typo

docs/literate/examples/08-earthquake.jl

@@ -2,7 +2,7 @@
 #
 # Now we consider a mechanical structure problem under ground-shaking Earthquake-like excitations. The problem is modeled by a second-order Random ODE driven by a random disturbance in the form of a transport process. The equation is inspired by the model in [Bogdanoff, Goldberg & Bernard (1961)](https://doi.org/10.1785/BSSA0510020293) (see also [Chapter 18]{NeckelRupp2013} and {HousnerJenning1964} with this and other models).
 #
-# There are a number of models for earthquake-type forcing, such as the ubiquotous Kanai-Tajimi and Clough-Penzien models, where the noise has a characteristic spectral density, determined by the mechanical properties of the ground layer. The ideia, from {Kanai1957}, is that the spectrum of the noise at bedrock is characterized by a constant pattern, while at the ground surface it is modified by the vibration property of the ground layer. This interaction between the bedrock and the ground layer is modeled as a stochastic oscillator driven by a zero-mean Gaussian white noise, and whose solution leads to a noise with a characteristic power spectrum.
+# There are a number of models for earthquake-type forcing, such as the ubiquitous Kanai-Tajimi and Clough-Penzien models, where the noise has a characteristic spectral density, determined by the mechanical properties of the ground layer. The ideia, from {Kanai1957}, is that the spectrum of the noise at bedrock is characterized by a constant pattern, while at the ground surface it is modified by the vibration property of the ground layer. This interaction between the bedrock and the ground layer is modeled as a stochastic oscillator driven by a zero-mean Gaussian white noise, and whose solution leads to a noise with a characteristic power spectrum.
 #
 # Another important aspect concerns the fact that the aftershocks tend to come in clusters, with the ocurrence of an event increasing the chances for subsequent events. As such, self-exciting intensity processes have been successful in modeling the arrival times of the aftershocks (see e.g. [Pratiwi, Slamet, Saputro & Respatiwulan (2017)](https://doi.org/10.1088/1742-6596/855/1/012033)). The decaying kernel is usually an inverse power law, starting with the celebrated Omori formula [T. Utsu, Y. Ogata & R. S. Matsu'ura, The centenary of the Omori formula for a decay law of aftershock activity, Journal of Physics of the Earth, Volume 43 (1995), no. 1, 1-33](https://doi.org/10.4294/jpe1952.43.1)). Exponentially decaying kernels are also used and, in this case, leads to a noise in the form of an exponentially decaying self-excited Hawkes process. The intensity, or rate, of this inhomogenous Poisson point process, for the interarrival times, is not directly related to the magnitude of the aftershocks, so this process should be coupled with another process for the magnitude of each shock.
 #

docs/src/examples/08-earthquake.md

@@ -6,7 +6,7 @@ EditURL = "https://github.com/rmsrosa/rode_conv_em/docs/literate/examples/08-ear
 
 Now we consider a mechanical structure problem under ground-shaking Earthquake-like excitations. The problem is modeled by a second-order Random ODE driven by a random disturbance in the form of a transport process. The equation is inspired by the model in [Bogdanoff, Goldberg & Bernard (1961)](https://doi.org/10.1785/BSSA0510020293) (see also [Chapter 18]{NeckelRupp2013} and {HousnerJenning1964} with this and other models).
 
-There are a number of models for earthquake-type forcing, such as the ubiquotous Kanai-Tajimi and Clough-Penzien models, where the noise has a characteristic spectral density, determined by the mechanical properties of the ground layer. The ideia, from {Kanai1957}, is that the spectrum of the noise at bedrock is characterized by a constant pattern, while at the ground surface it is modified by the vibration property of the ground layer. This interaction between the bedrock and the ground layer is modeled as a stochastic oscillator driven by a zero-mean Gaussian white noise, and whose solution leads to a noise with a characteristic power spectrum.
+There are a number of models for earthquake-type forcing, such as the ubiquitous Kanai-Tajimi and Clough-Penzien models, where the noise has a characteristic spectral density, determined by the mechanical properties of the ground layer. The ideia, from {Kanai1957}, is that the spectrum of the noise at bedrock is characterized by a constant pattern, while at the ground surface it is modified by the vibration property of the ground layer. This interaction between the bedrock and the ground layer is modeled as a stochastic oscillator driven by a zero-mean Gaussian white noise, and whose solution leads to a noise with a characteristic power spectrum.
 
 Another important aspect concerns the fact that the aftershocks tend to come in clusters, with the ocurrence of an event increasing the chances for subsequent events. As such, self-exciting intensity processes have been successful in modeling the arrival times of the aftershocks (see e.g. [Pratiwi, Slamet, Saputro & Respatiwulan (2017)](https://doi.org/10.1088/1742-6596/855/1/012033)). The decaying kernel is usually an inverse power law, starting with the celebrated Omori formula [T. Utsu, Y. Ogata & R. S. Matsu'ura, The centenary of the Omori formula for a decay law of aftershock activity, Journal of Physics of the Earth, Volume 43 (1995), no. 1, 1-33](https://doi.org/10.4294/jpe1952.43.1)). Exponentially decaying kernels are also used and, in this case, leads to a noise in the form of an exponentially decaying self-excited Hawkes process. The intensity, or rate, of this inhomogenous Poisson point process, for the interarrival times, is not directly related to the magnitude of the aftershocks, so this process should be coupled with another process for the magnitude of each shock.