The relative locations of multiplets in the vicinity of the WesternAlmerıa (southern Spain) earthquake series of 1993–1994

Daniel Stich,1 Gerardo Alguacil1,2 and Jose Morales1,2

1 Instituto Andaluz de Geofısica, Universidad de Granada, E-18071 Granada, Spain. E-mail: daniel@iag.ugr.es2 Departamento de Fısica Teorica y del Cosmos, Universidad de Granada, E-18071 Granada, Spain

Accepted 2001 May 1. Received 2001 March 30; in original form 2000 July 24

SUMMARY

We have analysed 721 earthquakes (1.5jmbj5.0) of the 1993–1994 Western Almerıa(southern Spain) series and the following seismicity in the area until 1998. Among thedata there are several multiplets, events characterized by very similar seismograms at theshort-period stations of the local network. We detected similar seismograms using cross-correlation analysis of the P and S arrivals and classified similar events into families, orclusters. We found 39 multiplet clusters of 3–33 events. Within each cluster, relocationsrelative to a master event have been calculated by using the interpolated cross-correlationmaxima for the precise relative timing of P and S phases at each station. Relative arrivaltimes have been compared for all the possible selections of the master event, and adjustedby forming the mean value after removing the outliers. The distribution of the stationsdoes not permit a satisfactory resolution of focal depths, but relative epicentres havebeen determined with an accuracy of a few tens of metres. Typically they draw well-definedlineaments and show two dominant strike directions: N120u–130uE and N60u–70uE.These directions are coincident with known fault systems in the area and with the sourceparameters of three of the largest events (Mw=4.8, 3.6 and 4.9), which were estimatedfrom waveform modelling of near-field acceleration records at a single station.

Consistent with previous studies, distances within multiplets (typically several tensof metres) are for the most part clearly smaller than the fracture radii of these events.This indicates repeated slip on the same fault segment. It was possible to obtain preciserelative locations between several nearby clusters, thereby imaging a very heterogeneousseismotectonic fine structure of the source area, i.e. the positions of adjacent active faultsegments and the fragmentation of the crust into small (approximately 1 km) tectonicblocks.

Key words: earthquake location, earthquake-source mechanism, fault tectonics, waveformanalysis.

I N T R O D U C T I O N

Earthquakes with nearby locations and similar source mech-

anisms radiate similar wavefields and generate similar ground

motions at the recording stations. Those events with seismograms

showing nearly identical waveform character are commonly

referred to as doublets (for a pair of events) or multiplets

(for larger sequences). Geller & Mueller (1980) suggested that

doublets and multiplets represent repeated rupture at the same

fault segment. The hypocentres of a multiplet sequence are

tightly clustered, and usually a standard location procedure is

not sufficiently accurate to resolve their spatial distribution.

The relative locations of multiplets can be determined very

precisely by making use of the seismograms’ similarity to obtain

an accurate relative timing of phase arrivals by cross-correlation

or cross-spectral techniques. Several authors have described

these methods:

A bibliography of the first decade of multiplet relocation

can be found in Deichmann & Garcia-Fernandez (1992); more

recent work includes Nadeau et al. (1994), Maurer & Deichmann

(1995), Cattaneo et al. (1997), Phillips et al. (1997) and Lees

(1998). The resulting relative locations give an image of the

distribution of points of maximum energy release on the rupture

surface rather than giving conventional hypocentres as points

where rupture started, because a finite window of signal is

evaluated instead of just the first-break onset (Fremont &

Malone 1987, Nadeau et al. 1994).

In the following we describe the application of multiplet

relocation to data from southernmost Spain, where a seismic

series occurred precisely in the epicentral area of the severe

Geophys. J. Int. (2001) 146, 801–812

# 2001 RAS 801

earthquakes of 1910 (I0=VIII MSK, mb= 6.3) and 1804

(I0= IX MSK): see Karnık (1969) and Vidal (1986). We

collected information on the tectonic fine structure of the

source area of the seismic series using two kinds of relative

location: (1) the relocations within the multiplets, to image the

orientation of the active fault segments; and (2) the relative

locations between individual multiplet clusters, to image the

relative positions of the corresponding fault segments. The source

parameters of three of the largest events (which do not belong

to any multiplet cluster) were estimated by modelling their

waveforms. We used near-field strong-motion recordings, for

which the short epicentral distances lead to well-constrained

Green’s functions.

E A R T H Q U A K E D A T A

Two moderate earthquakes occurring within 12 days marked

the beginning of a period of increased seismic activity in the

study area (longitude 3.2u–2.5uW, latitude 36.4u–37.0uN). The

earthquakes occurred on 1993 December 23 (14:22:35, mb=4.9)

and 1994 January 4 (8:03:14, mb=5.0) near the town of Adra,

separated by a distance of about 25 km. They were felt with

maximum intensity of I0=VII MSK. The earthquakes were

followed by a large number of smaller events (mbj4.1). During a

five-year period (from 1993 December to 1998 November), 721

events were recorded in the area by up to 18 fixed and portable

short-period vertical-component stations of the local seismic

network of the Instituto Andaluz de Geofısica (Fig. 1). About

half of the events followed the two major events during the winter

of 1993/94 and the spring of 1994, and further relative maxima

of the seismic activity were observed in the autumn of 1995

and the summer of 1996. Most of the events were located in the

upper crust at depths between 0 and 12 km. Only one permanent

and one portable short-period station (ADRA and PENX,

respectively) were deployed in the study area itself, enabling

recording at fairly short epicentral distances for events in the

northern and central part of the study area.

