ERTH2020 Introduction to Geophysics The Seismic Method. 1. Basic Concepts in Seismology. 1.1 Seismic Wave Types

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1 ERTH2020 Introduction to Geophysics The Seismic Method 1. Basic Concepts in Seismology 1.1 Seismic Wave Types Existence of different wave types The existence of different seismic wave types can be understood at various levels. In historical earthquake seismology, it was empirically noted that following an earthquake, distinct bursts of energy arrived at recording stations at different times. The first main burst of energy was referred to as a P-wave and the second as an S-wave. For shallower earthquakes, this was often followed by a long string of energy referred to as the surface waves. Figure 1 shows these wave arrivals on a typical seismogram of distant earthquakes, recorded at the UQ Charters Towers site. Figure 1: Typical seismogram of distant earthquakes, recorded at the UQ Charters Towers station.the smaller quake was in Santa Cruz (M = 5.1), and the larger one was in Indonesia (M = 5.9). The arrival times of P, S, surface (L) events are indicated. For both events, the S-P time is about 3.5 minutes, indicating that the earthquake is about 2200 km away. Both events are shallow (< 50km) and hence produce strong surface waves

2 ERTH2020 Basic Seismology - 2 The elastic wave equation The existence of different seismic wave types can also be predicted from a purely mathematical viewpoint. It is well known that the general wave equation describing the transmission of some function f through space at a speed v is given by 2 f t 2 = v2 ( 2 f x f y f z 2 ). (1) In seismology, the elastic wave equation describes how seismic waves travel through the earth. In its most general form it is slightly more complex then Equation 1, because it includes more than one wave type. However, it can be broken down into simpler equations which describe particular waves. For example, stress-strain analysis allows us to identify a compressional (i.e. push/pull) disturbance (θ), which is the divergence of ground displacement. The particular equation which describes how such a compressional disturbance transmits through the earth is 2 θ ( K + 4µ t = 3 2 ρ )( 2 θ x θ y θ z 2 ). (2) Comparing Equations 1 and 2 it is clear that this compressional wave is travelling at a velocity K + 4µ 3 v P = (3) ρ This wave is the P wave identified by earthquake seismologists. The parameters in the velocity term are considered in detail below. Similar mathematical analysis also reveals the existence of a rotational or shear disturbance (ζ). (This is the curl of the displacement.) The wave equation describing the transmission of this shear is 2 ζ ( µ )( 2 t = ζ 2 ρ x + 2 ζ 2 y + 2 ζ ). (4) 2 z 2 Again, comparing Equations 1 and 4 it is clear that this shear wave is travelling at a velocity µ v S = (5) ρ Other solutions lead to the prediction of various surface waves (Rayleigh, Love, Stonely, etc). The practical significance of all these solutions relates to the type of particle motion involved, and the velocities of the waves.

3 ERTH2020 Basic Seismology - 3 Particle motion of body waves P waves and S waves are called body waves. They can travel within the body of the earth. The most basic characteristic of the different waves relates to the way the particles of rock move as the wave passes. As shown by Figure 2, when a P wave passes, the particles move back and forward in the direction of the wave travel. For the S wave, the particle motion is in a plane perpendicular to this direction. Figure 2: Particle motions for body waves travelling from left to right. P-wave motion is in the direction of travel. S-wave motion is perpendicular to direction of travel.

4 ERTH2020 Basic Seismology - 4 Particle motion of surface waves As the name suggests surface waves must propogate close to the surface. Two common variations are the Rayleigh wave (ground roll) and the Love wave. As shown by Figure 3, when a Rayleigh wave passes, the particles move in a retrograde elliptical fashion. The Love wave requires a surface low-velocity layer. The particle motion is transverse, with high amplitude near the surface, and decreasing to zero at the base of the layer. Figure 3: Particle motions for surface waves. Rayleigh-wave motion is like a backflip (technically retrograde elliptical). Love-wave motion is transverse in a surface layer, with amplitude decreasing towards the base of the layer.

