Seismic methods References and suggested literature Prem V. Sharma: Environmental and engineering geophysics, Cambridge University Press BurVal Working Group: Groundwater Resources in Buried Valleys, Hannover 2006 Edited by Yoram Rubin and Susan S. Hubbard: Hydrogeophysics, Springer 2005 Edited by Reinhard Kirsch: Groundwater geophysics, Springer World Wide Web (but be careful because not everything is vetted) Seismology A very simplified and short definition: seismology is one of the geophysical studies which examines the propagation of seismic waves through the Earth. Seismology can be divided into two major fields by the energy of the source generating seismic waves: • earthquake seismology • and applied seismology. Earthquake seismology In the case of earthquake seismology the seismic waves mostly originate from earthquakes. The sources of seismic waves are characterized by the following properties: high energy and random occurrence (scientists cannot generate them intentionally). Earthquake seismology This copper engraving depicts the destruction caused by the 1755 Lisbon earthquake. https://en.wikipedia.org/wiki/Earthquake Earthquake seismology Due to the high energy of source, the generated seismic waves can get into the deeper parts of the Earth. By the surface measurements of reflected and refracted seismic waves, earthquake seismology is applicable to the study of the Earth's interior. http://serc.carleton.edu/quantskills/activities/interior_seismic.html Earthquake seismology The receivers of the seismic waves, the so-called seismometers, are located at seismological observatories and stations. These objects form a global network. The seismometers are listening to the motions of the Earth continuously. The measured time series of soil displacement, velocity and acceleration are called seismograms http://ida.ucsd.edu/?q=sts1-sensor http://lunar.earth.northwestern.edu/NUEPS/Maps _and_Images/images.html Applied seismology The so-called applied seismology is the other branch of seismology. In the case of applied seismology, artificial (man-made) source devices are used. The seismic waves can be generated by: • mechanical impacts • explosions, • and vibrations. An artificial seismic source is characterized by: • significantly lower energy than that of an earthquake, • and controlled occurrence of source event both in time and space. Applied seismology Because of the lower energy of sources, the investigation depth is limited to the upper part of the Earth's crust (max. n x 1000 m). The great advantage of applying artificial sources is that the measurements can be performed in a planned way both in time and space. Due to this planned implementation of seismic surveys, we can map the contacts of different natural and artifical objects located under the surface. By means of evaluated seismic images of subsurface, applied seismology may help the solution of several geological and geotechnical problems. Exploration seismology By the investigated depth intervals, applied seismology may be divided into two branches: exploration seismology, and near-surface seismology. Exploration seismology focuses on the study of deeper geologic structures. Its most important application is profiling and mapping sedimentary basins to find structures which can be related to the accumulation or deposition of raw materials (e.g. hydrocarbons). The investigation depth typically varies between a few kilometers and a few hundred meters. Exploration seismology An exploration seismic profile with the interpretation of reflecting horizons and structures. http://www.sub-surfrocks.co.uk/?page_id=66 Near-surface seismology As its name indicates, near-surface seismology concentrates on the subsurface structures which are relatively close to the surface. Shallow seismic surveys can help in solving some hydrogeological, environmental and geotechnical problems such as: • location of water table, water bearing fractured zones, cavities, sinkholes, • delineation of faults and fractures, • and determination of depth to bedrock. Near-surface seismology Investigation depth of shallow seismic surveys typically ranges from a few hundred meters to one meter. Due to the shallow investigation depth, it is enough to use source devices providing relatively small seismic energy. Essentially, this shallow version of applied seismology is used in hydrogeological investigations. Therefore we will concentrate on shallow seismic methods and their applications in hydrogeology. Near-surface seismology A shallow seismic reflection profile with a lithology bar on the left side. http://qjegh.lyellcollection.org/ Principles of solid mechanics Seismic investigations are based on the fact that seismic waves propagate with different velocities in different rocks. When an initial seismic waves coming from the source point arrive at a contact of two different rocks, they split into several waves propagating in different directions with different velocities. Some of them will get back to the surface where they can be detected by receivers. The arrival time data and the waveforms of signals obtained by recording waves carry information about