# Calculating 1D spectrum from 2D spectrum

1. Mar 19, 2010

### nkinar

Hello---

I am reading a paper which presents a method to determine attenuation (and Q factors) from reflection seismic data (Y. Wang, "Q analysis on reflection seismic data," Geophysical Research Letters, Vol. 31, 2004).

To perform signal processing on a seismic trace, the paper describes the following procedure:

(1) From the real and complex parts of the Gabor spectrum transform, compute the (real numbered) amplitude spectrum $$U(t, \omega)$$ on a seismic trace $$s(t)$$, where $$t$$ is the time (s), $$\omega$$ is the angular frequency (1/s), and $$\omega = 2 \pi f$$, where $$f$$ is the frequency in Hz.

(2) Define $$\chi = t \omega$$ as the product of $$t$$ and $$\omega$$, and transform the 2D spectrum $$U(t, \omega)$$ into the 1D spectrum $$U(t\omega) = U(\chi)$$.

The paper does not describe how to transform $$U(t, \omega)$$ into $$U(\chi)$$.

Would numerical integration be able to do this transformation? How might I proceed?