LITHOSPHERIC STRESS AS A CONTROL OVER RELATIONS BETWEEN FAULT PARAMETERS AND EARTHQUAKE MAGNITUDES

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2 Russian Geology Geologiya i Geofizika Vol. 42, No 9, pp , 2001 UDC LITHOSPHERIC STRESS AS A CONTROL OVER RELATIONS BETWEEN FAULT PARAMETERS AND EARTHQUAKE MAGNITUDES O.V. Lunina Institute of the Earth's Crust, Siberian Branch of the Russian Academy of Sciences, 128, ul. Lermontova, Irkutsk, , Russia Relations between the length of seismogenic rupture, amount of slip, and magnitude of earthquakes are investigated as a function of slip mechanism (normal, reverse, or strike slip) formed in different stress fields. The parameters of seismogenic strike-slip faults are closely correlated with earthquake magnitudes in any stress field. The relationships for normal and reverse faults are the most regular if they evolve under extension and compression, correspondingly, or in transtension and transpression fields. Compression is the most complicated environment for faulting of any kinematics. The results of the study can be used in paleoseismicity reconstructions. Seismogenic rupture, fault parameters, stress field, slip type. INTRODUCTION Correlation among length of seismogenic rupture, fault displacement, and earthquake magnitude is a topical problem pertinent to prediction of the magnitude of pending earthquakes and the dimensions of expected surface breakage. The relations between earthquake magnitude and the parameters of the causative fault have been largely investigated but without a special focus on their dependence on regional lithospheric stress, an important agent in geodynamic processes. In this paper the problem is revisited on the basis of new stress maps [1, 2]. The aim of the study was to analyze relations among fault parameters (rupture length and displacement) and earthquake magnitudes in terms of the geometry of slip type and the regional stress field. THE STATE OF THE ART Quantitative relationships between earthquake magnitudes and the parameters of the causative faults have received much recent attention. Since the studies by Tocher [3], relations among earthquake magnitude (M), rupture length (L), fault displacement (D), and between M and LD have been obtained for a number of active seismic regions and worldwide [4-13], and L and D were shown to increase proportionally to M. 1389

3 Many workers investigated these relations in terms of the influence of various factors, especially slip geometry [4, 12-15], and found the amount of co-seismic displacement to be different in strike-slip, normal, and reverse faults. The L/D/M relations were studied for earthquakes within plates and on plate boundaries [12, 13, 16], in the Alpean and Pacific seismic belts, on reactivated platforms [8, 11], in stable continental terrains [17], and for separate geographic regions [10, 18, 19]. Slemmons et al. [20] were the first to invoke stresses and to analyze different data sets for seismogenic faults formed under extension and under compression. They showed that D functions depend on stress type but L functions do not. Wells and Coppersmith [12], however, did not observe significant difference in regression coefficients for any relationships. Thus no unanimity was achieved about the effect of stress, possibly, because the kinematic classification of faults was ignored. A stress province may include faults of different geometries, and the parameters of faults evolving under different stress fields appear to be dissimilar. This dissimilarity may be expressed in relationships between fault parameters and earthquake magnitudes and influence the estimates of the latter. INITIAL DATA AND THEIR RELATION TO UPPER LITHOSPHERIC STRESS Initial data have been catalogued based on the published parameters of earthquakes and their causative faults [9, 12, 14, 21] and on studies of faults related to strong earthquakes [22, 23, etc.]. The catalogue includes 323 events that caused

4 surface rupture, with their origin times, locations, epicenter coordinates, regional stress, surface-wave magnitudes (M s ), slip geometries, rupture lengths (L), and maximum fault displacement (D), including horizontal (D h ), vertical (D v ), and total (D t ) offset calculated as a vector sum of slip components measured at the same site (see a fragment of the catalog in Table 1). 268 of 323 events have instrumental magnitudes. In case of discrepancy in fault parameters published in [9, 12, 14, 21], we referred to descriptions of the respective seismogenic rupture and put down the inferred data to the catalog with reference. The locations of earthquakes and their magnitudes were verified according to the Bulletin of the Seismological Society of America and the Harvard Catalog. Distribution of Seismic Events with Known Rupture Parameters in Different Stress Regions Table 2. Stress type Compre Transpressiotension Shear Trans- Extension Neutral stress ssion Number of events The selected earthquakes were spatially grouped according to types of regional stress (Table 2) on the basis of the map of upper lithospheric stress [2] showing its six main types: compression, extension, shear, transpression, transtension, and tectonically neutral stress. The latter is typical of platforms where stresses are much lower than in active seismic regions. The greatest number of earthquakes we studied occurs in zones of compression and shear. 14 events could not be located for the lack of epicenter coordinates and thus could not be assigned to a stress region; 55 events were excluded, as they did not have instrumental magnitudes. METHODS The initial data (fault parameters and earthquake magnitudes) were processed using least square regression analysis by the Statistica 5.0 software. As already mentioned, faults were classified on the basis of slip geometry (strike-slip, normal, and reverse faults) and location of earthquakes with respect to stress fields (compression, transpression, shear, extension, transtension). Relationships between M and L, M and D, L and D were obtained separately for faults of different geometries formed in different stresses, and with regard to slip geometry only. Fault displacement (D) is meant as maximum total displacement; L and D are taken as logarithms. RESULTS Quantitative relationships between the parameters of seismic faults of different geometries and earthquake magnitudes were obtained for the first time for separate samples of stress data (shear, extension, compression, transpression, and transtension). Strike-slip faults are most frequent seismogenic faults and most numerous in the database. The obtained statistical relationships of M and L, M and D, and L and D differ in different stress regions 1391

