Seismic Waves Under the Surface Seismic Waves Under the Surface Clip Art

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Properties and Applications of Love Surface Waves in Seismology and Biosensors

Submitted: May 8th, 2017 Reviewed: February 15th, 2018 Published: April 10th, 2018

DOI: 10.5772/intechopen.75479

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Abstract

Shear horizontal (SH) surface waves of the Beloved type are elastic surface waves propagating in layered waveguides, in which surface layer is "slower" than the substrate. Love surface waves are of primary importance in geophysics and seismology, since most structural damages in the wake of earthquakes are attributed to the devastating SH motion inherent to the Love surface waves. On the other paw, Beloved surface waves found benign applications in biosensors used in biology, medicine, and chemistry. In this chapter, we briefly sketch a mathematical model for Beloved surface waves and present examples of the resulting dispersion curves for phase and group velocities, attenuation also every bit the amplitude distribution as a function of the depth. Nosotros illustrate damages due to Love surface waves generated by earthquakes on real-life examples. In the following of this chapter, we present a number of representative examples for Dear wave biosensors, which have been already used to DNA characterization, bacteria and virus detection, measurements of toxic substances, etc. Nosotros promise that the reader, later on studying this affiliate, volition have a clear idea that deadly earthquakes and a beneficiary biosensor technology share the aforementioned physical phenomenon, which is the ground of a fascinating interdisciplinary research.

Keywords

• Honey waves
• biosensors
• earthquakes
• surface acoustic waves
• wireless sensors
• dispersion curves

• Piotr Kiełczyński*

  • Institute of Fundamental Technological Inquiry, Polish Academy of Sciences, Warsaw, Poland

*Address all correspondence to: pkielczy@ippt.pan.pl

1. Introduction

Information technology is interesting to note that many outstanding physicists (Kelvin, Michelson, and Jolly) expressed in the second half of the nineteenth century an opinion that classical physics (how we name information technology nowadays) is in principle completed and goose egg interesting or pregnant rests to be discovered. Needless to say, forecasting development of future events was always and still is a very risky business, specially in concrete sciences and engineering. Indeed, in these disciplines of human endeavors, one must accept into account not simply an inherently volatile human gene but also the impact of potential discoveries of unknown yet laws of nature, which oftentimes open new unanticipated possibilities and horizons. We may try to justify such an obvious complacency, attributed to the abovementioned scientists, by the historical spirit of the Belle Époque (1870–1914), that believed in harmony, good taste, optimism, unlimited progress and generally in positivistic philosophical ideas.

Anyhow, not waiting for the revolution heralded by quantum mechanics (1900) or full general theory of relativity (1917), classical physics was already shaken by the emergence of the theory of chaos (Poincaré 1882 and Hadamard 1898), which later on in the twentieth century will effectively eliminate deterministic clarification from many physical bug, such as weather forecasting, etc. Another new pregnant achievement of the classical physics (although non revolutionary) was the discovery of surface waves. At offset, elastic surface waves were discovered in solids (Rayleigh 1885 and Love 1911) and and so in electromagnetism (Zenneck 1907 and Sommerfeld 1909).

In fact, the existence of surface waves in solids was predicted mathematically by the celebrated British scientist Lord Rayleigh in 1885, who showed that rubberband surface waves can propagate forth a gratis surface of a semi-space body. By contrast to bulk waves, the amplitude of surface waves is confined to a narrow area next to the guiding surface. Since surface waves are a type of guided waves, they tin can propagate often longer distances than their majority counterparts and in improver, they are inherently sensitive to material backdrop in the vicinity of the guiding surface. It will be shown in the following of this affiliate that these two properties of surface waves are of crucial importance in geophysics and sensor technology.

Start, seismographs were constructed by British engineers in 1880, working in Japan for Meiji government. Consequently, the first long distance seismogram was registered in 1889 by German language astronomer Ernst von Rebeur-Paschwitz in Potsdam (Germany), who was able to detect seismic signals generated by an earthquake occurred in Japan, some 9000 km away from Potsdam (Berlin). It was obvious soon that long altitude seismograms brandish two different phases. First (preliminary tremor), a relatively weak indicate arriving with the velocity of bulk waves (P and S) and 2d (principal daze) with a much higher aamplitude arriving with the velocity close to that of Rayleigh surface waves. However, this Rayleigh wave hypothesis was non satisfactory, since large part of the master stupor energy was associated with the shear horizontal (SH) component of vibrations, absent by definition in Rayleigh surface waves composed of shear vertical (SV) and longitudinal (L) displacements. This dilemma was resolved in 1911 by the British physicist and mathematician Augustus Edward Hough Love by a brilliant stroke of thought [ane]. Firstly, Love postulated that the SH component in the primary shock is due to the arrival of a new type of surface waves (named later later his proper noun) with just one SH component of vibrations. Secondly, Love assumed that SH surface waves are guided by an extra surface layer existing on the Globe's surface, with properties unlike than those in the Earth's interior. Using contemporary language, we tin say that he made a direct hitting.