The tectonic setting of these earthquakes is at the transition

between the Betic Cordilleras and the Alboran Basin. The Betic

Cordilleras are, together with the Rif in Morocco, the western-

most part of the alpine mountain belt. The Betic Cordilleras

fold-and-thrust belt was formed both by the approximately

NW–SE-directed convergence of the African and Eurasian plates

since the Late Cretaceous and by the relative westward drift of

the Alboran domain (Betic–Rif mountains and Alboran Sea).

From the Early Miocene, extensional tectonics affected simul-

taneously the inner part of the Betic–Rif mountain chain and

crustal thinning formed the Alboran Basin (Watts et al. 1993;

Comas et al. 1997). Geodynamic models often try to explain

the coeval development of compressional and extensional

features in this area since the Miocene with some loss of litho-

sphere, for example slab break off (Blanco & Spakman 1993;

Zeck 1996), delamination of thickened lithosphere (Seber et al.

1996), or the convective removal of a thickened lithosphere

(Platt & Vissers 1989; Calvert et al. 2000). In the study area

itself, a regional ENEWSW extensional stress field is currently

dominant (Rodriguez-Fernandez & Martin-Penela 1993; Herraiz

et al. 2000).

D E T E C T I O N O F M U L T I P L E T S

The tight spatial clustering of events in the study area

corresponds to the occurrence of several multiplets. In order

to detect similar waveforms, a cross-correlation analysis was

performed (Deichmann & Garcia-Fernandez 1992; Maurer

& Deichmann 1995; Cattaneo et al. 1997). The similarity of

two waveforms (bandpass-filtered, 1–16Hz) was quantified as

the maximum value of the normalized correlation coefficient

function, calculated in moving windows around the P and S

onsets of the two recordings. On the picked phase arrival,

the left border of the zero-lag cross-correlation window was

anchored. Window lengths as well as maximal shifts between

the windows were 2 s for P and 3 s for S arrivals. Where only a

P reading was available, or the S-reading was attributed a low

-3.5 -2.5-4 -3 -2

36.5

37.5

37

AAPN

ALOJ

ATEJ

PARA

RESI

ACHM

ASMO

APHE

ASNV/FUE

CRT

ADRA

PENX

PALB

ACLR

AALM

PSAL

ACBG

ASCB

93/12/23

94/01/04

0 10 20 30 40 50km

Granada

Almería

Adra

Figure 1. Epicentres of events (circles) in the study area (box) and the distribution of the short-period stations of the Instituto Andaluz de Geofısica

(triangles) around the active zone. Axis labels are degrees latitude/longitude. Stars mark the epicentres of the two major events. Places referred to in

the text are annotated in italics.

802 D. Stich, G. Alguacil and J. Morales

# 2001 RAS, GJI 146, 801–812

quality, an appropriate zero-lag position of the S-wave cross-

correlation window was estimated from the origin time T0

[TS=VP /VS(TPxT0)+T0], using an average VP /VS ratio for

this region of 1.73 (Serrano 1999). Considering the length and

the maximal shift (3 s each) of the S-wave correlation window,

this approach is not sensitive to local anomalies of the VP/VS

ratio. After calculating the cross-correlation maxima at all the

individual stations in this way, the overall similarity of the P

and S phases of the two events was defined as a mean value of

the cross-correlations at the individual stations. Prior to forming

the mean, the lowest cross-correlations (25 per cent) were rejected

because they were considered to suffer from data insufficiencies

(see Maurer & Deichmann 1995).

In order to classify similar events into clusters, Maurer &

Deichmann’s (1995) algorithm was used. Two events are deter-

mined to belong to the same multiplet sequence (cluster) if they

exceed three threshold values applied to the P-wave similarity,

the S-wave similarity, and the normalized scalar product of the

corresponding rows of the S-wave cross-correlation matrix (the

latter is termed the cluster separation threshold). Application

of the cluster separation threshold rejects those pairs of events

that show somehow similar waveforms but do not coincide in

their behaviour towards the other events of the catalogue; the

reliability of the cluster assignment is thus increased compared

with an algorithm that evaluates P and S similarities only. the

influence and appropriate values of the individual thresholds

are discussed in detail in Maurer & Deichmann (1995). We

optimized the thresholds for this data set by trial and error,

with the aim of obtaining a large percentage of clustered events

but keeping a high waveform similarity within all the individual

clusters. Using thresholds of 0.5 for the P similarity, 0.75 for

the S similarity, and 0.5 for the cluster separation, we detected

39 multiplet clusters, each with 3–33 members (Fig. 2). They

contain 40 per cent of the initial data set. For comparison: using

a two-threshold approach (P and S, Aster & Scott 1993) and

the same trial-and-error procedure to optimize the thresholds,

we detected 23 clusters containing 31 per cent of the initial data

set.

On several occasions the cross-correlations between seismo-

grams of two different clusters are in the range of 0.6–0.75,

as compared with average values of about 0.4 for arbitrarily

selected seismograms within this data set. Such intermediate

cross-correlations, although not sufficient to classify these events

into one common cluster, again correspond to fairly similar

waveforms, and the clusters involved can be assumed to have

nearby locations and similar focal mechanisms. We will use this

information for precise relative locations between these clusters,

as described in the last section. Groups of similar clusters have

been identified by inspection of the waveforms and the cross-

correlation matrix. We found eight groups of similar clusters,

each containing 2–5 individual clusters.

The absolute locations of the clusters (Fig. 3) were calculated

as the mean of all well-constrained locations of the individual

events of the cluster, assuming that the cluster extensions are

small compared with the single-event location errors (quality

criteria: phase readings at 10 or more stations; rms error <0.25 s).

