## Jan 14 Don’t ignore seismic attenuation

In general terms, seismic attenuation is the loss of elastic energy contained in a seismic wave, occurring through either anelastic or elastic behaviour. Anelastic loss, or intrinsic attenuation, is a result of the properties of the propagation medium. It causes a fraction of the wave’s energy to be converted into other forms such as heat or fluid motion. Non-intrinsic effects like multiple scattering are collected under the term apparent attenuation; they are so many and varied that intrinsic attenuation is difficult to isolate.

Attenuation of a seismic wave results in amplitude loss, phase shifts due to the associated dispersion, and the loss of resolution over time. This makes interpretation of the stacked data more difficult, and introduces an amplitude gradient in pre-stack data that is not predicted by reflectivity alone. These problems can be mitigated by the use of an inverse $$Q$$-filter which attempts to reverse the attenuation effects based on a measured attenuation field. Measures of attenuation are useful in their own right, because through them we can infer reservoir properties for characterization purposes.

The mechanisms of intrinsic attenuation have been referred to as either jostling or sloshing losses, relating to losses from dry-frame or fluid-solid interactions respectively. Jostling effects involve the deformation or relative movement of the rock matrix, for example due to friction from intergranular motion or the relative motion of crack faces. More significant in magnitude are the sloshing effects, which occur when pore fluids move relative to the rock frame. These fluid effects are characterized by the scale over which pressure is equalized, from large-scale Biot flow, between the rock frame and the fluid, to squirt flow caused by the compression of cracks and pores.

Attenuation may be described as the exponential decay of a seismic wave from an initial amplitude $$A_0$$ to an attenuated state $$A$$ over distance $$z$$, quantified by an attenuation coefficient $$\alpha$$:

$$A = A_0 e^{-\alpha z}$$

Various models describe the behaviour of $$\alpha$$ with frequency, and the relation- ship between the frequency-dependent velocity $$V(f)$$ and the quality factor $$Q$$. Although many of the intrinsic attenuation mechanisms, specifically the sloshing losses, are dependent on frequency, $$Q$$ is often assumed to be constant over the limited bandwidth of seismic experiments, resulting in $$\alpha$$ being linear with respect to frequency:

$$\alpha = \pi f / V Q$$

$$Q$$ may also be defined by the complex behaviour of the elastic modulus $$M$$:

$$Q = \text{Re}(M) / \text{Im}(M)$$

Seismic attenuation may be measured from different experimental configurations and at different frequency scales. The general method is to analyse the change in amplitude or frequency content or both, with propagation distance. For exploration seismic, two of the more common approaches are:

1. Spectral ratio — The spectrum is observed at two points along its travel- path, $$S_1(f)$$ and $$S_2(f)$$, with a time separation $$\Delta t$$. There is an inverse linear relationship between $$Q$$ and the natural logarithm of the ratio of $$S_2$$ to $$S_1$$:

$$\ln \left[ \frac{S_2(f)}{S_1(f)} \right] = - \frac{\pi\, \Delta t\, f}{Q} + \ln (PG)$$

The intercept term is determined by frequency independent amplitude effects such as energy partitioning $$P$$ and geometric spreading $$G$$.

2. Frequency shift — In which the shift of the centre frequency of the spectrum is related to attenuation of a modelled spectrum.

Seismic attenuation is rarely estimated — it is an often overlooked attribute. But the desire for quantitative geophysical attributes and improved data quality should win it more attention, especially as high-fidelity data allow ever more quantitative analysis. The effects of attenuation can no longer be ignored