Abstract

Spectral analysis of earthquake recordings provides fundamental seismological

information. It is used for magnitude calculation, estimation of attenuation, and

the determination of fault rupture properties including slip area, stress drop, and radiated

energy. Further applications are found in site-effect studies and for the calibration

of simulation and empirically based ground-motion prediction equations.

We identified two main limitations of the spectral fitting methods currently used in

the literature. First, the frequency-dependent noise level is not properly accounted for.

Second, there are no mathematically defensible techniques to fit a parametric spectrum

to a seismogram with gaps.

When analyzing an earthquake recording, it is well known that the noise level is not

the same at different frequencies, that is, the noise spectrum is colored. The different,

frequency-dependent, noise levels are mainly due to ambient noise and sensor noise.

Methods in the literature do not properly account for the presence of colored noise.

Seismograms with gaps are usually discarded due to the lack of methodologies to

use them. Modern digital seismograms are occasionally clipped at the arrival of the

strongest ground motion. This is also critical in the study of historical earthquakes in

which few seismograms are available and gaps are common, significantly decreasing

the number of useful records.

In this work, we propose a method to overcome these two limitations. We show

that the spectral fitting can be greatly improved and earthquakes with extremely low

signal-to-noise ratio can be fitted. We show that the impact of gaps on the estimated

parameters is minor when a small fraction of the total energy is missing. We also

present a strategy to reconstruct the missing portion of the seismogram.