5 Regression Equations for Strike-slip Faults in Different Stress Regions Table 3. No Stress type Equation σ а σ b S r n F p < 1 Shear lgl = -3,37 + 0,70 M 0,43 0,06 0,30 0, , lgd = -6,13 + 0,88 M 0,59 0,08 0,38 0, , Extension lgl = -1,88 + 0,48 M 1,05 0,15 0,17 0,84 6 9,69 3, lgd = -9,43 + 1,37 M 1,75 0,26 0,29 0, ,67 3, Compression lgl = -1,35 + 0,37 M 0,68 0,10 0,33 0, ,36 1, lgd = -3,86 + 0,59 M 0,49 0,07 0,34 0, , Transtension lgl = -3,75 + 0,76 M 0,63 0,09 0,21 0, ,59 1, lgd = -6,23 + 0,90 M 1,62 0,24 0,51 0, ,34 1, Transpression lgl = -2,43 + 0,58 M 0,40 0,06 0,26 0, , lgd = -5,34 + 0,77 M 0,65 0,09 0,35 0, ,60 8, No division lgl = -1,95 + 0,49 M 0,28 0,04 0,37 0, , lgd = -4,86 + 0,71 M 0,32 0,05 0,41 0, , Note. L is rupture length, km; D is maximum fault displacement, m; M is earthquake magnitude; σ а and σ b are standard errors in equations of the type of y = a + bx; S is standard error in argument; r is correlation coefficient; n is number of correlated pairs; F is Fisher criterion; p is significance. (Table 3, Fig. 1). The difference is better evident for faults formed in alternative settings (compression extension shear), and the relations for regions of shear, transpression, and transtension stresses are more similar. a b Fig. 1. Fault parameters plotted against earthquake magnitudes (M) for strike-slip faults formed in different stress regions. Regression lines for different stress regions: 1- shear; 2 extension; 3 compression; 4 transtension; 5 transpression. 1392

6 Strike-slip faults in shear, transpression, and transtension fields show a more rapid L increase with M than those formed under pure compression or extension (Fig. 1, a). The longest strike-slip faults occur in regions of shear stress. The M-dependent D increase is more rapid in zones of extension and the slowest in shear and compression regions (Fig. 1, b). The L-dependent D increase is also more rapid in extension regions. The behavior of D and L is concordant in shear and compression settings, but the D values are dissimilar at the same L because of different free terms in regression equations: At L = 50 km, displacements are 1.6 m on strike-slip faults formed under shear, and 5.6 and 2.7 m on faults in compression and extension regions, respectively. Thus the values of L and D differ in different stress fields, which influences the related estimates of earthquake magnitudes and fault parameters. For comparison we calculated magnitudes from the functions found for strike-slip faults at different L and D (Table 4) and obtained a difference of or more in many magnitudes, which is comparable with errors in paleoseismicity reconstructions [4]. The rightmost column of Table 4 gives averaged magnitudes from equations for all strike-slip faults irrespective of stress division, and it is obvious that more accurate magnitude estimates and higher correlation coefficients are those based on both fault geometry and stress type. Earthquake Magnitudes Calculated from Equations for Strike-slip Faults Table 4. Magnitudes for strike-slip faults in different stress regions Magnitudes for all strike-slip faults L, km Shear Extension Compression Transtension Transpression 1 5,34 4,73 5,59 5,07 4,70 5, ,40 6,20 6,72 6,27 6,10 6, ,15 7,23 7,51 7,11 7,08 7, ,47 7,67 7,85 7,47 7,50 7, ,65 7,93 8,05 7,68 7,75 7, ,79 8,11 8,2 7,83 7,92 7,84 D, m 0,1 6,06 6,25 5,29 6,01 5,90 5,81 0,5 6,67 6,68 6,18 6,58 6,61 6,52 1 6,93 6,87 6,56 6,83 6,92 6,82 2,5 7,28 7,11 7,07 7,16 7,32 7,22 5 7,54 7,30 7,45 7,40 7,62 7,53 7,5 7,70 7,41 7,67 7,55 7,80 7, ,80 7,49 7,83 7,65 7,93 7,83 The dissimilarity of the obtained functions for different stress regions is easily explainable. Regions of shear stress have the most favorable conditions for strike-slip faulting, and the M-dependent L increase is more rapid and the range of rupture lengths is broader in strike-slip faults formed under shear, transpression, and transtension than in other environments. At the same time, strike-slip faults in regions of pure compression or extension are less important than faults of other geometries. Modeling of strike-slip faults [24] also revealed specific features of their inner structure in compression and extension fields. 1393