The majority of the detected multiplets occurred around the

site of the mb=5, 1994 January 4 event. All detected multiplets

are located between depths of 3 and 8 km. For some of the

clusters, however, the depth estimate is uncertain due to the large

distance to the closest recording stations (see Fig. 1).

0 100 200 300 400 500 600 700

catalogue-number of event

3

6

9

12

15

18

21

24

27

30

33

36

39

multiplet-cluster

1994 1995 1996 1997 1998

calendar date of event

3

6

9

12

15

18

21

24

27

30

33

36

39

multiplet-cluster

Figure 2. Classification of 289 events (40 per cent of the initial catalogue)

into 39 multiplet sequences with at least three members. A further 34

doublets have been detected. In the top plot, the assignment is plotted

against the order of occurrence; in the bottom, against the actual

occurrence time of the events.

0 5 10 15 20 [km]

-3.2 -3.0 -2.8 -2.6

36.4

36.6

36.8

37.0

02

01

25

11/1813

10

16/19/21/28/38

15/17/20

0705

27

26

33/34/36

23

03/06/09/14/2412

22/29

39

3704/08

35

30/31/32

Figure 3. Locations of multiplets; cluster numbers according to Fig. 2

are labelled. Axis labels are in degrees latitude/longitude. For similar,

nearby clusters (see text), one common location is given. The depths of

the multiplets vary between 3 and 8 km. Stars mark the epicentres of the

two major events (cf. Fig. 1). Most multiplets occurred around the site

of the 1994 January 4 event.

Multiplets of the Western Almerıa earthquake series 803

# 2001 RAS, GJI 146, 801–812

P R E C I S E R E L A T I V E T I M I N G O F P A N D SP H A S E S O F M U L T I P L E T S

The information on the relative location of two nearby events

comes packaged in the slight variations of their relative arrival

times among the network stations. For a precise timing, the

relative arrival times of the picked or estimated wave onsets

were adjusted by the time lags corresponding to the maxima

of the cross-correlation functions. Window lengths and maxi-

mal shifts of the cross-correlation analysis remain 2 s for P and

3 s for S arrivals (except for recordings of clusters 01 and 02

at ADRA, where the short P–S times do not permit long

windows). We overcame the resolution limit of the sampling

rate by polynomial interpolation of the cross-correlation peak,

thereby increasing the precision of relative timing by one order

of magnitude (10 msp1 ms).

Although the relative location makes use of the master-event

technique (see below), the cross-correlation analysis was per-

formed for all the pairs of events within a cluster, at all active

stations. For recordings with P readings only, the zero-lag

position of the S-wave correlation window was calculated from

the origin time and VP/VS ratio (see above). At stations with no

phase reading at all, the zero-lag positions of the windows for P

and S arrivals were obtained from the location and origin time

of the event, using ray-tracing in a layered velocity model. The

model reduces to a one-layer model for direct arrivals of the

multiplets, all of them located in the uppermost layer (0–12 km,

VP=5.9 km sx1, VS=3.4 km sx1; Serrano 1999). Actually,

the lithosphere in the area shows significant lateral variations

corresponding to the very different characteristics of the Betic

Cordilleras’ fold-and-thrust belt and the extensional basin of

the Alboran Sea; however, striking lateral variations are observed

mainly below 12 km depth. In the upper crust, seismic velocities

(Banda et al. 1992; Danobeitia et al. 1998; Carbonell et al.

1998; Serrano et al. 1998) are fairly constant over a wide area

on- and offshore, except for surface low-velocity anomalies in

Neogene deposits.

Considering the large epicentral distances of some of the

recording stations, the similarity of waveforms will frequently

be obscured by noise, and consequently the cross-correlation

might pick a maximum that does not give an accurate relative

timing of the arrivals. A criterion to test relative arrival times is

that the ‘direct’ relative timing of P and S arrivals between

master A and slave B (DtBA) should be virtually identical to the

sum of the relative timings via a third event C at the same

station (DtBC+DtCA). Forming this sum simulates the replace-

ment of the former master event A by the new master C. Hence

relative arrival times have been compared for all possible

selections of the master event, the erroneous pickings (outliers)

have been removed, and the mean and standard deviation of

the remaining values define the relative timing and its standard

error for the following inversion. For our data, this control

and adjustment of relative arrival times was essential for a

successful relocation procedure.

The precise relative timing would be pointless in the presence

of unresolved timing inaccuracies among the instruments.

Two subnetworks provided data for this research, with central

recording sites in Granada and Almerıa, respectively. Time

differences between the two independent clocks are unknown

for some epochs of synchronization malfunction and cannot

be corrected. This problem will be addressed during the inver-

sion. Within the subnetworks, signals are telemetered to the

central recording sites and all stations have a common time

base. Usually, the stations are digitized in a fixed order, and

digitization delays do not affect the relative timing. Exceptions

occurred due to changes in the pattern of portable stations, and

in consequence stations have been digitized through different

channels over different periods of time. This error, termed

the digitization skew error by Poupinet et al. (1984), can be

corrected by subtracting the digitization delay between the

involved channels for those event pairs that were affected by

a change. A correction of similar form is necessary to account

for a modification in the equipment in 1996, because the

digitization delays afterwards are considerably smaller.

R E L A T I V E L O C A T I O N O F M U L T I P L E T S

All events of a cluster were located relative to a master event.

The small cluster extensions permit a linear approximation,

based on the assumption of constant velocities in the source

volume and parallel ray paths towards a given recording station.