It is noteworthy that the being of Rayleigh and Dearest surface waves was first predicted mathematically prior to their experimental confirmation. This shows how beneficial can be the mutual interaction betwixt the theory and experiment. Indeed, the theory indicates directions of future experimental research and the experiment confirms or renders the theory obsolete. It is worth noticing that the existence of a new type of electromagnetic surface waves was predicted mathematically quite recently, i.eastward., in 1988, and before long confirmed experimentally.

It is interesting to note that Love surface waves have direct counterparts in electromagnetism (optical planar waveguides) and breakthrough mechanics (particle motion in a breakthrough well). By contrast, a similar statement is non truthful for Rayleigh surface waves, which therefore remain a unique phenomenon inside the frame of the classical theory of elasticity.

Surface waves of the Love type accept a number of unique features. Firstly, they have only one SH component of vibrations. As a result, Dearest surface waves are insensitive to the loading with liquids of cypher or negligible viscosities. Thus, Love surface waves can propagate long distances without a pregnant attenuation. Indeed, Honey waves propagating many times around the World's circumference accept been observed experimentally. On the other mitt, information technology was discovered much after (1981) that Love waves are very well suited for measurements of viscoelastic properties of liquids. Secondly, the mathematical description of Love surface waves is much simpler than that for Rayleigh surface waves. A relative simplicity of the mathematical model enables for directly physical insight in the process of Love wave propagation, attenuation, etc.

The idea to employ Love surface waves for measurements of viscoelastic properties of liquids was presented for the outset time in 1981 by Kiełczyński and Płowiec in their Smooth patent [two]. In 1987, the theory of the new method was presented by Kiełczyński and Pajewski on the international arena at the European Mechanics Colloquium 226 in Nottingham, UK [3]. In 1988, they presented this new method with equations and experimental results at the IEEE 1988 Ultrasonic Symposium in Chicago [iv]. In 1989, Kiełczyński and Płowiec published a detailed theory and experimental results in the prestigious Journal of the Acoustical Society of America [v]. It is noteworthy that subsequent publications on Dear wave sensors for liquid label appeared in U.s. not earlier than in 1992 [6], but present, we witness about 100 publications per twelvemonth on that discipline [7].

We hope that the reader, after studying this chapter, volition concur that the nature has many dissimilar faces and that the aforementioned physical phenomenon can be sometimes deadly (earthquakes) and in dissimilar circumstances, can be casher (biosensor engineering). As a issue, SH surface waves of the Love type are an interesting case of an interdisciplinary research.

This chapter is organized every bit follows. Section 2 presents main characteristics and properties of Beloved surface waves, including basic mathematical model and examples of dispersion curves and aamplitude distributions. More advanced mathematical handling of the Dearest surface waves can be constitute, for instance, in [8]. Section 3 shows the importance of Love surface waves in geophysics and seismology. Section 4 describes applications of Love surface waves in biosensors used in biology, medicine, chemistry, etc. Section 5 contains word of the chronological development of SH ultrasonic sensors starting from bulk moving ridge sensors and then first surface moving ridge sensors. We show also that the results of research conducted in Seismology and geophysics tin can be transferred to biosensor technology and vice versa. Conclusions and propositions for time to come research in biosensor technology employing Dear surface waves are given in Section 6.

In add-on to biosensors, Dearest surface waves are used in chemosensors, in non-destructive testing (NDT) of materials, and in sensors of various physical quantities such as:

1. humidity of air [9];

2. spatial distribution of elastic parameters in solid functionally graded materials (FGM) [10];

3. rubberband parameters of nanolayers [eleven];

4. porosity of the medium [12]; and

5. dielectric constant of liquids [13].

Recently, Love surface waves were also employed in the construction of the magnetic field sensor organization with outstanding characteristics (sensitivity, dynamic range, etc.) [14].

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2. Properties of Honey surface waves

Shear horizontal (SH) surface waves of the Dearest type are elastic waves propagating in a surface waveguide, which is composed of a surface layer rigidly bonded to an elastic substrate, see Figure 1. The existence of an elastic surface layer is a necessary condition for propagation of Honey surface waves, since information technology can be easily shown that on an elastic half-infinite alone, SH surface waves cannot exist. The extra surface layer must besides be "slower" than the substrate, i.due east., the following condition must hold [15]:

where v one and 5 2 are phase velocities of bulk shear waves in the surface layer and substrate, respectively. In fact, the condition expressed by Eq. (1) allows for entrapment of partial waves in the surface layer due to the total reflection phenomenon occurring at the layer-substrate interface ( x 2 = h ). By dissimilarity, if the condition given by Eq. (ane) is not satisfied ( v 1 > 5 2 ), then Love waves are evanescent in the direction of propagation x one and, on average, no net ability is transmitted along the surface waveguide.

Figure 1.

Basic structure of a gratis Beloved moving ridge waveguide, non loaded with a viscoelastic liquid. An elastic surface layer of thickness "h" and a shear velocity v 1 is rigidly bonded to the underlying semi-infinitive substrate with a shear velocity 5 2 .