7 Thus the relations among parameters of strike-slip faults in compression, extension, and shear regions are strongly different, and the similarity of relations for shear, transpression, and transtension regions indicates that the component of compression or extension in the latter is of minor importance in strike-slip faulting. Normal faults are less frequent seismic faults. Reliable relationships of their parameters and earthquake magnitudes were obtained only for regions of extension and transtension (Table 5), where the correlation coefficients are fairly high (r = ) except for L = f(m) in normal faults formed under transtension (r = 0.59). Regression Equations for Normal Faults Evolved in different Stress Regions Table 5. No Stress type Equation σ а σ b S r n F p < 1 Extension lgl = -1,71 + 0,46 M 0,41 0,06 0,18 0, ,59 3, lgd = -4,92 + 0,73 M 0,91 0,14 0,52 0, , Transtension lgl = -2,39 + 0,53 M 1,06 0,16 0,46 0, ,33 2, lgd = -6,38 + 0,93 M 1,03 0,15 0,42 0, , Compression lgl = 0,65 + 0,05 M 1,20 0,18 0,24 0,17 5 0,09 7, No division lgl = -1,52 + 0,41 M 0,59 0,09 0,40 0, ,65 2, lgd = -5,15 + 0,76 M 0,59 0,09 0,43 0, , Note: Same as in table 3. The D = f(m) plot (Fig. 2, a) is steeper for faults evolved under transtension than under pure extension, but in the latter D increases much more rapidly with L (Fig. 2, b). a b Fig. 2. Fault parameters plotted against earthquake magnitudes (M) for normal faults formed in different stress regions. Regression lines for different stress regions: 1 extension; 2 transtension. 1394

8 Normal faults in compression regions are represented by only five M L and M D pairs on which no statistically significant relationships could be obtained. Thus regional stresses influence the relations among L and D and earthquake magnitudes in normal faults as well, and the shear component plays a significant role in normal faulting in transtension regions. Reverse and thrust faults mostly develop in compression or transpression stress fields and are slightly less frequent in shear regions. Recent seismogenic ruptures of thrust geometry are rarely found in extension and transtension regions. The highest L = f(m) and D = f (M) correlation coefficients are observed in transpression regions (r = and r = 0.89, respectively, Table 6). Displacements on reverse faults evolved in shear regions show poor correlation with M and L (r = 0.22 and 0.28, respectively). Regression Equations for Reverse Faults Evolved in different Stress Regions Table 6. No Stress type Equation σ а σ b S r n F p < 1 Compression lgl = -1,77 + 0,46 M 0,35 0,05 0,22 0, , lgd = -2,12 + 0,35 M 0,56 0,08 0,32 0, ,67 2, Transpression lgl = -3,13 + 0,65 M 0,65 0,10 0,27 0, ,60 1, lgd = -5,40 + 0,79 M 0,80 0,11 0,38 0, ,54 1, Shear lgl = -2,20 + 0,50 M 1,11 0,17 0,33 0, ,30 1, lgd = -1,11 + 0,15 M 1,68 0,25 0,45 0,22 9 0,37 5, No division lgl = -2,07 + 0,50 M 0,33 0,05 0,25 0, , lgd = -3,31 + 0,50 M 0,54 0,08 0,41 0, ,75 5, Note: Same as in table 3. a b Fig. 3. Fault parameters plotted against earthquake magnitudes (M) for reverse faults formed in different stress regions. Regression lines for different stress regions: 1 compression; 2 transpression; 3 shear. 1395