The aforementioned timing inaccuracies between the two sub-

networks mean we cannot assign common origin times to all

observations of an event pair. In general, the relative origin

times will differ with respect to the clocks of the two sub-

networks. Therefore the inversion has to treat relative origin

times of observations at the Almerıa and observations at

the Granada stations as two independent model parameters

(DT0,Gra, DT0,Alm). The relative timing of P and S phases

between master and slave event at a station k depends on the

model parameters (DT0,Gra, DT0,Alm and the relative location

vector d=[Dx; Dy; Dz], pointing from the master to the slave

event):

*tkP,S ¼

*T0,Gra �d . nk

VP,S, for stations digitized in Granada

*T0,Alm � d . nk

VP,S, for stations digitized in Almer��a

8>>>><>>>>:

(1)

where nk is the unit-length normal vector in the direction

of the emergent ray to the kth recording station, and VP,S are

the velocities of P,S-wave propagation at the hypocentre. The

temporal variations of the velocity field, concerning, for example,

anisotropy or VP/VS ratio, are assumed to be insignificant

(velocity variations and multiplets are treated in Poupinet et al.

1984 and Haase et al. 1995).

All available relative timings of P and S phases at all network

stations lead to a system of linear equations. The elements of

the forward matrix depend on the velocity distribution, cluster

location and station locations, and were calculated for the pre-

viously described one-layer velocity model (VP=5.9 km sx1,

VS=3.4 km sx1). The model parameters were obtained by a

least-squares inversion using singular value decomposition

(Press et al. 1989). No weighting of individual data values was

introduced into the inversion owing to the rather arbitrary

definition of data errors.

The standard errors of the model parameters are described

by the model covariance matrix. The largest model standard

errors, reaching hundreds of metres, correspond to the principal

error axes pointing in more or less a vertical direction: the depth

804 D. Stich, G. Alguacil and J. Morales

# 2001 RAS, GJI 146, 801–812

resolution is very low as a result of the lack of observations at

short epicentral distances. The horizontal errors of the relative

locations are typically a few tens of metres. Average residuals

for the relative locations are about 5 ms, approximately 50 times

less than for the absolute locations. Three examples of multi-

plet relocations are plotted in Fig. 4 and given numerically

in Table 1. The model standard errors do not include the

uncertainties of the forward matrix, introduced by errors of

the velocity model or absolute cluster location. Errors are likely

to be caused by wrong estimates of cluster depths and by dis-

regarding vertical velocity gradients. Both affect the take-off angle

of the emergent ray, further reducing the resolution of relative

depths. Consequently, relative depths were not interpreted.

S P A T I A L A N D T E M P O R A LD I S T R I B U T I O N O F T H E R E L O C A T E DM U L T I P L E T S

The epicentres of relocated multiplets are tightly grouped,

typically within a few hundred metres. Often the epicentres

produce well-defined lineaments. The distances between the epi-

centres are usually small in comparison with the fracture size of

the earthquakes; histograms of estimated fracture diameter and

closest distance are given in Fig. 5, and some numerical values

are given in Table 1. Fracture areas for several events of the

multiplet sequences have been estimated from their displace-

ment amplitude spectra (Garcıa-Garcıa 1995; Garcıa-Garcıa

Table 1. Relative locations (Dx, Dy, Dz), minor (dmin) and major (dmax) axes of the 68 per cent confidence ellipsoids and rms errors of the residuals

(rmsrel, rms) within three multiplet sequences (cf. Fig. 4). The rupture diameter (2r, Garcıa-Garcıa 1995) and the epicentre distance to the nearest

neighbour (dmin) are given for comparison, see text.

Event

NuDate Time Mag Relative location

Dx [m] Dy [m] Dz [m] dmin [m] dmax [m] rmsrel rms 2r [m] dmin [m]

