# Seismic attenuation

SEISMIC ATTENUATION

## What is seismic attenuation?

Seismic attenuation is an intrinsic property of rocks causing dissipation of energy as seismic waves propagate through the subsurface. It results in the decay of amplitude of the seismic waves. Attenuation is related to velocity dispersion.[1] The energy of seismic wave is conserved if it travels through a perfectly elastic medium. Propagating seismic waves loose energy due to[2]

• Geometrical spreading (wavefront radiating from a point source is distributed over a spherical surface of increasing size)
• Absorption (anelastic attenuation)
• Scattering (elastic attenuation)

Seismic wave amplitudes vary as they travel across the Earth. As the wavefront moves out from the source, the initial energy released in the seismic wave is spread over an increasing area and therefore the intensity of the wave decreases with distance (the case of geometric spreading). However, the geometric spreading alone cannot describe the attenuation of seismic wave energy. The decrease of the kinetic energy of seismic waves is also due to the energy absorption caused the imperfections in the earth. This is the case when the elastic energy is completely transmitted to the mantle.

##### Anelastic attenuation

There is another factor that affects seismic amplitudes. This is the energy loss due to anelastic processes or internal friction during wave propagation.[3] This is called intrinsic or anelastic attenuation. Intrinsic attenuation occurs mostly during shear wave motion associated with lateral movements of lattice and grain boundaries.

When traveling through subsurface, an elastic wave's mechanical energy is converted to heat energy due to friction and changes in viscosity. It occurs at interface boundaries such as water, gas, formation and grain boundaries.[2] This transformation results in decrease in amplitude and pulse broadening. As the wave travels away from the source, the pulse broadens with increasing distances. As the wave spreads, attenuation removes the high frequency component of the pulse.

##### Scattering

Attenuation is frequency-dependent and is strongly affected by scattering. Scattering is an important factor caused by the heterogeneity of the Earth's crust and mantle and availability of hydrocarbon reservoirs.[3] Scattering theory states that rocks containing oil and gas can cause energy attenuation in seismic waves, particularly the high frequency waves, passing through them. Frequency-dependent attenuation can be used to detect hydrocarbons. Figure 1 shows the variation of attenuation with frequency helping to locate and map reservoir containing oil and gas.

Figure 1ː Attenuation of seismic wave energy. Creditː[1]

Scattering is different from other types of attenuation since the integrated energy in the total wavefield remains constant. Scattering of high-frequency seismic waves demonstrates the existence of small scale heterogeneities in the lithosphere. The scattered waves are incoherent since the scatterers are considered to be randomly distributed. Due to incoherence the phase may be neglected and the scattered wave power is the sum of all the power from each scattered wave. Wave propagation in 2-D and 3-D inhomogeneous medium can reveal various attenuation results depending on what wavefield estimates are being utilized.

Scattering is computed using a ratio of the inhomogeneity of the medium a to the wavelength.

k=2π/wavelength

ka << 0.01 (quasi-homogeneous medium) - no significant scattering;

ka < 0.1 (Rayleigh scattering) - produces apparent Q and anisotropy;

0.1 < ka < 10 (Mie scattering) - produces strong attenuation and distinguishable scattering in the signal.

## Quality Factor Q

Attenuation is measured by a dimensionless quality known as the rock quality factor Q or attenuation factor. It is assumed that Q is linked to the physical state of the rock. Q is as ratio of stored energy to dispersed energy. It measures a relative energy loss per oscillation cycle. Q increases when the density and the velocity of the material increases. In the Earth’s crust and mantle Q ranges from 10 to 1000.

Q= (energy of seismic wave)÷(energy lost during one cycle of wave) =2πE/∆E

where E is the energy of seismic wave and ∆E is the energy change per cycle.
We often come across the inverse quality factor Q-1, where Q is inversely related to the strength of the attenuation. It means more attenuation in the regions where Q is low than where Q is high.

