tube insulate the lava within. Lava tubes can account for a large portion of shield volcano activity; for example, an estimated 58% of the lava forming Kīlauea comes from lava tubes. In some shield volcano eruptions, basaltic lava pours out of a long fissure instead of a central vent, and shrouds the countryside with a long band of volcanic material in the form of a broad plateau . Plateaus of this type exist in Iceland, Washington, Oregon, and Idaho;

15498-553: The way it has been computed). In 2002, Higham formalized the notion of nearness using the Frobenius norm and provided a method for computing the nearest correlation matrix using the Dykstra's projection algorithm , of which an implementation is available as an online Web API. This sparked interest in the subject, with new theoretical (e.g., computing the nearest correlation matrix with factor structure ) and numerical (e.g. usage

15624-721: The world is the Hawaiian–Emperor seamount chain, a chain of hotspot volcanoes in the Pacific Ocean. The volcanoes follow a distinct evolutionary pattern of growth and death. The chain contains at least 43 major volcanoes, and Meiji Seamount at its terminus near the Kuril–Kamchatka Trench is 85 million years old. The youngest part of the chain is Hawaii, where the volcanoes are characterized by frequent rift eruptions, their large size (thousands of km in volume), and their rough, decentralized shape. Rift zones are

15750-683: The world with a permanent lava lake, which has been active since at least 1967, and possibly since 1906. Other volcanic centers include Menengai , a massive shield caldera, and Mount Marsabit in Kenya. Shield volcanoes are not limited to Earth; they have been found on Mars , Venus , and Jupiter's moon, Io . The shield volcanoes of Mars are very similar to the shield volcanoes on Earth. On both planets, they have gently sloping flanks, collapse craters along their central structure, and are built of highly fluid lavas. Volcanic features on Mars were observed long before they were first studied in detail during

15876-434: The world. These are eruptive features which occur along linear fissure vents and are distinguished from shield volcanoes by the lack of an identifiable primary eruptive center. Active shield volcanoes experience near-continuous eruptive activity over extremely long periods of time, resulting in the gradual build-up of edifices that can reach extremely large dimensions. With the exclusion of flood basalts, mature shields are

#120879