Cluster 02, 11 events, absolute location 2.994uW, 36.866uN; 6.5 km depth

691 93/12/23 19:22:38 1.9 25 14 x70 31 417 0.0017 0.07 130 14

697 93/12/24 1:33:50 1.9 0 13 130 18 207 0.0019 0.12 130 13

699 93/12/24 12:42: 8 2.9 26 0 x361 16 236 0.0018 0.29 620 14

958 94/ 1/22 7:23:35 2.7 10 146 x165 39 258 0.0054 0.21 378 93

1319 94/ 3/12 7:31:31 2.8 41 56 80 7 47 0.0025 0.31 422 15

1321 94/ 3/12 8:25: 8 2.9 master event 0.40 469 13

1537 94/ 6/19 5:45:58 2.5 26 54 x33 8 52 0.0034 0.29 299 15

4335 96/ 4/17 12:26:49 2.2 154 106 x537 19 200 0.0054 0.11 203 36

4457 96/ 5/ 9 10: 5:50 2.1 286 148 x502 27 354 0.0052 0.08 176 138

5317 96/ 9/21 17:43:20 2.5 118 114 x1139 23 383 0.0059 0.22 299 36

6686 97/12/12 22:18:56 2.5 125 74 x389 19 341 0.0039 0.17 299 40

Cluster 12, 18 events, absolute location 2.848uW, 36.659uN; 5.9 km depth

770 94/ 1/ 5 1:27:51 2.0 327 x182 319 30 659 0.0030 0.20 152 7

771 94/ 1/ 5 1:42:14 2.2 493 x211 154 38 772 0.0037 0.27 203 76

784 94/ 1/ 5 11: 5: 8 1.9 339 x185 1090 35 604 0.0069 0.15 130 12

790 94/ 1/ 5 17:50:18 2.5 282 x154 516 32 931 0.0041 0.21 299 15

797 94/ 1/ 5 21:36: 0 2.3 324 x189 x10 15 306 0.0060 0.19 232 7

807 94/ 1/ 6 8:56: 8 1.9 267 x157 66 55 1338 0.0028 0.22 130 15

809 94/ 1/ 6 12:33:37 2.5 244 x78 464 15 270 0.0066 0.25 299 77

826 94/ 1/ 7 9:22:38 2.2 1 3 78 30 575 0.0027 0.28 203 3

832 94/ 1/ 7 21: 5: 3 2.1 167 x84 x94 26 746 0.0019 0.31 176 28

842 94/ 1/ 8 12:23:19 2.5 x163 45 121 14 281 0.0070 0.26 299 87

854 94/ 1/ 9 9:56:54 2.8 master event 0.23 422 3

870 94/ 1/13 1:41: 0 1.9 159 x111 457 35 715 0.0032 0.21 130 28

913 94/ 1/16 22:54:37 2.0 x404 326 x7 52 664 0.0028 0.15 152 370

964 94/ 1/22 22:18:42 2.0 62 67 x74 64 1555 0.0026 0.22 152 88

1027 94/ 1/28 1: 6:12 2.8 x79 21 x621 15 636 0.0042 0.23 422 81

1166 94/ 2/10 5: 4:34 1.7 667 x408 47 33 687 0.0029 0.21 93 120

1176 94/ 2/10 22:15:17 1.9 178 18 316 39 878 0.0068 0.24 130 102

4898 96/ 7/12 16:20:58 2.9 434 x259 90 31 736 0.0051 0.21 469 76

Cluster 22, 9 events, absolute location x2.851uW, 36.670uN; 4.8 km depth

953 94/ 1/21 12:58:18 2.3 66 x17 102 16 271 0.0026 0.26 232 13

962 94/ 1/22 18:45:49 1.9 73 x28 748 40 831 0.0027 0.31 130 13

963 94/ 1/22 19:29:48 2.5 121 x41 203 8 228 0.0027 0.23 299 38

967 94/ 1/23 14:20:26 2.7 master event 0.25 378 41

977 94/ 1/24 12:24: 5 3.0 x81 12 18 8 209 0.0037 0.24 440 68

987 94/ 1/24 20:33:22 1.6 35 x23 x294 13 344 0.0004 0.15 77 31

1001 94/ 1/25 17:40:27 3.0 70 29 143 14 320 0.0073 0.19 560 46

1015 94/ 1/26 18:36:19 3.2 x111 74 92 10 240 0.0037 0.22 633 68

1040 94/ 1/29 14:58:14 3.2 134 x77 177 14 358 0.0036 0.23 440 38

Multiplets of the Western Almerıa earthquake series 805

# 2001 RAS, GJI 146, 801–812

et al. 1996), using the circular source model of Brune (1970) to

relate the fracture size to the corner frequency of the spectra.

An empirical scaling law between fracture radius and magni-

tude (Garcıa-Garcıa 1995) permits the estimation of fracture

radii for the other events in the study area:

logmb ¼ ð0:33+0:11Þ log r½km� þ ð0:67+0:06Þ : (2)

On the assumption that the vertical cluster extensions do

not exceed some 100 m, this relation indicates that repeated

(typically 3- to 10-fold) rupture of the same source is charac-

teristic of the multiplet sequences. Repeated rupture requires a

short-term temporal variability of shear stresses and/or frictional

resistance along the faults (see, for example, Deichmann &

Garcia-Fernandez 1992). The vast majority of the detected multi-

plets contain at least one event, usually several, with estimated

fracture diameter clearly exceeding the extension of the whole

epicentre accumulation (see Table 1 and Figs 9 and 10 below).

Planes have been fitted to the hypocentre distributions of

each cluster to reveal the orientation of the active fault seg-

ments. All these planes dip nearly vertically, an artefact caused

by the low depth resolution and the large vertical scatter of

the relocated multiplets. Consequently, computed strike values

represent apparent (2-D) strikes rather than actual strikes. A

pronounced horizontal elongation of the epicentre distribution,

however, suggests that the apparent strike represents the actual

strike well, and events occurred at similar depths and/or on a

steep dipping fault plane.

The multiplet strike values with standard deviations (estimated

from random dislocations of the relocated hypocentres) less then

15u show two dominant directions: N120u–130uE and N60u–70uE(Fig. 6). Both directions are consistent with the strike of major

Neogene fault systems in the study area (Rodriguez-Fernandez

& Martin-Penela 1993). Most of the multiplets represent the

Figure 4. Relative locations within three multiplet sequences (horizontal planes of the 68 per cent confidence ellipsoids). Catalogue numbers

according to Table 1 are labelled. The master-event location in this and subsequent similar figures is at coordinate (0,0). The selected multiplets show

the two dominant strike directions of N60u–70uE and N120u–130uE (see text). Most multiplet clusters have an extension of a few hundreds of metres,

like clusters 2 and 22.

0 120 240 360 480 600 720 840 960

distance (black) and diameter (grey) [m]

0

25

50

75

100

events

Figure 5. Histograms of the fracture diameters of the multiplets

(according to eq. 2, grey) and the distance between epicentres from the

nearest neighbour within the sequence (black). Average fracture diameters

are a factor of about 5 larger than the distances between events; 74 per

cent of the event distances, but only 4 per cent of the fracture diameters,

are below 80 m.

