Seismic methods

Andreas Vad, winter semester 2017/18

Seismic methods are techniques to derive geological data from the observation and analysis of the propagation of elastic waves. The elastic waves are artificially generated (in contrast to seismology, where they come from natural sources). Since the propagation of elastic waves beneath and along the surface of the earth is due to several influences and furthermore depends on the wave form, several seismic methods have been developed.^[1]

Basic physical background

Seismic waves are elastic waves that are generated by mechanical stimulation of a source, from where they propagate in any direction that supports mechanical displacement. Therefore, elastic waves propagate through solids, liquids and gases and can be transferred from one to another, but in contrast to electromagnetic waves they cannot penetrate vacuum.^[2]

There are two important classes of waveforms for seismic analysis:

Body waves: In a uniform material body waves spread spherically from the source of the disturbance. In solid materials there are two types of body waves: ^[3]

• P- wave (or compressional or pressure or primary wave): It is the fastest wave form and can transit solids, liquids and gasses (in liquids and gases P- waves are called acoustic waves). The direction of particle oscillation for P- waves is identical to the direction of their propagation.
• S- wave (or secondary or transverse or shear wave): S- waves are slightly slower than P- waves. Particles oscillate perpendicular to the direction of propagation. S- waves only transit media that support shear forces. They therefore don’t propagate in liquids and gases.

Surface waves: Surface waves propagate along a surface with a smaller velocity than body waves. They have the property that they diminish exponentially with distance to the surface. For seismic analysis the Rayleigh- and the Love- wave are important.

Speed of propagation: The speed of propagation depends on the elastic properties of the medium. The velocities of the P- wave $//<![CDATA[ \begin{array}{l}v_p\end{array} //]]>$, the S- wave $//<![CDATA[ \begin{array}{l}v_s\end{array} //]]>$ and Rayleigh- wave $//<![CDATA[ \begin{array}{l}v_r\end{array} //]]>$ are interrelated according to equation (1).

(1): $//<![CDATA[ \begin{array}{l}\left(2-\frac{v_r^2}{v_s^2 }\right)^2-4\sqrt{1-\frac{v_r^2}{v_s^2 } } \sqrt{1-\frac{v_r^2}{v_p^2 } }=0\end{array} //]]>$

The velocity of the P- wave is:

(2): $//<![CDATA[ \begin{array}{l}v_p=\sqrt{\frac{ε(1-σ)}{ρ(1+σ)(1-2σ)} }\end{array} //]]>$

The velocity of the S- wave is:

(3): $//<![CDATA[ \begin{array}{l}v_s=\sqrt{\frac{ε}{2ρ(1+σ)} }\end{array} //]]>$

In equation (2) and (3) ε is the effective E modulus, ρ the density and σ the Poisson’s ratio.

In an elastic medium a seismic disturbance spreads in all directions from the source. Any point on the formed wavefront is considered a new source of disturbance. The vector normal to the wavefront is the direction of propogation. On the boundary of two media with different elastic properties the wave energy is refracted, reflected and/ or converted. The share of refracted, reflected and converted wave energy is determined by elastic properties of the medium and the striking angle of the normal vector onto the boundary. Figure 1 illustrates a possible configuration.

The P- wave $//<![CDATA[ \begin{array}{l}A_p\end{array} //]]>$ hits the boundary between two media with different properties. It then splits into four different wave beams. A reflected $//<![CDATA[ \begin{array}{l}R_{pp}\end{array} //]]>$ and transmitted P- wave $//<![CDATA[ \begin{array}{l}T_{pp}\end{array} //]]>$ as well as a reflected $//<![CDATA[ \begin{array}{l}R_{ps}\end{array} //]]>$ and transmitted $//<![CDATA[ \begin{array}{l}T_{ps}\end{array} //]]>$ S- wave are generated. The relationship between their velocities and angles is defined according to Snellius:

(4): $//<![CDATA[ \begin{array}{l}\frac{\sin⁡(α_1 )}{v_{p1}} =\frac{\sin⁡(β_1 )}{v_{s1}} =\frac{\sin⁡(α_2 )}{v_{p2}} =\frac{\sin⁡(β_2 )}{v_{s2}}\end{array} //]]>$

The share of the reflected energy at normal incidence can be described by the reflection coefficient $//<![CDATA[ \begin{array}{l}R_{1,2}\end{array} //]]>$. It is the ratio of the reflected intensity $//<![CDATA[ \begin{array}{l}I_2\end{array} //]]>$ and the initial intensity $//<![CDATA[ \begin{array}{l}I_1\end{array} //]]>$ and can be formulated with the acoustic Impedance $//<![CDATA[ \begin{array}{l}Z=ρ·v \left[\frac{kg}{(m^2 s)}\right]\end{array} //]]>$.