2.one. Dispersion equation of the Dearest surface wave

Mechanical deportation u three of a fourth dimension-harmonic Love surface wave propagating in the management x i has the following form:

where the function f 10 2 describes the amplitude of the Love wave as a function of the depth ( x 2 axis), m = ω / v p is the wavenumber of the Dearest wave, ω = two πf is its angular frequency, v p is the phase velocity of the Honey wave and j = − 1 . Since the surface waveguide is causeless to be lossless, the wavenumber 1000 in Eq. (2) is a real quantity.

Substitution of Eq. (two) into Newton'south equation of motility leads to the Helmholtz differential equation for the transverse amplitude f x 2 . Solutions of the resulting Helmholtz differential equation have the following form [16]:

f 10 2 = A cos q 1 x 2 cos q 1 h , for 0 ≤ x two < h surface layer A e − q ii x 2 − h , for h ≤ x 2 substrate

E3

where

and A is an arbitrary constant. In isotropic solids, Love surface waves have two stress components, τ 23 and τ 13 , associated with the SH displacement u 3 . From Eq. (3), it follows that stress τ 23 tin can exist expressed by the following formula:

τ 23 ten 2 = µ ane , 2 ∂ f ten 2 ∂ ten 2 = − µ 1 q one A sin q one ten ii cos q one h , for 0 ≤ x 2 < h surface layer − µ 2 q two A east − q two x 2 − h , for h ≤ ten two substrate

E6

where μ ane and μ 2 are shear moduli of elasticity in the surface layer and substrate, respectively.

The mechanical displacement u 3 and the associated stress τ 23 must satisfy the appropriate boundary conditions, i.e., the continuity of u iii and τ 23 at interfaces 10 two = 0 (gratuitous guiding surface) and 10 2 = h (the interface between the surface layer and the substrate). Substituting Eqs. (3) and (vi) into the purlieus weather condition at x ii = 0 and x 2 = h , one obtains the following dispersion relation [16], for Love surface waves propagating in a planar waveguide shown in Figure 1:

Using Eq. (4), one can rewrite Eq. (vii) in a more than explicit form equally:

F ω one thousand ω = μ 1 1 five 1 2 − one v p 2 tan two π 1 v 1 two − 1 v p 2 fh − μ ii one v p 2 − 1 5 2 ii = 0

E8

Eq. (eight) shows that the unknown phase velocity five p of the Love surface wave is de facto an explicit function of the normalized product frequency-thickness fh , with five ane and five 2 , being parameters. This holding does not, however, hold for lossy Dear wave waveguides where the elastic moduli μ 1 , μ ii as well equally the velocities 5 1 and v two are implicit functions of the frequency f and are evidently independent of the surface layer thickness h .

The dispersion relation Eq. (8) is a transcendental algebraic equation for the unknown phase velocity v p and therefore can be solved only numerically using, for example, the Newton-Raphson iterative method [17].

ii.2. Modal structure of the Love surface moving ridge

The dispersion relation [Eq. (8)] reveals that phase velocity v p of the Love surface wave is a role of frequency. Hence, Honey surface waves are dispersive. Moreover, since the function tangent in Eq. (8) is periodic, i.e., tan q one h = tan q i h + nπ , where n = 0 , 1 , 2 , … , etc . , Love surface waves display a multimode structure.

The amplitude f x 2 of the fundamental ( north = 0 ) mode of the Love surface moving ridge, as a function of the distance 10 2 from the guiding surface x 2 = 0 , is shown in Figure 2. It is clear that for sufficiently high frequencies, the energy of the Love wave is concentrated mostly in the surface layer in the vicinity of the guiding surface x 2 = 0 . By differentiation of Eq. (3), information technology is easy to prove that the maximum of the amplitude f x 2 occurs exactly at the free surface x 2 = 0 . By contrast, the associated stress τ 23 vanishes at x two = 0 , i.due east., at the free surface of the waveguide.

Effigy two.

Amplitude of the fundamental (n = 0) Love wave mode, as a function of the normalized depth x 2 / h , in a copper-steel waveguide, for different wave frequencies f = iii, v, and vii MHz, and surface layer thickness h = 100 μm.

two.3. Stage and grouping velocity of the Dearest surface wave

The total derivative of the implicit function F ω k ω in the dispersion relation [Eq. (vii)] with respect to the athwart frequency ω equals:

Since grouping velocity 5 g of the Beloved surface moving ridge, which describes the speed at which pulse envelope of the Dear surface moving ridge propagates, is defined as dω dk from Eq. 9, information technology is clear that:

5 g = dω dk = − ∂ ∂ k F ω m ω ∂ ∂ ω F ω yard ω

E10

As a consequence, using Eqs. (vii) and (10), one can testify [8, 15, 16, 17, 18, xix] that grouping v k and phase 5 p velocities of the Love surface wave are connected via the post-obit algebraic equation:

v m v p v 2 2 = μ i q 2 h sin 2 q ane h 2 q one h + 1 + μ ii cos 2 q 1 h μ 1 q 2 h v 2 5 i ii sin 2 q 1 h 2 q i h + 1 + μ 2 cos ii q 1 h

E11

Eqs. (7) and (11) bear witness that stage five p and group v g velocities of the Dear surface wave in the low ( f → 0 ) and loftier ( f → ∞ ) frequency limits are the same and equal, respectively, v 2 and 5 1 .