806 D. Stich, G. Alguacil and J. Morales

# 2001 RAS, GJI 146, 801–812

N120u–130uE direction, corresponding to a fault system with

important recent displacement in the ENE–WSW extensional

stress field. The N60u–70uE faults were formed by a Pliocene

stress field and have an unfavourable orientation to the current

regional field. The diffuse distribution of seismicity in the central

part of the study area suggests a volume of fractured material,

containing parallel branches of the N120u–130uE fault system,

rather than just one single fault at the site of the second major

event. We will confirm this suspicion later when treating the

relative location between clusters in this zone.

Multiplet sequences may continue over a long period of

time, like clusters 1 and 2 (the latter over almost 4 years), or

may contain a short burst of activity only, like cluster 30

(33 events over 11 days) or cluster 38 (11 events over 4 days).

Any interpretation of temporal characteristics or chronological

order within multiplet sequences is intrinsically limited, because

probably most of the detected clusters do not represent com-

plete sequences. (There are at least two reasons for this: the

catalogue is not complete down to small magnitudes, and the

multiplet detection procedure might fail for noisy recordings or

an event with just a slightly different mechanism.) Nevertheless,

we report some observations.

(1) The interevent times of repeated rupture within the multi-

plet sequences vary greatly between minutes and years, and one

might expect some scaling between event size and interevent

time due to both a continuous accumulation of shear stress

and fault healing processes (see Marone et al. 1995). However,

there seems to be no relation between magnitude and interevent

time.

(2) Magnitudes showed no chronological characteristics

over a sequence; that is, the largest event may occur at the

beginning, the end, or somewhere in the middle of the multiplet

sequence.

(3) In general, no lateral migration of the epicentres over

a multiplet sequence occurred, the only exception might be

cluster 2 (Fig. 4), where the later events tend to be situated

farther to the northeast. Sometimes, the last events of the clusters

tend to be farther off the cluster midpoint, compared with the

initial events.

M O D E L L I N G O F N E A R - F I E L D S T R O N G -M O T I O N R E C O R D I N G S A T A S I N G L ES T A T I O N

For the two principal earthquakes of the series, estimations

of source parameters are available from two previous studies,

one evaluating the first-motion polarities of P waves (Rueda

et al. 1996), and one using waveform modelling of broad-band

recordings at regional distances (>300 km, Thio et al. 1999).

A Harvard centroid moment tensor (CMT) solution exists for

the first event (Dziewonski et al. 1994). At least for the 1994

January 4 event, available data are not consistent (Table 2),

and we decided to estimate source parameters independently by

analysing waveforms of strong-motion recordings at station

ADRA at short (<20 km) epicentral distances. The modelling

of near-source seismograms benefits from a well-constrained

velocity model and hence well-constrained Green’s functions.

Source-parameter estimation from a single, near-field station is

treated in, for example, Kanamori et al. (1990) and Singh et al.

(1997).

The two major events generated near-source acceleration

traces with good signal-to-noise ratio, and one major aftershock

(1993 December 23, 18:00:08, mb=4.0) was also evaluated.

The acceleration traces were rotated to separate radial and

transverse components of the horizontal seismograms, and

0 5 10 15 20 km

-3.2 -3.0 -2.8 -2.6

36.4

36.6

36.8

37.0

Figure 6. Comparison of the apparent strikes of the multiplet

relocations (grey lines) and the strike of the fault planes of the two

major events (see Table 3) with positions and directions of Neogene

faults in the study area (black lines). Faults redrawn from Rodriguez-

Fernandez & Martin-Penela (1993). Axis labels are degrees latitude/

longitude.

Table 2. Source parameters of the two major events of the series according to previous studies (see text).

1993 December 23 Plane A Plane B Seismic Moment

Harvard CMT solution 335 43 x88 152 47 x92 8.5r1023 dyn.cm, MW=5.2

Rueda et al. (1996) 300 70 x130 188 44 x29

Thio et al. (1999) 326 38 x94 151 52 x87 MW=5.1

1994 January 4 Plane A Plane B Seismic Moment

Rueda et al. (1996) 170 65 x31 274 63 x152

Thio et al. (1999) 220 25 90 40 65 90 MW=4.7

Multiplets of the Western Almerıa earthquake series 807

# 2001 RAS, GJI 146, 801–812

double-integrated to obtain displacement. Green’s functions

for the layered earth model were computed using Bouchon’s

(1981) algorithm; synthetic seismograms were generated for

a set of focal mechanisms and compared with the observed

displacement. A surface low-velocity layer (thickness 1.5 km,

VP=4.0 km sx1, VS=2.3 km sx1) was added to the previously

described velocity model to account for the Neogene deposits in

the vicinity of the station.

The displacement records (Fig. 7) of the two major earth-

quakes appear rather complex, indicating several subevents,

while the smaller event shows a single pulse. For the closer

events (those on 1993 December 23), the near-field displace-

ment is clearly visible between the P and S arrivals. Most of the

main features of the displacement waveforms can be matched

with the source parameters in Table 3. The source radii were

estimated for a circular fault after Boatwright (1980), and the

static stress drops after Keilis-Borok (1959).

For the first major event, showing three distinct pulses, we

obtained a total moment release of 2.0r1023dyn cm (MW=4.8),

a total duration of 0.75 s, and a focal mechanism similar to

the result of Rueda et al. (1996): a steep plane striking 300uwith a normal and a right-lateral component of slip. Differences

in the ratio of SV and SH amplitudes between the two initial

pulses and the third pulse were matched by a minor rotation

of the slip vector. The mechanisms agree with the regional stress

field (ENE–WSW extension, Rodriguez-Fernandez & Martin-

Penela 1993). For the mb=4 aftershock, at the same location,

a similar mechanism was modelled, the seismic moment was

3.0r1022 dyn cm (MW=3.6), and the duration 0.24 s. These focal

mechanisms are different from those obtained by Dziewonski et al.