(5): $//<![CDATA[ \begin{array}{l}R_{1,2}=\frac{I_2}{I_1} =\frac{Z_2-Z_1}{Z_2+Z_1}=\frac{ρ_2 v_2-ρ_1 v_1}{ρ_2 v_2+ρ_1 v_1 }\end{array} //]]>$

At non- normal incidence a mode conversion like illustrated in figure 1 occurs. The shares of the reflected P- and S- waves as well as the refracted P- and S- waves can then be described by the Zoeppritz equations.^[4]

Basic principle of a seismic measurement

A seismic wave is generated and its time of travel through a body or along a surface to an array of receivers (geophones) is measured. Based on the travel times the path of the waves can be reconstructed.

Seismic equipment includes a seismic source, geophones and seismographs.

The source of the artificially generated seismic disturbance may be a hammer hitting the ground, weight drops, a rifle shot, a harmonic oscillator, waterborne mechanisms or explosives.

The sensors measuring the reflected or refracted seismic energy are called geophones. The received signals are sensed by an accelerometer or velocity transducer, converted into voltage and amplified multiple times on a relative basis. There are several designs depending on which waveforms shall be analysed. Furthermore, there are more sophisticated geophones for special applications. The frequency band respond is another criterion that should be considered while selecting the appropriate geophone. ^[2] In marine applications hydrophones are used which convert pressure into electrical signals. ^[5]

Modern seismographs record the voltage signals of the geophones as digital data at discrete times. Older seismographs transfer the voltage input analogical onto paper.

The analysis and interpretation of the stored data is the duty of the geophysicist. It requires know how and experience.

Overview of the seismic methods

Seismic methods can be classified according to the wave type. Either body waves or surface waves are analysed.

Seismic methods that analyse body waves can be based on reflection, refraction or transmission. ^[6]

Reflection seismics

Figure 2 shows schematically a measurement based on the reflections of 3 ground layers. Due to the differences in the acoustic impedance, seismic waves are reflected and refracted between ground layers with different properties (density and elastic behaviour). If the velocity v of the seismic wave and the distance between source and geophone x is known, the depth d of this boundary can be calculated by measuring the travel time of the reflected wave:

(6): $//<![CDATA[ \begin{array}{l}t=\frac{2\sqrt{d^2+(x/2)^2 }}{v}\end{array} //]]>$

Using several geophones, the geologic structure can be reconstructed by correlating related reflexions from different geophones (figure 3).

Figure 4 illustrates the common depth point method (CDP). Using two sources and two receivers with the same relative distance to one another, they have the same reflection point in the ground layer, but with different travel times. This can be utilized to calculate the propagation speed in the ground. ^[2] This process can be done with more source/ geophone pairs. These source/ geophone pairs have only the same reflection point if the reflecting layer is horizontal. At leaned layers the reflection points are spread, which results in an error in the depth resolution.

Refraction seismics

Like the reflected wave, the refracted wave can be used to determine the depth of ground layers. In figure 5 the pathway of a refracted wave is illustrated.

The refracted wave propagates along the boundary of two layers. The condition is that $//<![CDATA[ \begin{array}{l}α_2\end{array} //]]>$ equals 90 ° We obtain the critical angle $//<![CDATA[ \begin{array}{l}α_c\end{array} //]]>$ using Snellius law of equation (4):

(7): $//<![CDATA[ \begin{array}{l}\sin⁡(α_c )=\frac{v_1}{v_2}\end{array} //]]>$

The travel time for a, in n layers refracted, wave is obtained by formula (8):^[7]

(8): $//<![CDATA[ \begin{array}{l}t=\frac{x·sin⁡(β_1 )}{v_1} +\sum_{i=1}^{n-1}h_i·\frac{\cos⁡(α_i )+\cos⁡(β_i )}{v_i}\end{array} //]]>$

The advantage of refraction methods over reflection methods is that the travel times are greater. Therefore, near surface observations can be analysed. The problem with reflection methods at near surface observations is that the signals resulting from the surface waves and the signals resulting from the reflection are temporally too close to each other.^[7]

Surface wave seismics

Surface wave methods are applied to investigate the near surface structures, detect inhomogeneities or to investigate the pavement substrate strength.

Transmission seismics

In transmission seismics the travel time of a direct seismic wave is measured with aim to determine the elastic properties of the ground. There are 3 possible configurations:

• Crosshole: The source and the geophone are each positioned in a borehole.
• Downhole: Only the geophone is in the borehole. The source is situated on the surface.
• Uphole: The source is in the borehole, the geophone on the surface.