the subsurface structure. In order to understand how seismic methods work and what we can expect from them, we must know the principles of solid mechanics. The concept of an elastic body The so-called elastic body is a theoretical model in solid mechanics. By means of this model, we can describe the behaviour of solid materials. Especially their deformation is studied, when they are under the action of forces. The most important property of an elastic body is the elasticity. Elasticity is the ability of a body to resist a distorting influence and to recover its original size and shape when the influence is removed. The concept of an elastic body Fluids do not show elastic behaviour because they have no definite shapes. But solid rocks can be considered as elastic bodies in the range of their very small deformation. Because the propagation of seismic waves far enough from the source causes very small deformation inside the rocks, the seismic behaviour of rocks may be studied by using the model of elastic body Stress When an external force begins to act on the surface of an elastic body, an internal force will arise inside the body to resist the external effect. This internal force called stress is a surface force which acts across the internal surface elements of the body. So, the stress is the consequence of the external forces acting on a body. Stress The figure tries to demonstrate the stress across a surface element (yellow ellipse) separating two volume elements of the body. The bottom element exerts a stress on the top element The greater purple arrow located at the center of the surface element represents the resultant of the stress distributed over the surface element (small arrows). https://en.wikipedia.org/wiki/Stress_(mechanics) Stress In other words, stress is a physical quantity which expresses the internal forces exerted by the neighbouring particles of a material on each other. In a static case, the magnitude and the direction of stress may change from point to point inside the body (static case means the external surface force does not change in time). So, the stress is described by a vector field mathematically: 𝜎റ = 𝜎( റ 𝑟)= റ 𝜎റ 𝑥, 𝑦, 𝑧 where 𝜎റ is the stress vector at a given point inside a body, 𝑟റ is the radius vector of the point and x,y,z are the rectangular Cartesian coordinates of the point. Stress In a dynamic case, the stress depends on not only space but time. So, a time and space dependent vector field describes the stress state of a body: 𝜎റ = 𝜎(𝑡, റ 𝑟)= റ 𝜎റ 𝑡, 𝑥, 𝑦, 𝑧 where t is the time The dimension of stress is the same as that of pressure, so its unit is pascal (Pa, newton per square meter) in the International System, or psi (pound per square inch) in the Imperial system. Since the magnitude of stress expressed in Pa is usually a very high value, the use of MPa is more common in engineering practice. Types of loading Loading means the application of an external force to an object. Depending on the type of loading, different stress and strain fields arise inside a body. There are five fundamental types of loading: tension, compression, bending, shear, and torsion. From a seismic point of view, tension, compression and shear loading are of importance. Types of stress A stress vector can be decomposed into two components: • normal stress (is perpendicular to the unit surface) • and shear stress (is parallel with the unit surface.) http://homepage.ufp.pt/biblioteca/WebBasPrinTectonics/BasPrincTectonics/Page2.htm The normal stress component n or is perpendicular to the unit surface. It is also called compressive or tensile stress depending on the type of loading (compression or tension) induces the normal stress component. Normal stress In the case of compression and tension, the external surface forces act on the surface of a body at right angles. But the directions of forces at the two ends of the body are opposed. Compression causes contraction while tension causes extraction along the axis of loading. Compression generates compressive stress (with a negative sign, n< 0) while tension generates tensile stress (with a positive sign, n> 0) inside the body. The sign of stress is determined by the sign of change in length. Normal stress Independently from its sign, a normal stress field always entails a deformation which changes both the shape and the volume of the body. The figure demonstrates the effects of tensile (or tensional) and compressive (or compressional) stress. (http://magnet.fsu.edu/~odom/1000/deformation/def.html) Shear stress The other component of a stress vector, which is parallel with the unit surface of two neighbouring volume elements, is referred to as shear stress or . Shear stress is caused by external forces acting tangentially to the surface of a body (tangential force). A shear stress field entails a deformation which modifies only the shape of body. The volume does not change. (http://magnet.fsu.edu/~odom/1000/deformation/def.html) Volumetric stress Beside the two fundamental types of stress (normal and shear), another type of stress, the so-called volumetric stress (V) is also important in engineering practice. A volumetric