5 ERTH2020 Basic Seismology Body Wave Velocities When we find the solutions of the seismic wave equation we obtain the velocities of propagation of the different wave types. As noted above, for the body waves we have K + 4µ 3 v P = ρ µ v S = ρ (6) (7) Here K is the bulk modulus (or incompresibility), µ is the shear modulus (or rigidity) and ρ is the density. These three physical properties can all be measured in a laboratory. If we consider realistic values of these parameters we deduce two important practical results. (i) V P /V S Ratio and Poisson s ratio For many competent rocks the P-wave velocity is about twice the S-wave velocity. The precise value of the V P /V S ratio (termed γ) is a useful indicator of rock strength. For example in granites γ could be as low as 1.7, while in softer rocks (shales) it might be 2.3. In the near surface weathered zone, very high values of γ can be observed (5-10). Geotechnical and mining engineers prefer to use Poisson s ratio (σ) to describe rock strength. It can be derived from the velocity ratio via σ = γ2 2 2(γ 2 1) (8) Substitution indicates that stronger rocks could have σ around 0.25, while weaker rocks could have σ around 0.4. Finally, note that γ (or σ) are generally more indicative of rock strength than v P or v S individually.

6 ERTH2020 Basic Seismology - 6 (ii) Body-wave velocities in the presence of fluids Fluids have zero rigidity. That is µ is zero. Fluids also have reduced (but non-zero) incompresibility K. Consideration of the above equations immediately reveals that: P-waves will travel in a fuid (although more slowly than in rock). S-waves will not travel in a fluid. The second of these results was very important in the successful prediction that the earth s outer core was fluid (Figure 4). Figure 4: S-waves travelling from an earthquake are not observed beyond an epicentral distance of 103. This is because they cannot travel through the liquid outer core. In applied seismology, S-waves will not travel through the ocean, and this is relevant in marine exploration. The different behaviour of P and S waves in porous rocks is also very important (and sometimes poorly understood). Porous rocks are typically at least 80% rock (if porosity is 20 %). The S-waves can travel through the rock matrix, essentially ignoring the fluid. That is, S-waves respond only to the geology, whilst P-waves are influenced both by geology and fluid content. This difference is very important in the exploration for porous rocks (e.g. hydrocarbon reservoirs, groundwater aquifers).

7 ERTH2020 Basic Seismology - 7 Consider the example in Figure 5, which shows a porous limestone reservoir overlain by a shale cap rock. In the left hand model, the limestone holds water, and on the right it holds hydrocarbon, which has significantly reduced the P-wave velocity contrast at the boundary. This renders the interface invisible to P-waves. However, the S velocity is unaffected, meaning that the reservoir can be mapped using S-waves. (The relevant concept of reflection coefficient is explored in more detail below.) Figure 5: Porous limestone reservoir overlain by shale cap rock. In the left hand model, the limestone holds water. Introduction of hydrocarbon to the reservoir (right) reduces the P-wave velocity, but does not change the S-wave velocity significantly. 1.3 Surface Wave Velocities Rayleigh waves In the simplest case of a homogenous earth, the Rayleigh wave travels along the surface at a velocity of about v R = 0.9v S. In the real-earth situation, there are normally layers of different velocity near the surface. In this case, the highest-frequency Rayleigh waves travel at a velocity of 0.9v S1 (i.e. they travel close to the surface). Waves with progressively lower frequency penetrate deeper, and hence sense layers with higher velocity. That is, lower-frequency Rayleigh waves travel with higher velocities. This phenomenon (velocity dependent on frequency) is called dispersion. On a seismic shot record, this is manifested as a band of Rayleigh-style energy, rather than a single well defined event (see Figure 6). This more complicated mix of various Rayleigh wave events is generally referred to as ground roll.

8 ERTH2020 Basic Seismology - 8 Figure 6: Vibroseis shot record from central Australia. The energy labelled A indicates the low velocity end of the dispersive ground roll band. Other ground-roll components with higher velocity (lower slope) are also visible (labelled B). Love waves As noted above, propagation of Love waves requires a surface low-velocity layer. The Love wave is dispersive, with velocities lying between the S-wave velocities in the surface layer and the underlying layer. More complex love waves exist in multi-layered systems. Interactions between surface and body waves The bulk of reflection seismology is carried out using vertical-component geophones. Due to ray bending near the surface (Snell s Law, see below), reflected (and refracted) waves are travelling almost vertically when they arrive at the geophone. This means that normal vertical-component reflection surveys record predominantly reflected and refracted P-waves, and also ground roll (because it is elliptical and has a strong vertical component). These normal surveys do not record reflected or refracted S-waves, or

