# Talk: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. Attenuation is related to velocity dispersion.[1] The energy of seismic wave is conserved if it travels through a perfectly elastic medium. Two types of attenuation existː[2]

- Absorption (anelastic attenuation)

- Scattering (elastic attenuation)

When traveling through subsurface, an elastic wave's mechanical energy is converted to heat energy due to friction and variations 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.

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] 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= (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.

Typical range of Q values

Q≈30 for weathered sedimentary rocks

Q≈1000 for granite

Q≈10,000 for steel

When Q is frequency dependent, the situation gets rather complicated.[4]

Q(f)=Q0×f²

The Earth's mantle absorption model demonstrates that mantle absorption increases at frequencies from about 0.0001 to 1Hz.[4]

The following seismic data are used to measure seismic attenuation:

- 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. Surface wave attenuation pattern is shown in Figure below.

Rayleigh Wave Attenuation vs. Depth

## 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.[2] [5] The model suggests that temperature is a primary 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.[6] 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.

## References

1. M. Batzle, Ronny Hofmann, Manika Prasad, Gautam Kumar, L. Duranti, and De‐hua Han (2005) Seismic attenuation: observations and mechanisms. SEG Technical Program Expanded Abstracts 2005: pp. 1565-1568. https://doi.org/10.1190/1.2147991
2. Joseph J. Durek, Göran Ekström; A radial model of anelasticity consistent with long-period surface-wave attenuation. Bulletin of the Seismological Society of America ; 86 (1A): 144–158.
3. Shapiro, S. A. and Kneib, G. (1993), Seismic Attenuation By Scattering: Theory and Numerical Results. Geophysical Journal International, 114: 373–391. doi:10.1111/j.1365-246X.1993.tb03925.x
4. Terry D. Jones (1985) Frequency‐dependent seismic attenuation: Effect on wave propagation. SEG Technical Program Expanded Abstracts 1985: pp. 359-361.
5. Dalton, C. A., and G. Ekström (2006), Global models of surface wave attenuation, J. Geophys. Res., 111, B05317, doi:10.1029/2005JB003997.
6. Kenneth W. Winkler and Amos Nur (1982). ”Seismic attenuation: Effects of pore fluids and frictional‐sliding.” GEOPHYSICS, 47(1), 1-15. https://doi.org/10.1190/1.1441276