(1994) or Thio et al. (1999), both of which indicate smaller dip,

pure normal displacement, and a strike direction of about 335u.The total moment release of the 1994 January 4 event was

2.3r1023 dyn cm (MW=4.9). The displacement records show

two distinct pulses, with the shape of the first one fitted well by

three overlapping subevents with identical focal mechanism.

This mechanism is similar to the solutions for the other events:

a steep plane striking 310u with a normal and a right-lateral

component of slip. The solution is different from those of

Rueda et al. (1996) and Thio et al. (1999), but consistent with

the strike directions of most multiplet clusters around the

epicentre. The second pulse shows very different ratios between

SH, SV and P amplitudes compared to the initial pulse, and the

displacement cannot be matched with a mechanism similar to

the previous ones. A rough fit was obtained for a 240u-striking

fault plane, consistent with the other dominant strike direction

Table 3. Source parameters of the two major events and one aftershock of the series, leading to the fit of the near-source waveforms given in Fig. 7.

The subevents of the two major events are given in chronological order

1993 December 23 Plane A Plane B MO [dyn.cm] r [km] Ds [bar]

subevent 1 300 80 x120 193 32 x19 1.0r1023 1.5 12.2

subevent 2 300 80 x120 193 32 x19 1.5 12.2

subevent 3 300 80 x145 203 56 x12 1.0r1023 2.0 5.5

Dec 23 aftershock Plane A Plane B MO [dyn.cm] r [km] Ds [bar]

300 55 x120 165 45 x55 3.0r1022 1.0 1.2

1994 January 4 Plane A Plane B MO [dyn.cm] r [km] Ds [bar]

subevent 1 310 70 x130 198 44 x29 2.1r1022 1.0 9.2

subevent 2 310 70 x130 198 44 x29 4.2r1022 0.5 147.0

subevent 3 310 70 x130 198 44 x29 7.7r1022 1.7 6.8

2nd source 240 70 60 120 36 144 9.0r1022 0.8 76.9

-0.035

-0.030

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

0.005

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

-0.40

-0.30

-0.20

-0.10

0.00

0.10

[cm]

[cm]

[cm]1s

1s

1s

December 23, 1993

January 4, 1994

December 23, 1993

M =4.8

m =4.9

w

b

M =4.9

m =5.0

w

b

M =3.6

m =4.0

w

b

Figure 7. Observed (solid) and modelled (dashed) displacement wave-

forms of three of the largest events of the series (mb=4.9, 4.0 and 5.0).

Traces from top to bottom: transverse, radial and vertical components

of displacement. Synthetics were calculated for the source parameters

given in Table 3. Double-couple fault-plane solutions are plotted in equal-

area projection. The two focal mechanisms for each of the major events

correspond to the different mechanisms of subevents (in chronological

order from left to right, cf. Table 3).

808 D. Stich, G. Alguacil and J. Morales

# 2001 RAS, GJI 146, 801–812

of multiplet clusters in the area. This solution gives a reverse

component of fault slip and does not agree with the regional

stress field (Rodriguez-Fernandez & Martin-Penela 1993; Herraiz

et al. 2000). It indicates an abrupt change of the local stresses

for the first and second sources of this earthquake. Pure reverse

faulting for this event was suggested by Thio et al. (1999). A

plausible explanation for the sudden occurrence of a compressive

local stress field will be given in the next section.

Figure 8. Relative locations of multiplets for the clusters 30/31/32 (labelled as A, B, C for clarity). The individual strike directions of the clusters are

given as dotted lines. The three clusters, containing all the detected multiplet activity in autumn 95, broadly overlap (see text).

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800-1000

-800

-600

-400

-200

0

200

A

relative location - east [m]

rela

tive

location

-nort

h[m

]

AA A

AA

AA

A

BB

BB

B B

BB

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800-1000

-800

-600

-400

-200

0

200

relative location - east [m]

rela

tive

loca

tio

n-

no

rth

[m]

Figure 9. Relative locations of multiplets of the clusters 22/29 (labelled as A, B; upper map) and 33/34/36 (labelled as A, B, C; lower map). The strike

directions of the two or three, respectively, accumulations are given as dotted lines and were obtained by fitting planes to the individual accumulations.

The estimated fracture diameters of the largest events (according to an empirical scaling law, see text) of each accumulation are drawn as solid lines in

the direction of the average strike of the clusters (N117uE, N119uE); they approximate the length of the active fault segment. The fault segments almost

touch but do not overlap, and the accumulations represent the activity of adjacent segments along the fault system.

Multiplets of the Western Almerıa earthquake series 809

# 2001 RAS, GJI 146, 801–812

P R E C I S E R E L A T I V E L O C A T I O N S O FN E A R B Y C L U S T E R S A N D T H E S M A L L -S C A L E H E T E R O G E N E I T Y O F T H ES O U R C E A R E A

The very similar events classified into one cluster usually

represent repeated rupture of the same source, and their spatial

distribution reveals the orientation of one fault segment. We

expected to obtain more comprehensive information on the fine

structure of the source area from the precise relative locations of

different multiplets, with events typically belonging to different

fault segments. Therefore we used the previously detected clusters

with intermediate intercluster cross-correlations. Their waveform

similarity still permits the use of cross-correlation techniques

for relative timing.