The phase velocity resulting from the solution of Eq. (8) and the group velocity determined past Eq. (11) of the primal mode of Dear surface waves, as a function of the normalized frequency fh , are given in Figure three. From Effigy 3, information technology is axiomatic that for depression frequencies, the phase and group velocities of Honey surface waves approach asymptotically that of bulk shear waves v 2 in the substrate. On the other hand, at loftier frequency limit, the phase and group velocities of the Love moving ridge tend to the velocity five 1 , namely to the velocity of bulk shear waves in the surface layer.

Figure three.

Phase v p and group v g velocities of the key mode of the Love surface wave propagating in a copper-stainless steel waveguide, every bit a function of the normalized frequency-thickness product fh [MHz-mm], 5 1 = 2223.5 m / s , and v 2 = 3017 m / s .

2.4. Influence of a viscoelastic liquid loading Love wave waveguides

Information technology is noteworthy that in waveguides loaded with a lossy, viscoelastic liquid, the wavenumber 1000 of the Honey surface moving ridge is a complex quantity, i.e., k = ω / 5 p + jα , where α is the coefficient of attenuation of the Love moving ridge. 3 virtually popular viscoelastic liquids are described past Kelvin-Voigt, Newton and Maxwell models, respectively [20]. The dispersion relation of Honey surface waves propagating in waveguides loaded with a viscous liquid can exist establish in [21]. In lossy waveguides, the grouping velocity of Love waves cannot be rigorously defined [22]. As a result, the formula eleven is valid only approximately in lossy Love wave waveguides. Equally a matter of fact, in a waveguide loaded with a viscoelastic liquid, the amplitude of the Love moving ridge is non-zero in a thin layer of the liquid adjacent to the surface layer of the waveguide. The penetration of the Love wave energy into the side by side liquid is of crucial importance in understanding the functioning of Love wave biosensors. Indeed, if Love wave energy was not penetrating in the measured liquid, the parameters of the Beloved moving ridge might non be affected past the liquid and the performance of the whole sensor would be essentially impossible.

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3. Beloved surface waves in seismology

Since Dear surface waves were originally discovered in seismology, we give here a brief clarification of their applications in seismic and geophysical inquiry.

Propagation of Love surface waves on the Globe'due south surface is made possible by layered construction of the Earth. The outermost layer of the Globe, the crust, is fabricated of solid rocks composed of lighter elements. Thickness of the crust varies from 5 to x km nether oceans (oceanic crust) to 30–70 km under continents (continental crust). The crust sits on mantle, which in plow covers the outer and inner core. The destructive power of earthquakes is mainly due to waves traveling in this sparse crustal layer [23].

As predicted past Honey, the velocity of SH bulk waves increases with depth [24], i.e., as a function of distance from the free surface of the Earth.

The frequency of Dearest waves generated past earthquakes is rather low comparison to that used in sensor technology and ranges typically from 10 mHz to ten Hz.

3.1. Investigation of the Earth'due south interior with Dear surface waves

Dear and Rayleigh surface waves travel along corking circumvolve paths around the world. Surface waves from potent earthquakes may travel several times around the Earth without a significant attenuation. They are termed global Rayleigh wave impulses [25]. An case of surface waves traveling multiply around the Earth [26] is given in Effigy 4.

Figure iv.

Illustration of a seismogram of Rayleigh surface waves triggered past an earthquake. Note that, Rayleigh moving ridge packet traveled viii times around the Earth'south circumference.

Seismic waves, generated both by natural earthquakes and by man-made sources, have delivered an enormous amount of information about the Earth's interior (subsurface properties of Earth's chaff). In classical seismology, Earth is modeled as a sequence of compatible horizontal layers (or spherical shells) having different rubberband properties and 1 determines these properties from travel times and dispersion of seismic waves [27].

Honey surface waves have been successfully employed in a tomographic reconstruction of the physical backdrop of World's upper drapery [28] as well equally in diamond, gilded, and copper exploration in Australia, Southward America, and S Africa [29].

Surface waves generated by earthquakes or man-made explosions were used in quantitative recovery of Earth's parameters as a function of depth. These seismic inverse problems helped to discover many fine details of the Earth's interior [thirty, 31, 32].

It is noteworthy that many theoretical methods were initially originated in seismology and geophysics before their transfer to the surface wave sensor engineering science (see Table 1 in Section 5.5).

Developments	Seismology	Biosensors
Basic theory	Love [1]	Kiełczyński [3]
Multilayered waveguides (transfer matrix method)	Haskell [72]	Kiełczyński [8]
Viscoelastic waveguides (theoretical analysis)	Sezawa [73]	Kiełczyński [74]
Changed problems	Dorman [76]	Kiełczyński [77]
Nonlinear waves	Kalyanasundarm [78]	—
Phased arrays	Frosch [79]	—
Tomography	Nakanishi [80]	—
Higher-club modes	Haskell [81]	—
Alone waves	Bataille [82]	—
Energy harvesting	Qu [83]	—
Waveguides with nanomaterials	—	Penza [84]
Piezoelectric waveguides	—	Kovacs [6]
Resonators	—	Kovacs [67]
Delay lines	—	Tournois [19]

Tabular array i.

