Engineering geology
geodetic and seismic data

Post-seismic relaxation from geodetic and seismic data


The physics of the earthquake and post-shock process remains vague. The nature of changes occurring in the rocks on the threshold of a large earthquake, in the main shock moment, and during the aftershock sequence remains unclear. The seismic efficiency value and the ratio of the released seismic energy to simultaneous co-seismic displacements hardly will remain unchangeable during the preparation and implementation of a large earthquake and during the subsequent aftershock sequence. Mostly simple to compare these values for the main shock and the aftershock sequence in general, without going into detail on the individual stages of the healing process. The subject is examined below for the case of the Parkfield earthquake (2004, M = 6, California, USA).

Data and method

The aftershock process of Parkfield earthquake (2004, M = 6, California, USA) is analyzed on the base of geodetic and seismic data joint examination. The reason for choosing this event is that it was possible to receive and jointly analyze the rather denser local GPS network data (SOPAC Internet archive, Fig. 1) and sufficiently detailed information on aftershock sequence (

Fig. 1. GPS network (white square points) and principal baselines used in creep analysis (black segments). Main faults are given red. The main shock and stronger (M > 4) aftershocks are given as yellow points of different size.

The GPS data processed using original technique and routines [1] show, that the seismic process is accompanied by a strong horizontal deformation developing in a long relaxation process of roughly exponential behavior with displacements oriented in agreement with the seismic ones (Fig. 2).

Fig. 2. Creep plane displacement behavior before and after the earthquake (red dots are marked creep values, blue small dots are fixed one sigma margin intervals 1σ).

Free adjustment of GPS baseline vectors were used for the vector displacement determination. Two baselines crossed the rupture zone were selected for the determination of creep displacements dij of the fault flanges. Creep displacements were computed as

where u is a projection of the horizontal displacement vector on the main line of seismogenic fault, i,j correspondent points of GPS baseline.

The relaxation process gives evidence that the release of the elastic deformation accumulated previously occurs not only during the main shock but it continuous rather long time afterwards. The process of relaxations lasts about 400 days after the main shock occurrence, approximately the same duration time of the process of aftershock sequence (Fig. 3).

Fig. 3. Omori law of the Parkfield earthquake aftershock sequence. The aftershock activity lasts approximate 500 days.

Tendencies of increase of the current b-value and increase in the current mean aftershock depth values also last about 500 days (Fig. 4). These tendencies testify for the existence of a definite relaxation process that lasts about 400–500 days after the main shock.

Fig. 4. Changes of mean current b-value (a) and mean aftershock depth (b) after Parkfield earthquakes with time expired since the main shock.

The b-values and mean aftershock depths were determined for the groups of subsequent events followed one after another (Fig. 4). A number of events in a group were determined as a compromise between a requirement to reveal the temporal change in seismic characteristics in more detail and of suitable accuracy of estimations. Neighboring groups were collected with a shift of n/2 events. The b-values were calculated using maximum likelihood method [2].

Note that the tendency of b-value decreasing at the main shock occurrence was verified recently both in field and laboratory data [3], [4]. The tendency of decrease of the b-value in the vicinity of strong earthquakes were found also to be typical of strong earthquakes that was shown in result of examination of the behavior of seismicity in the general vicinity of strong (M > 7) events [4], [5]. And the similar tendencies in change of the mean aftershock depth values were found recently from a dense local seismic network data in the vicinity of the large platform earthquake in the north-west India (2001, M = 7.7) [6] and from the examination of the aftershock sequence data of Great Andaman, Simushir and Tohoku earthquakes [7], [8]. Interpretation of this tendency presents an essential interest because of the probable connection of these phenomena with change in the deep fluid regime. The deep fluid escaping from the lithosphere through the highly fractured media after the large earthquake occurrence appears to be the mostly probable reason of an essential decrease of mean depth of earlier aftershocks (Fig. 4b). Fig. 2, Fig. 3, Fig. 4 testify for the process of relaxation that lasted for about 400–500 days.

Elastic/inelastic problem

There is a problem in seismology on the seismic efficiency – what part of the deformation takes place via the seismic rupture and which part releases via an aseismic deformation. The foreshock, main shock and post-shock periods appear to be very different in this point. As can be seen from Fig. 2, the deformation occurring during the main shock and during aftershock activity has about the same value. But the released seismic energy differs very considerably, specifically, the seismic energy released in the main shock is about 9.1 × 1019 erg, whereas the total seismic energy released in the aftershock sequence is 1.2 × 1018 erg only. It means that elastic/inelastic deformation ratio decrease very essentially for aftershocks comparing with the main shock.

The same feature is valid for a few other strong earthquakes where the needed information was found to be available.

It is unclear does this change is connected to an increase of seismic efficiency for stronger earthquakes or seismic efficiency decreases essentially in process of aftershock relaxation due to a temporary increase in fracturing after the main event occurrence. We prefer the second variant of the explanation.


A tendency of an essential change of b-value, fractal dimension value, and mean aftershock depth value appear to be typical of the aftershock sequences besides the Omori law.

The duration of aftershock process was shown in a number of cases to be close to the duration of relaxation in post-shock deformation obtained from GPS measurements.

The ratio of a released seismic energy to deformation value considerably decreases for aftershock process comparing with the main shock. The nature of this difference is unclear. The difference could take place if stronger earthquakes have essentially higher seismic efficiency than the moderate ones. One can suggest also that low seismic energy/total deformation ratio is typical of relaxation aftershock processes. This effect can be connected with an increase in fracturing of media during an aftershock sequence occurring just after the main shock. This suggestion is supported with decrease in the mean earthquake depth in the close vicinity of large events. The increase in fracturing and the following healing process could both change essentially the seismic energy/total deformation ratio and mean earthquake depth because more rapid penetration of the deep fluid to shallow layers through the fractured media.

Source: Post-seismic relaxation from geodetic and seismic data

Authors: Mikhail V.Rodkin, Vladimir I.Kaftan

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