stress field occurs when an elastic body is equally loaded by compressional forces in all directions. In nature, hydrostatic and lithostatic pressures cause volumetric stress in solid materials (e.g. rocks). Similarly to normal stress, the volumetric stress also entails a deformation which modifies not only the shape but also the volume of a body. (http://magnet.fsu.edu/~odom/1000/deformation/def.html) Strain The change in stress field (caused by the effect of external forces) results in the displacement of particles inside the body which appears in the form of deformation (the change of shape and/or volume). The deformation is described by the so-called strain which quantifies the relative displacement of particles inside the body. Relative displacement means that the actual position of a particle is related to its initial position. Relative displacement can be characterized by change in length and/or angle change between line segments inside the material. Strain The figure shows a simple case of deformation which occurs when a bar is stretched by tension forces. Here, the strain is expressed as the ratio of change in length to the original length. https://www.nde-ed.org/ EducationResources/CommunityCollege/Materials/Mechanical/StressStrain.htm Strain Similarly to stress, the magnitude and direction of strain may change from point to point inside the body in the case of static load. So, also the strain is described by a vector field. When the body is dynamically loded, the strain depends not only on space but time. In the case of elastic deformation, the body completely recovers its original configuration after the external load has finished. It means that elastic deformation is reversible. On the contrary, plastic deformation is irreversible, because the body does not recover its original shape and volume after the load. Types of strain in engineering practice The relative change in length is quantified by the so-called engineering strain or Cauchy strain. It gives the ratio of change in length to the original length by the formula below: ∆𝐿 𝜀𝑒𝑛𝑔 = , 𝐿 where eng denotes the engineering strain, L is the original length of the line segment and L symbolizes the change in length. Because this type of strain is obtained by the division of two quantities with the same unit, it is a dimensionless quantity. Types of strain in engineering practice We can often meet the terms longitudinal (or axial) and transverse strains in relation to compression or tension. Longitudinal strain is actually the engineering strain measured along the longer axes of an elongated body, while transverse strain means the engineering strain measured in the cross-sectional direction of the body. They can be expressed by the following formulae: 𝜀𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙 = ∆𝐿 𝐿 𝜀𝑡𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑠𝑒 = ∆𝐷 𝐷 where L is the original length in the axial direction, L is the change in length in the same direction, D is the original length in the cross-sectional direction and D is the change in length in the same direction. Types of strain in engineering practice This figure demonstrates the meaning of longitudinal and transverse strains. A cylinder shaped body is stretched by tensional forces acting on its two ends. Due to the tensile stress arisen inside the body, the axial size will increase, while the cross-sectional size will decrease. The sign of strain is positive if the length of line segments inside the body increases (in the given direction), and it is negative if they shorten. http://physicscatalyst.com/mech/elasticity_2.php Types of strain in engineering practice Not only the length of line segments but also the angles between the line segments may be changed inside the body by the effect of external loading. The angle change of line segments is quantified by the angular distortion. It gives how the angle has changed between two, originally perpendicular line segments inside the body. The so-called shear strain is defined by the tangent of angular distortion: 𝜀𝑠ℎ𝑒𝑎𝑟 = tan 𝛾 where is the angular distortion in radian. The shear strain is also a dimensionless quantity. Types of strain in engineering practice This figure tries to illustrate how the shear strain can be derived from the angular distortion , the original length of a line segment L and the transverse displacement x. https://en.wikipedia.org/wiki/Shear_modulus The external forces (F) are shearing forces with opposite directions. This tangential pair of forces produces a shearing stress field inside the body which entails the shearing deformation of the body. This deformation is manifested in the form of angular distortions of the material line segments. Types of strain in engineering practice The so-called volumetric strain is induced by a volumetric stress field and it is defined as the ratio of change in volume to the original volume: ∆𝑉 𝜀𝑉 = 𝑉 where V denotes the original volume of a body and V is the volume change. Similarly to the previous types of strain, it is also a dimensionless quantity. (http://magnet.fsu.edu/~odom/1000/deformation/def.html) Elastic moduli for homogeneous