Chronology of developments in Love wave biosensors and Honey wave seismology.

3.2. Structural damages due to Love surface waves generated by earthquakes

An example of structural damages made past surface waves of the Beloved type is shown in Figure five. It is credible that railway tracks were deformed by stiff shear horizontal SH forces parallel to the Earth's surface. Dear surface waves together with Rayleigh surface waves are the nigh devastating waves occurring during earthquakes.

Figure v.

Twisted railroad tracks, an case of structural damages due to SH displacement of Dearest surface waves in the backwash of an earthquake.

three.3. Awarding of metamaterials to minimize devastating effects of Beloved surface waves in the backwash of earthquakes

It is interesting to note that recently developed earthquake engineered metamaterials open a new way to counterattack seismic waves [33, 34]. The metamaterials actively command the seismic waves by providing an additional shield around the protected building rather than reconstructing the edifice construction. Compared with common engineering solutions, the advantage of the metamaterial method is that it can not only attenuate seismic waves before they attain critical targets, but as well protect a distributed area rather than an individual building. The periodic arrangement of metamaterial structure creates frequency band gaps, which effectively prevent surface waves propagation on the Globe's surface via a Bragg scattering mechanism.

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iv. Biosensors employing Dear surface waves

A biosensor can be described as a device which can generate a bespeak (usually electric) that is proportional to the concentration of a particular biomaterial or chemicals in the presence of a number of interfering species [35]. This tin can be accomplished using biological recognition elements such as enzymes, antibodies, receptors, tissues, and microorganisms as sensitive materials considering of their selective functionality for target analytes along with an appropriate transducer.

4.1. Confinement of the energy of Honey surface waves near the complimentary surface of the waveguide

High sensitivity of Love surface wave sensors can be explained by spatial concentration of the energy of Love waves. Indeed, information technology was shown in Section 2 that the free energy of Love surface waves is localized mostly in the vicinity of the complimentary guiding surface (Figure i), looking in both sides from it. Moreover, the amplitude of Love surface waves reaches maximum at the complimentary guiding surface x 2 = 0 (Effigy two). Therefore, nosotros can await that propagation of Love surface waves will be to a lesser or college extent perturbed by a material (such as liquid) being in contact with the guiding surface. This feature of Love waves was exploited in the construction of diverse biosensors used for detection and quantification of many of import parameters of biological and chemic substances [21, 36, 37, 38, 39, 40].

4.2. Correlation betwixt concentration of the measured analyte and parameters of the Love surface wave

Surface waves of the Love type are specially suited to measure parameters of viscoelastic liquids, polymers, gels, etc., providing that they can course a good mechanical contact (absorption and adhesion) with free surface of the waveguide. Since Love surface waves are, in principle, mechanical waves, they can measure the following mechanical parameters of an adjacent medium: density, modulus of elasticity, and viscosity. In waveguides composed of piezoelectric elements (substrate and/or surface layer), dielectric constant of the adjacent medium will also affect the propagation of Love surface waves. In practice, nosotros are interested in detection and quantification other more specific properties of biological and chemic materials, such as concentration and presence of proteins, antibodies, toxins, bacteria, viruses, size and shape of Deoxyribonucleic acid, etc. Therefore, the side by side step in the development of Love moving ridge sensors is to correlate (experimentally or analytically) the abovementioned specific properties of the measured analytes with changes in density, viscosity, and elastic moduli of the surface (sensing) layer. Finally, we have to measure changes in phase velocity and attenuation of Love surface waves, which are due to changes in density, viscosity, and elastic moduli of this surface layer. It should exist noticed that part of Dearest moving ridge energy enters into the measured liquid to some distance (penetration depth) from the guiding surface. Such an energy redistribution changes certainly the phase velocity and attenuation of the Honey surface wave. In practice, we oftentimes adopt a more empirical approach, i.e., we measure out straight changes in phase velocity and attenuation of Dearest waves, as a role of the aforementioned specific backdrop of the measured textile, such as the concentration of proteins and so on, without referring to changes in density, viscosity or elastic modulus of the measured textile. Yet, the former step is indispensable during modeling, blueprint, and optimization of Beloved surface wave sensors.

4.3. Parameters of the Beloved surface wave measured

As with other types of wave motility, we can measure in principle two parameters of Love surface waves, i.e., their phase and amplitude. Polarization of SH surface waves of the Honey blazon is constant and therefore does non provide any additional information about the medium of propagation. Phase Φ x 1 t measurements in radians are directly related to the phase velocity v p of Love surface waves via the following equation:

Similarly, amplitude A measurements are correlated with the coefficient of attenuation α (in Np/m) of Beloved surface waves every bit follows:

where A 1 and A 2 are 2 amplitudes of the moving ridge measured at points 10 i and x ii , respectively ( 10 2 > 10 1 ). In order to obtain the coefficient of attenuation in dB / 1000 , the coefficient α given by Eq. (13) must be multiplied by 20 log e ≈ viii.686 .

four.four. Sensors working in a resonator and delay line configurations

Stage and amplitude characteristics of Honey surface waves tin can be measured in a airtight loop configuration by placing Dear wave filibuster line in a feedback circuit of an electric oscillator (resonator). Some other possibility is to use network analyzer, which provides phase shift and insertion loss of the Dearest moving ridge sensor working in an open loop configuration, due to the load of the sensor with a measured material. The typical frequency range used past Love wave sensors is from 50 MHz to 500 MHz [vii].