However, these lower waveform similarities do not allow

a reliable relative timing at many stations, and an attempt to

relocate all events of the similar clusters relative to one master

event did not lead to very precise results. Instead, only certain

selected event pairs with particularly high similarity and good

data quality were used to relocate two clusters, thereby obtaining

a shift vector between the master events of the two clusters. The

previously relocated multiplets within the clusters were left

in their places. Usually the master-event shift vectors showed

little scatter when derived from different event pairs (standard

deviations of tens of metres in horizontal directions), and again

the relative epicentres can be determined quite precisely.

We observed three different spatial patterns of the seismicity

of similar clusters and present them with one or two examples

each. The first pattern, for example represented by the clusters

30/31/32 (Fig. 8), shows broad overlapping of the epicentral

distributions of the individual multiplets. The differences in

waveform between the clusters were caused by different focal

depths (in particular the tendency of clusters 30 and 31 to be

slightly shifted perpendicular to the overall strike direction

might indicate different depths on a dipping fault) or a slight

variation of the mechanism.

Among other similar clusters, no spatial overlapping is

observed. Events are accumulated within each multiplet cluster

and separated from other clusters. The relative locations between

clusters are often nearly in-line with the individual strikes

(Fig. 9). These clusters should belong to adjacent segments along

-800 -600 -400 -200 0 200 400 600 800 1000 1200 1400 1600

-1000

-800

-600

-400

-200

0

200

400

A

relative location - east [m]

rela

tive

location

-nort

h[m

]

A

A

B

BBB

B

CCCCC

C

CC

DD

DD

-1400 -1200 -1000 -800 -600 -400 -200 0 200 400 600 800 1000

-200

0

200

400

600

800

1000

relative location - east [m]

rela

tive

location

-nort

h[m

]

Figure 10. Relative locations of multiplets of the clusters 3/6/9/14 (labelled as A, B, C, D; upper map) and 16/19/21/28/38 (labelled as A, B, C, D, E;

lower map). The strike directions were obtained by fitting planes to the individual accumulations and are given as dotted lines if their standard

deviation is less than 15u (all except clusters 6 and 16). The estimated fracture diameters of the largest event of each accumulation are drawn as solid

lines in the direction of the average strike of the clusters (N70uE, N130uE). The clusters reveal the simultaneous activity of (sub) parallel branches of a

fault system. The two cluster groups have nearly identical locations, and the superposition of the N70uE and N130uE fault systems indicates

fragmentation of the crust into small blocks (see text).

810 D. Stich, G. Alguacil and J. Morales

# 2001 RAS, GJI 146, 801–812

a seismic fault system. Using eq. (2) for the estimation of the

fracture diameters of the largest events of each accumulation

(to approximate the length of the active fault segment), it turns

out that the distances of the accumulations are determined

quite exactly by these fracture diameters. This means that the

fracture areas of adjacent clusters approximately touch each

other.

The third pattern of seismicity shows separated clusters with

relative locations obviously not in-line with the individual strikes,

thereby revealing simultaneous activity on (sub) parallel faults

(Fig. 10). We found an example for the N70uE and the N130uEdirections. Since the fault-plane dip and relative depths of the

events are not resolved, only a rough estimation of the distances

between the parallel faults is possible (500 m and 1300 m,

respectively, for the N70uE faults, and 700 m for the N130uEfaults). Besides parallel faults, another example of adjacent

fault segments can be seen in the figure. The relative locations

of the N70uE structures follow an N120u–130uE lineament.

The absolute locations of the two cluster-groups with (sub)

parallel faults in Fig. 10 are almost identical (compare Fig. 3),

and the superposition of the two different (N70uE and N130uE)

fault systems indicates fragmentation of the crust into small

(approximately 1 km) blocks near the site of the major 1994

January 4 event. This scale of fragmentation coincides with

typical extensions of the multiplet fracture areas. This suggests

that the parallel branches of the N70uE and N130uE fault

systems delimit the individual fault segments along each

other. The small-scale fragmentation also explains the complex

displacement records of the two major events; they have

affected several fault segments. The estimated fracture size of

the individual subevents (Table 3) coincides with the scale of

fragmentation.

The small-scale fragmentation is an appropriate scenario for

a complex redistribution of local shear stresses after each event

and will probably cause a very heterogeneous and temporally

variable stress field in the area. This might be the driving

mechanism of repeated rupture within the multiplet sequences.

A heterogeneous stress field in the upper crust was deduced

previously in two other study areas within the Alboran domain,

based on the observations that the small to moderate earth-

quakes do not necessarily reflect the mean state of stress of the

entire region. (Galindo-Zaldıvar et al. 1999; Medina 1995). In

our study, the heterogeneity of the local stress field is verified

by the reactivation of the Pliocene N60u–70uE fault system by

several multiplet sequences, in disagreement with the present-

day regional ENE–WSW extension in the area (Rodriguez-

Fernandez & Martin-Penela 1993; Herraiz et al. 2000). In the

present-day regional stress field, the Pliocene faults may act as

oversteps between different branches or en-echelon structures of

the N120ux130uE fault system and release stresses introduced

by dislocations along individual segments of the N120u–130uEfaults. The displacement along both fault systems will result in

rotation and tilting of the small tectonic blocks.

A C K N O W L E D G M E N T S

We are very grateful to Hansruedi Maurer from ETH Zurich

for his multiplet cluster detection software. The research

was supported by the European Commission (Marie-Curie

research training contract ERB4001GT980288) and by the

CICYT-Project AMB99-0795-C02-01.

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