9 ERTH2020 Basic Seismology - 9 Love waves, because their particle motion is close to horizontal. Because the ground roll travels relatively slowly across the surface, it can often interfere with reflected P-waves from deep interfaces. In Figure 6, this is seen over much of the central part of the record. Methods have been developed to reduce this interference (geophone groups, velocity filtering). Multi-component recording A less common mode of recording uses 3-component geophones, which are able to record all wave types (P, S, ground roll, Love waves.) This is a topic of considerable research over the past 20 years. Because of the different response of the earth to P and S waves (e.g. fluids), integrated P and S reflection using 3-component geophones can add significantly to the geological characterisation of the subsurface. 1.4 Snell s Law and the Ray Parameter As derived in ERTH2020, a simple application of Fermat s principle of least time leads to Snell s Law, which describes the direction taken by all seismic waves at a boundary between two different materials. Consider the simple case of a P wave incident on a boundary at an angle i 1. Snells Law requires sin i 1 v 1 = sin i 2 v 2 (9) where v 1 and v 1 are the velocities on either side of the boundary, and i 2 is the angle made by the transmitted ray with the normal. In applied seismology we call the quantity ( sini ) the ray parameter (p), and say that the ray parameter must remain constant v for a ray and its offspring (reflections, transmissions, conversions). Mode conversion When a P wave hits an interface at non-normal incidence, a shearing component is applied to the interface, and this yields mode-converted S-waves (both reflected and transmitted). Conversely an incident S-wave can impart a component of compression on the interface, yielding mode-converted P waves. Snell s law controls the direction taken by all waves, via a logical extension of Equation 9, as shown in Figure 7. Critical refraction When the incident ray hits the interface at a special angle, then the transmitted ray can travel at an angle of 90 to the normal (Figure 8). This special angle is called the critical angle (i C ) and the phenomenom is referred to as critical refraction. From Snell s law, we can see that the critical angle is defined by sin i C = v 1 /v 2. Note that critical refraction can only occur if v 2 > v 1. This is the normal situation in the earth, but velocity inversions are a lso relatively common. The phenomenon of critical refraction is the basis of the so-called seismic refraction method of exploration.

10 ERTH2020 Basic Seismology - 10 Figure 7: An incident P-wave (at non-normal incidence) produces reflected and transmitted P and S waves, whose directions are controlled by Snell s law. All rays in the figure have the same ray parameter ( sin i v ). Figure 8: Critical refraction occurs when an incident wave hits an interface at the critical angle.

11 ERTH2020 Basic Seismology Seismic reflection and seismic refraction methods In general, whenever we initiate a seismic source at or near the surface, there is potential for many of the wave types discussed above to be produced, either directly or by conversion. In applied seismology, there are two distinct exploration methods which use body waves. These are referred to as the seismic reflection and seismic refraction methods. The distinction is based on the wave path which is being analysed. See Figure 9. Seismic reflection uses reflected energy to construct geological imagery, commonly over the depth range 50m - 50km. Seismic refraction is widely used to map the weathering zone (0-50m) although the method is sometimes also used at crustal scale. It is interesting that the major use of refraction is to provide near-surface models to be used in reflection processing. Figure 6, discussed earlier, was a production record from a reflection survey. It contains both reflection events (green, pink) and refraction events (yellow, blue). Note that there are also other specialised techniques (e.g. MASW) which analyse surface waves to provide near-surface information. Figure 9: In applied seismology, two important body-wave paths are analysed, and these require distinct interpretation methods. A seismic source generates reflected waves (solid) and refracted waves (dashed). In geophysics the latter term generally refers to waves which have undergone critical refraction along a boundary.