The construction and cantankerous section of a typical Dear wave biosensor is shown in Figure 6a and b. A relatively thick (0.5–1.0 mm) substrate provides mechanical support for the whole sensor. Often the substrate material is piezoelectric (AT-cut quartz material [41]). In this case, a pair of interdigital transducers (IDTs) tin exist deposited on the substrate to form a delay line of the sensor. The guiding layer (SiO₂, ZnO, PMMA, etc.), deposited directly on the substrate, provides entrapment for surface wave energy. The sensing layer, made of gilt (Au) or a polymer, usually very thin (˜50-100 nm), serves as an immobilization surface area for the measured biological material. This thin-sensing layer interacts straight with the measured material (liquid) and serves often as a selector of the specific target substance, such as antigen, to be measured.

Figure half-dozen.

a) Layered structure of a typical Love wave sensor not withal connected to the external driving circuit and b) cross-section of this sensor structure + loading liquid.

4.5. Sensors controlled remotely by wireless devices

An interesting solution for Love wave sensors was proposed in [42], where the Dearest wave sensor works in a wireless configuration without an external power supply. This design has many unique advantages, i.e., the sensor tin can exist permanently implanted in a patient torso to monitor continuously the selected belongings of a biological liquid. Readings of the sensor tin be made on demand, totally noninvasively by a reading device continued to a broader computer organisation of patient monitoring. Another implementation of a remotely controlled wireless Dearest wave sensor was presented in [43]. The proposed sensor can measure simultaneously 2 different analytes using Love surface waves with a frequency of 440 MHz.

Wireless bioelectronics sensors may be used in a variety of fields including: healthcare, ecology monitoring, food quality control, and defense.

4.vi. Examples of laboratory and industrial grade Love wave sensors

To apply the measured analyte to the Love wave sensor, the sensor is often equipped with a flow cell, which separates interdigital transducers from sensing expanse of the waveguide [44]. A laboratory course Beloved moving ridge sensor equipped with a flow cell is shown in Figure 7.

Figure vii.

An example of a laboratory grade Love wave sensor with a menstruation cell [42].

A prototype of an commercial ready Love wave sensor was presented in 2015 in Ref. [45]. A 250 MHz delay line Dear moving ridge immunosensor was designed on the ST quartz substrate with a thin gold layer of thickness ˜ninety nm used as a guiding and sensing expanse, for antibodies or antigens can be easily immobilized on a gold surface. The changes of Love wave velocity and attenuation were due to antibodies-antigens interactions. A disposable examination cassette with embedded Love wave immunosensor is connected to a handheld electronic reader, which in plow is continued wirelessly via bluetooth to a smartphone or a reckoner. This device is a stiff candidate for clinical and personnel healthcare applications.

4.vii. Examples of analytes measured by Beloved wave biosensors

Dear moving ridge biosensors have been used in measurement and detection of a large number of substances (analytes) [44]. Every bit representative examples, nosotros tin can mention the following:

• concentration of bovine serum albumin [46];

• real-fourth dimension detection of antigen-antibody interactions in liquids (immunosensor) [47];

• simultaneous detection of Legionella and E. coli bacteria [48];

• virus and bacteria detection in liquids [49];

• detection of pathogenic spores Bacillus anthracis below inhalation infectious levels [50];

• investigation of lipid specificity of human being antimicrobial peptides [51];

• Sin Nombre Virus detection at levels lower than those typical for human patients suffering from hantavirus cardiopulmonary syndrome [52];

• detection of nanoparticles in liquid media [53];

• okadaic acid detection [54];

• written report of protein layers [55];

• antibody binding detection [56];

• toxicity of heavy metals [57];

• size and shape of Dna [58];

• real-time detection of hepatitis B [59];

• liquid chromatography [60];

• immunosensors for detection of pesticide residues and metabolites in fruit juices [61];

• detection of cocaine [62]; and

• detection of carbaryl pesticide [63].

4.viii. Desired characteristics (features) of industrial grade Love moving ridge sensors

This rather impressive list of achievements in R&D activities on biosensor technology suggests that biosensors employing Love surface waves have a huge potential. Notwithstanding, in order to compete with other types of biosensors, such equally optical sensors based on the surface plasmon resonance [64], the biosensors employing Love surface waves should possess the following characteristics:

• loftier sensitivity to the measured property (measurand);

• high selectivity to the measured property (measurand);

• low limit of detection;

• zero temperature coefficient (high-thermal stability);

• high repeatability and stability;

• possibility of multiple reuse; and

• cost-effectiveness.