Typical range of Q values in the Earth

Rock type Qp Qs
Shale 30 10
Sandstone 58 31
Granite 250 70-250
Peridotite 650 280

When Q is frequency dependent i.e. each frequency looses the same amount of energy per cycle, the situation gets rather complicated.[4] For frequencies up to 1.0Hz the quality factor Q is independent of frequency. As the frequencies increase, Q becomes frequency dependent and normally Q increases with frequency. The Earth's mantle absorption model reveals that mantle absorption increases at frequencies from about 0.0001 to 1Hz.[4] A common way to determine Q is by getting the amplitude and frequency of the seismic wave at some point during its propagation.

Q(f)=Q0×f²

Figure 2. Seismic attenuation with distance for body waves and surface waves. Creditː[2]

General rule applied to the seismic attenuation can be written as
High frequencies – more oscillations – more attenuation
Low frequencies – less oscillations – less attenuation

As a result, the high frequencies decay very rapidly creating a pulse broadening. In the Earth we observe that Qp is larger than Qs. This is due to the fact that intrinsic attenuation is predominantly caused by shear motion involved between particles at grain boundaries that causes more frictional heating.[2] Figure 2 displays seismic attenuation with distance for body waves and surface waves.

Fluids in porous rocks move under transient stress perturbation that promotes frequency dependency in the seismic attenuation. Experimental studies on low frequency attenuation of rocks displayed the importance of the pore fluids in producing a frequency depended seismic response of the rocks.

Figure 3. Rayleigh Wave Attenuation vs. Depth. Creditː[3]

In contrast, a vacuum-dried rocks demonstrate a negligible dependency of the seismic response on frequency. [5] The ability of fluid to move through interconnected pores is regulated by the frequency of the wave. The fluid has no time to relocate following a pressure gradient caused by a propagating wave under the high frequency conditions. In the low frequency, fluid has enough time to flow until pore pressure is equalized at all scales.

The following data types are used to measure seismic attenuationː

• Free oscillations (Normal Modes)
• Surface waves
• Body waves (P and S)

Each mode has its own amplitude decay rate and thus the attenuation factor Q has to be calculated for each mode. Different values of Qs result from the way each mode samples the Earth. Surface wave attenuation pattern is shown in Figure 3.

Figure 4. Global Attenuation Model. Creditː[4]

## Attenuation structure through the Earth's subsurface

Global attenuation model below has been obtained from the normal modes and surface waves displays the highest attenuation in the asthenosphere and inner core and low attenuation in the lithosphere and lower mantle (Figure 4).[2] [6] Global surface wave attenuation models correspond closely with shear velocity, suggesting that the temperature is the main controlling factor.

## Seismic attenuation and rock properties

The attenuation is directly related to the composition of the Earth's layers. Thus it changes whenever the changes in the layering composition occur. This property of attenuation allows scientists to identify variations in rock properties. Measurements of seismic attenuation can also provide information of fluid content or zones of high permeability.[7] Greater porosity and higher Vp/Vs correspond to higher attenuation. Completely dry rocks display negligible attenuation. Fluid motion between pores and presence of volatiles can induce a loss. Shaly sandstone shows greater attenuation despite the fact that a macroscopic fluid flow is compromised.

## Applications of attenuation

Seismic attenuation is in rocks is proportional to frequency, the higher-frequency components of propagating seismic waves are more attenuated than the lower-frequency components. Q is sensitive to clay volume, pressure, saturation, and fracture, therefore seismic attenuation can be used for lithology discrimination. The effect of saturation and pore pressure on attenuation is greater on the order of magnitude than the effect of saturation on velocity. Seismic attenuation is a powerful attribute that is sensitive to hydrocarbon accumulation, fluid-saturated fractures, and rugosity. Thus attenuation is extremely useful for reservoir characterization. The ratio of compressional to shear attenuations is applied as hydrocarbon indictor in well logs.[8] Qp /Qs < 1 indicates presence of gas or condensate, while Qp /Qs - 1 indicates 'full water' or 'oil + water' saturation. The upper mantle demonstrates a prevailing shear attenuation not bulk attenuation so Qp / Qs ratios are usually small in partially molten materials. At the same time, rocks near their melting point have large Vp/Vs ratios (Vp/Vs > 2). Estimates of seismic attenuation combined with Vp and Vs variations provide information of the physical state of the upper mantle and explain the impact of temperature, composition and melt friction.