12 ERTH2020 Basic Seismology Introduction to seismic reflection Commercially, the most important branch of applied seismology is seismic reflection, which has been heavily used in hydrocarbon exploration and more recently in hardrock, engineering and environmental geophysics. A fundamental parameter which indicates whether an interface will be a good target for seismic reflection is the reflection coefficient. Near-normal incidence When a P wave strikes an interface at an angle close to normal, the reflection coefficient is defined as the ratio of reflected amplitude to incident amplitude. c = A r A i = Z 2 Z 1 Z 2 + Z 1. (10) Here Z is the acoustic impedance of a layer defined as product of density and velocity. Z = ρv (11) Most sedimentary interfaces (sand / shale etc) have a relatively small reflection coefficient (< 0.1), implying that the amplitude of the reflected wave is < 10% of the incident-wave amplitude. More effective reflecting interfaces include unconformities, the water bottom, and coal. These can have reflection coefficients of magnitude We can a lso define a transmission coefficient, which describes the ratio of the transmittedwave amplitude to the incident-wave amplitude. Reflection polarity t = A t A i = 1 c = 2Z 1 Z 2 + Z 1. (12) Consider Equation 10. If the second material has higher acoustic impedance (basically is harder ), Z 2 > Z 1 and c is positive. Conversely, if Z 2 < Z 1, then c is negative. Ultimately this controls whether the recorded pulse appears as a positive voltage or negative voltage. Figure 10 gives a simple example for land recording on a geophone. (Note that for marine recording on a hydrophone the voltages would be the opposite to that on a geophone.)

13 ERTH2020 Basic Seismology - 13 Figure 10: Consider a compressional source (explosion, hammer) which generates a compressive pulse (push). The sketch shows the two cases for reflection from an interface having positive c (left) and negative c (right). In each case the resultant reflection polarity is indicated at the bottom. Recall that a geophone gives positive voltage if pushed from above, and negative voltage if pushed from below. Non-normal incidence Equations 10 and 12 in theory hold for normal incidence. In practice they are generally usable for angles up to about Rigorous analysis of non-normal incidence is achieved using the Zoeppritz equations (equivalent to Knott equations). A commonly used approximation is the Shuey approximation which is accurate up to about 40. The variation of reflectivity with incident angle (i.e. with offset) is the basis of the concept of AVO (Amplitude vs offset) which has been widely used in exploration. Seismic Reflection Imagery Figure 6 showed a typical 2D land reflection shot record. In a typical seismic survey thousands of such records are acquired. These are then combined together using a methodology referred to as seismic processing. The resulting images (e.g. Figures 11 12) are important in geological interpretation, particularly in sedimentary systems.

14 ERTH2020 Basic Seismology - 14 Figure 11: Seismic reflection section resulting from processing of a large number of reflection shot records. This image is used in gas exploration. The vertical axis represents about 5km, and the horizontal axis is of order 50 km. Figure 12: Coal-scale seismic reflection section resulting from processing of a large number of reflection shot records. The vertical axis represents about 1km, and the horizontal axis is of order 10 km.

15 ERTH2020 Basic Seismology Introduction to seismic refraction Physical basis of seismic refraction As indicated in Figure 9 the rays exploited in seismic refraction are formed by critical refraction at the interface. It is not intuitively obvious why a ray should then return upward to the geophone. In fact, from the point at which the critical ray strikes the boundary, a set of new waves termed head waves arise, and these travel back to the surface also at the critical angle (Figure 13). The mechanism for these waves is interesting and is further explained in a separate note (headwaves.pdf ). Figure 13: The seismic refraction method is based on the generation of a criticallyrefracted wave which skims along an interface. In turn, this results in head waves which travel back to the surface, also at the critical angle. Seismic refraction amplitudes The so-called head-wave coefficient provides an indication of the amplitude of the refraction arrival. It is a complex expression involving densities, P velocities, and S velocities in the layers on either side of the interface. It is interesting that head-wave coefficients are larger for low-contrast interfaces (i.e. as v 1 /v 2 approaches unity. Intuitively this makes sense when ray orientations are considered (Figure 14) Finally, note that for a compressional source, the headwave will always arrive as a compression at the base of the geophone, causing a negative-voltage. This often helps identification of the refraction arrival time.

16 ERTH2020 Basic Seismology - 16 Figure 14: In high-contrast situations (left) the head wave has a very different orientation to the critically refracted ray, resulting in smaller amplitude transfer. Conversely, for low-contract situations, orientations are similar, and amplitude transfer is greater.