At present, none of the above targets have been fully achieved. Beloved wave biosensors are, in general, withal in the laboratory research phase, where most developments are focused on the proof of concept and construction of a working prototype. Only one European visitor offers today commercially available Love wave sensors [7]. All the same, as it was shown in this section, Dear wave biosensors tin can be used to measurements of a surprisingly large number of biological substances (analytes) with a quite remarkable accuracy and sensitivity. Therefore, in our opinion, Love moving ridge biosensors will reach presently an industrial grade level with numerous existent-life applications in biological science, medicine (clinical do), and chemistry.

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five. Give-and-take

v.1. Older sensors using bulk SH waves

It is interesting to note that first acoustic sensors for measurements of viscoelastic backdrop of liquids used to this terminate bulk (non surface) SH waves propagating in a solid buffer, loaded on one side with a measured viscoelastic liquid. This idea appeared in 1950 in works of such prominent ultrasonic scientists Mason and McSkimmin [65]. However, the chief drawback of the bulk moving ridge sensors was their inherent low sensitivity. For example, to perform measurements with a h2o-loaded sensor, one had to observe almost 50 sequent reflections in the solid buffer.

5.ii. Emergence of new sensors using SH surface waves of the Love blazon

The breakthrough came with a proposition to employ to this end SH surface waves of the Love and Bleustein-Gulyaev types. This idea was first articulated by Kiełczyński and Płowiec in 1981 in their Polish patent no 130040 [2]. In 1987, the theory of the new method was presented by Kiełczyński and Pajewski on the international loonshit at the European Mechanics Colloquium 226 in Nottingham, Great britain [3]. In 1988, this new method, with equations and experimental results, was presented by Kiełczyński and Pajewski at IEEE 1988 Ultrasonic Symposium in Chicago [4]. In 1989, Kiełczyński and Płowiec published detailed theory and experimental results in the prestigious Journal of the Acoustical Gild of America [5]. Their theory [3, 4, five] was based on the Auld's perturbative technique [66] and gave satisfactory results for liquids of viscosities upward to ˜10 Pas. The master advantage of the Dear surface wave sensors is their very high sensitivity, namely the sensitivity of a few orders of magnitude (x² to 10⁴) higher than that of their bulk SH waves counterparts [3, 4, 5]. As a outcome, measurements of the viscosity of water (˜1 mPas) and other biological substances (based largely on water) was no longer a claiming, what was the instance with bulk SH wave sensors. In other words, due to the employment of SH surface waves, the way for development of the corresponding biosensors was widely open.

It should be noticed that next publications on the Dearest wave sensors for liquid characterization appeared in the open literature not earlier than in 1992 [6]. In fact, in papers published in 1992, Kovacs and Venema [67], and, in 1993, Gizeli et al. [68] confirmed our earlier discovery [3, 4, five] that Love surface waves are much more sensitive to viscous loading than other types of SH waves. In another newspaper published in 1992, Gizeli et al. [69] developed theoretical assay for Love wave sensors, using the same Auld's perturbative technique [66] equally that employed by us in papers [iii, 4, 5].

It is interesting to note that ii other types of SH waves, i.eastward., leaky SH SAW waves and plate SH waves, were also tried to measure viscosity of liquids. Leaky SH SAW waves were proposed in 1987 [lxx] by Moriizumi et al. and SH plate waves in 1988 by Martin et al. [71]. However, these two types of SH waves were quickly abandoned, since the corresponding viscosity sensors were of inherently low sensitivity, hard in practical realization and difficult in theoretical analysis (leaky SH SAW waves). In fact, the energy of SH plate waves is uniformly distributed across the whole thickness of the plate. Therefore, SH plate waves are non so sensitive to viscid loading as Beloved surface waves, whose energy is highly concentrated in the surface layer of the waveguide. On the other paw, leaky SH SAW waves are not pure SH waves and contains in principle all three components of vibrations, not only the SH 1. In particular, the component perpendicular to free surface of the waveguide will continuously radiate energy into the next liquid. This will cause an additional attenuation for leaky SH SAW waves, which will be duplicate from that due to the gluey loading measured.

v.3. Mathematical apparatus and numerical methods used in analysis of Dear surface waves

R&D activities in seismology and biosensor technology using Dear surface waves focus inevitably on different problems and challenges. The main reason for these differences is the nature and scale of Love surface waves used in seismology and biosensor technology, i.e., in seismology, they are a natural phenomenon and in biosensors, they are controlled within human-made devices. It is instructive to compare the chronology of developments made in seismology and in biosensor technology (meet Table one). In fact, the theory of Dearest waves published in 1911 [1] was developed for the simplest surface wave waveguide, namely for that composed of linear, isotropic, and lossless materials (surface layer on a substrate). Since loading viscoelastic liquids are always lossy, the corresponding theory of Love wave sensors had to use perturbative [3] or numerical methods [37]. The theory of Beloved waves in multilayered waveguides, developed in Seismology [72], uses a conventional transfer-matrix method based on the unproblematic matrix algebra. By contrast, the theory developed for biosensors extends the transfer-matrix method to a more advanced formalism of matrix differential equations with eigenvectors and eigenvalues and operator functions [eight]. First theories of Love waves propagating in viscoelastic waveguides, were adult in Seismology [73], long before the appearance of mod fast digital computers. Past contrast, the corresponding theory developed for biosensors [74] in 2016 heavily relates on numerical methods.