Other signals that are received by the geophones are:

• Noise, due to the weather or ambient sources (aeroplanes, …)
• Air wave: the direct wave from source to geophone
• Head waves, conical waves
• Multiple reflections: A wave that is reflected in turns between two ground layers multiple times
• Superposition of different wave types

Analysis and evaluation

Resolution

The resolution depends on the used frequencies. The higher the frequencies the better the resolution, but the lower the depth of penetration. Also, at near surface observations the frequency must be high to distinguish the body waves from the surface waves, as they are recorded at nearly the same time.

Migration

Due to leaned, discontinuous layers or obstacles in the ground the recorded structure in a time- distance diagram does not correspond to the real structure of the ground. Examples for these artefacts are a recorded structure in the shape of a “bow tie” which corresponds to a curved valley or a diffraction hyperbola which corresponds to a point reflector. Migration is the process of removing these artefacts.^[7]

The analysis and evaluation of the received data contains several steps:

• Control of the validity of the data
• Demultiplexing: Analysis of the data at each seismograph
• Amplitude correction
• Static corrections (for example with the known topography)
• CDP- surveying: seismographs, which have the same CDP can be stacked to improve the Signal to noise ratio (SNR)
• Deconvolution: removal of multiple reflections; equalization of the amplitude of all frequencies
• Bandpass filter: reduction of noise → improvement of SNR
• Migration

Other Applications^[2][8][9]

Seismic Reflection Methods

• Common-Offset Seismic Reflection Method
• Subbottom Profiling
• Fathometer Surveys
• Oil field detection
• Pile foundations (seismic methods)

Surface Wave Methods

• Spectral Analysis of Surface Waves (SASW)
• Common-Offset Rayleigh Wave Method
• Enhancements of the seismic interferometry in civil engineering
• Non- destructive testing of surficial regions of materials

Transmission Methods

• Ultra- seismic methods

Relation to non-destructive testing

Seismic methods are closely related to the following non- destructive methods: Impact-Echo, Ultrasonic Pulse-Echo Method, Ultrasound transmission tomography and Ultrasound transmission testing. The difference is the application. Analysis and evaluation techniques from seismic methods can be applied on the evaluation of ultrasonic data and vice versa.^[10] The SAFT Algorithm is one example.

Literature

• Große, C.: Einführung in die Zerstörungsfreie Prüfung im Ingenieurwesen. 2017. Munich. Department for non-destructive testing
• Clauser, C.: Einführung in die Geophysik.Globale physikalische Felder und Prozesse in der Erde. Berlin, Heidelberg: Springer- Verlag. ISBN: 978-3-642-04496-0 2017
• Bitzer, K.: Geophysikalische Methoden. (n.d.). Bayreuth. Abteilung Geologie, Universität Bayreuth. p.65, p.93-104.

References

1. Österreichische Geophysikalische Gesellschaft: Seismic Methods. 2018. Retrieved 02 27, 2018. from http://en.geophysik.at/index.php/methods/seismic-methods
2. U.S. Environmental Protection Agency: Seismic Methods. 2016. Retrieved 02 28, 2018. from https://archive.epa.gov/esd/archive-geophysics/web/html/index-10.html
3. Große, C.: Einführung in die Zerstörungsfreie Prüfung im Ingenieurwesen. 2017. Munich. Department for non-destructive testing. Technical University of Munich
4. Clauser, C.: Einführung in die Geophysik. 2014. Globale physikalische Felder und Prozesse in der Erde. Berlin, Heidelberg: Springer- Verlag. ISBN: 978-3-642-04496-0 2017
5. ONDA Corporation: OndaCorp. Retrieved 02 28, 2018, from http://ondacorp.com/Handbook/#p=14
6. GGU Gesellschaft für Geophysikalische Untersuchungen mbH: Geophysik- Zerstörungsfreie Prüfung. (n.d.). Retrieved 02 28, 2018, from http://www.ggukarlsruhe.de/Messverfahren_Geophysik_zersto/Ubersicht_uber_seismische_Verf/hauptteil_ubersicht_uber_seismische_verf.html
7. Bitzer, K.: Geophysikalische Methoden. (n.d.). Bayreuth. Abteilung Geologie, Universität Bayreuth. p.65, p.93-104
8. Niederleithinger, E.: Neue Ideen für die zerstörungsfreie Prüfung von Beton. 2014. Seismische Interferometrie und mehr. (B. B. -prüfung, Hrsg.) DGZfP-Jahrestagung 2014 – Di.1.C.1
9. Wang, H., Chung- Yue, W., Hsin- Ju, W., & Nguyen, T.: Ultra-Seismic Depth Evaluation on Model Piles- A Pilot Experiment. 2017. Taipei, Taiwan: Department of Civil Engineering, National Central University
10. Niederleithinger, E.: Geophysik und Zerstörungsfreie Prüfung im Bauwesen. 2014. Fachtagung Bauwerksdiagnose 2014. Berlin: BAM Bundesanstalt für Materialforschung und -prüfung