and isotropic materials As we have seen, the stress has a connection with the strain. The mathematical relationship between these two quantity is established by the so-called elastic modulus. In the case of homogeneous and isotropic materials, the elastic modulus is a scalar quantity which measures the resistance of a material to elastic deformation. So, it is an important parameter which characterizes the elasticity of a material. In the range of elastic deformations the value of elastic modulus is a constant. Each material has its own constant. Depending on the type of stress and strain and the measurement configuration, several types of elastic moduli are defined in practice. The most frequently used four elastic moduli are the following: • Young's modulus (or elastic modulus), • Poisson's ratio, • shear modulus • and bulk modulus. Elastic moduli for homogeneous and isotropic materials Young's modulus (commonly denoted by E) measures the tensile elasticity, or the tendency of a material body to deform along its longitudinal axis when tensile forces act on it. It is defined by the ratio of tensile stress to the longitudinal strain: where E is the Young's modulus, F is the tensile force, A is the cross-sectional area on which the force acts ΔL is the change in length, and L is the original length of the body. Its unit is pascal (Pa) in System International. Elastic moduli for homogeneous and isotropic materials (http://hydrogen.physik.uni-wuppertal.de/hyperphysics/hyperphysics/hbase/permot3.html) This figure demonstrates the measurement configuration by which the Young's modulus of a material can be determined. In order to deform a material with a higher value of Young's modulus, a greater force has to be applied. It has a significant resistance to deformation. A soft material has a low value of Young's modulus, while a stiff or rigid material has a very high value of Young's modulus. So, we can say that the Young's modulus is the measure of stiffness. Elastic moduli for homogeneous and isotropic materials Poisson's ratio (generally denoted by ) is the measure of the socalled Poisson effect. This phenomenon means that a body compressed in one direction modifies its size not only in the direction of loading but also in the direction perpendicular to the compression. Poisson's ratio is defined by the negative ratio of transverse strain to the longitudinal strain. where L is the original length in the axial direction, L is the change in axial length, D is the original length in the transverse direction and D is the change in transverse length. It is a dimensionless quantity. Elastic moduli for homogeneous and isotropic materials This figure illustrates the measurement configuration by which the Poisson's ratio of a material can be determined. http://www.pavementinteractive.org/article/poi ssons-ratio/ Most of the materials expand in transverse directions when they are compressed in axial direction. Their Poisson's ratio is positive and ranges from 0 to 0.5. A perfectly incompressible (theoretical) material would have a Poisson's ratio of value 0.5. Elastic moduli for homogeneous and isotropic materials The shear modulus or modulus of rigidity (G or ) measures the tendency of a material body to the deformation when a pair of sharing forces acts on its two opposite sides. (Sharing forces acting in a pair have the same magnitude but opposite directions. They tangentially act on the surface areas.) The shear modulus is defined by the ratio of shear stress to the shear strain. where Fshear is the magnitude of the shear force, A is the area on which the force acts and is the angular distortion. Its unit is pascal in System International. Elastic moduli for homogeneous and isotropic materials https://en.wikipedia.org/wiki/Shear_modulus This figure illustrates the measurement configuration by which the shear modulus of a material can be determined. A material with a higher value of shear modulus exerts stronger resistance to shearing deformation. Fluids have a shear modulus of value 0 which means that they cannot resist shearing deformations at all. Elastic moduli for homogeneous and isotropic materials The so-called bulk modulus (K) measures the volumetric elasticity, or the tendency of a body to deform when it is equally compressed in all directions. It is defined by the ratio of volumetric stress to the volumetric strain. where Fcompression is the compressional force acting on the entire surface of the body, A is the surface of the body, V is the original volume of the body and V is the change in volume. Its unit is pascal (Pa) in System International. Elastic moduli for homogeneous and isotropic materials This figure demonstrates the measurement configuration by which the bulk modulus of a material can be determined. http://faculty.uaeu.ac.ae/~maamar/physics1/121.html The lower the value of the bulk modulus the more compressible the material. Gaseous materials are characterized by very low values of bulk modulus. The inverse bulk modulus gives the compressibility of a material (). Actually, the bulk modulus can be considered as an extension of Young's modulus to three dimensions.