v.4. Milestones in developments of Love wave seismology and Honey wave biosensors

Test of Table 1 reveals that a number of R&D activities already well established in Seismology were not yet initiated in biosensor technology. As examples, 1 can mention the applications of nonlinear Love waves, higher-lodge Love wave modes or solitary waves. This suggests that in future research, it may be advantageous to employ higher-order modes, nonlinear Love waves, metamaterials, etc., to increase biosensors sensitivity [75] or lower their limit of detection. Other technologies not yet used in biosensor technology are phased array and tomography. Indeed, applied to biosensors they may allow for a second label of the analyte distribution, electronic beam steering, focusing, etc. These indications for future research in biosensor technology show clearly advantages of multidisciplinary R&D activities, in this example seismology and biosensor engineering. Indeed, it is much easier to conform an existing technology already developed in other fields to a new domain than to invent a new applied science from scratch without whatsoever prior feedback.

five.five. Novelty of the nowadays chapter

Despite the fact that the commencement theory of Love surface waves was published as early as in 1911 [i], surprisingly, a large number of issues concerning the theory of Dearest surface waves take non yet been solved.

This chapter contains theoretical foundations and calculation results regarding the propagation of the Love moving ridge in various media. A new interpretation of the Love wave dispersion equation was given. This equation is presented in the grade of an implicit function of two variables, i.east., ( ω , grand ). This allowed to evaluate the belittling dependencies on group velocity of Love wave propagating in a broad class of layered waveguides, e.g., in graded waveguides. This problem will be the subject field of time to come writer'south works.

The obtained results can exist employed in the blueprint and optimization of not just biosensors only too chemosensors and sensors of physical quantities that apply Love waves. In addition, the obtained results can exist used in seismology and geophysics for the estimation of seismograms and determining the distribution of elastic parameters of the Earth'due south crust.

This affiliate contains likewise a novel comparison of milestones in developments fabricated in Honey wave seismology and Love wave biosensors (see Department 5.iv). Since Love wave biosensors appeared exactly lxx years [2] subsequently emergence of Beloved surface waves in seismology [1], it is not surprising that many discoveries and developments were made first in seismology and then transferred to biosensors (meet Table 1). This cross-pollination between the ii seemingly distant branches of science is very benign and can significantly accelerate developments made in either of them.

Advertizing

six. Conclusions

In this express infinite chapter, it was impossible to address or even mention all interesting problems relevant to the properties and applications of Dearest surface waves in seismology and biosensor engineering science. Instead, nosotros tried to present only principal backdrop of the Honey surface waves, such as their dispersive nature, phase and group velocities, amplitude distribution, etc., as well as their most iconic applications in seismology and biosensor technology. Nosotros think that presentation of the Love surface waves R&D activities in a broader historical perspective gives an invaluable insight in the process of developments made in this fascinating interdisciplinary domain of research.

In this chapter, we attempted to present a variety of aspects that can be attributed to SH surface waves of the Love type. Equally a matter of fact, Dr. Jekyll and Mr. Hyde Dearest surface waves possess simultaneously two diametrically different faces, i.e., first benign (biosensors) and second mortiferous (earthquakes). The good news is that developments made in one of these domains can be easily transferred to the 2nd one and vice versa. In fact, Dearest surface waves were start discovered in seismology (1911). They finally enabled for precise interpretation of seismograms registered in the aftermath of earthquakes. Beneficiary applications (biosensors) of Love surface waves were announced exactly 70 years later (1981) in a Smooth patent.

Since earthquake is a natural miracle, we have little or no influence on its occurrence and dynamics. Past dissimilarity, the construction and the operation of biosensors tin exist optimized past mathematical modeling and experimental studies. Now, the mathematical modeling of Dear wave biosensors is an agile domain of research. On the other hand, progress in electronics and computer technology will lead to evolution of new compact and reliable instrumentation working in conjunction with Love wave biosensors.

Despite their centennial heritage, Dear surface waves are bailiwick of an intensive research activity. For case, one tin mention the application of inverse trouble techniques to recover material parameters of surface layers from measurements of velocity and attenuation of Dearest surface waves. Inverse trouble techniques accept been successfully employed in seismology and geophysics [25] and recently likewise pioneered by the authors [74, 77, 85] and others [86, 87] in the biosensor technology.

Other open problems in the theory and technique of Love surface waves are not-linear Love waves, extremely tedious Love waves [88], Dearest waves in layered nanostructures [89], energy harvesting with Love waves, and metamaterial-based seismic shielding, [33, 34], etc.

Finally, coming dorsum to the idea expressed at the get-go of the introduction in this affiliate, we want to assure the reader that there exist yet many significant unresolved bug in the theory and technique of the Love surface waves, which deserve to be addressed in future R&D activities. We hope that this affiliate may exist helpful in this try.

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Written By

Piotr Kiełczyński

Submitted: May 8th, 2017 Reviewed: Feb 15th, 2018 Published: April 10th, 2018

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Eatables Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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