9 The L = f (M) and D = f (M) plots for reverse faults evolved under different stresses (Fig. 3) show that those in transpression regions have smaller earthquake magnitudes corresponding to same L and D and a more rapid L-dependent D increase relative to other stress environments. Therefore, transpression stress fields provide the most favorable geodynamic conditions for reverse and thrust faulting. The type of stress is especially significant in D functions. DISCUSSION The parameters of strike-slip faults are best correlated with earthquake magnitudes (r = ) except for L = f(m) in regions of compression (r = 0.65) in which other correlation coefficients are also generally lower. Note that faults evolved under compression show slower L and D increase with M and D increase with L. This regularity was earlier recognized for reverse faults [4] and is attributed to the motions of fault walls against gravity. Slow M-dependent L and D increase is also typical of strike-slip faults formed under compression; M functions for normal faults remain unclear for the shortage of data. Therefore, seismogenic faulting of different geometries in regions of compression occurs in the most complicated conditions, as it is the most energy consuming and requires longer stress accumulation [25]. The relationships based on two factors yield more accurate estimates of the studied parameters and show higher correlation coefficients than those based uniquely on slip kinematics. Difference in regression equations indicates dissimilar mechanisms of seismiogenic faulting in different stress regions. Reverse faults in shear fields and normal faults in compression fields show poorly correlated parameters (No. 6 in Table 6 and No. 5 in Table 5), which may worsen the reliability of functions for faults classified on the basis of slip type only. Other equations are correlated at p much below 1 %, except for few equations where it is within % (Nos. 3 and 8 in Table 3 and No. 5 in Table 6). Strike-slip faults form in any tectonic environment and the relations of their parameters and earthquake magnitudes strongly depend on regional stress type. It was well noted [4] that strike-slip faulting is a pure image of seismotectonic process. Following Ruzhich [27] we believe that magnitude is rather a relative estimate of tectonic energy spent on seismotectonic failure, i.e., seismic energy is only a part of tectonic energy, although M is traditionally estimated as equivalent of mean seismic energy released in an earthquake source per unit time [26]. Different relations of parameters of strikeslip faults and earthquake magnitudes in different stress regions are accounted for by controlling factors of faulting. In shear stress field these are major long ruptures in which L increases rapidly with M, and the tectonic energy must be spent uniformly on fault displacement and on rupture growth. In compression and extension regions, strike slips are subsidiary faults which emerge most often as confining features for thrust or normal faults [28, 29]. As noted above, displacement is much greater on strike-slip faults evolved in compression fields at the same rupture length but the same L increase is caused by a greater M increase. Most likely, in strike-slip faulting under compression more tectonic energy is spent on displacement than on rupture lengthening. The presence of strike-slip faults in compression regions is due to favorable conditions for horizontal strain [25]. Relative estimates of tectonic energy necessary for coseismic fault displacement can be inferred from D = f(m) plots (Fig. 1, 1396

10 b). The same increment of displacement on strike-slip faults in extension regions requires less energy than in compression fields. In this respect, strike-slip faults in shear and transpression or transtension fields have an intermediate position. These results are consistent with the known facts that faulting in collision zones consumes times more energy than in spreading zones [30]. Faults with vertical slip are less frequent. Normal faults occur mainly in extension and transtension regions, and reverse faults prevail in regions of compression and transpression. Transpression regions are especially favorable for reverse faulting, as rupture lengthening or displacement increase require less energy than in regions of pure compression. Normal faults in regions of extension, at the same M within the main range of magnitudes show greater displacements than normal faults in transpression fields. The greater the M value the greater similarity of displacements in the two stress types. Perhaps, displacement on normal faults during relatively weak earthquakes in transtension regions is impeded by shear strain, which is easily overcome in larger events. Note that the slip geometry in sources of few large earthquakes disagrees with the general regional stress field. Zoback [1] and Sherman [31] pointed to the existence of local variations in magnitude and direction of stress at different levels and hypothesized that these earthquakes reflect rather deformation induced by interaction of active faults than a response to regional stress. CONCLUSIONS 1. Regional stress field and slip geometry both are key controlling factors for relations of earthquake magnitudes with the parameters of the causative faults and should be taken into consideration in the relevant implications. 2. Strike-slip faults are universal seismic faults. Correlation of their parameters with earthquake magnitudes is good in any stress field and only changes as a function of their role in different tectonic settings. In shear, transpression, and transtension regions, seismotectonic energy is spent uniformly on rupture growth and fault displacement. In compression stress fields, a greater portion of energy is accommodated in displacement than in rupture lengthening. 3. Normal and reverse seismic faults show the best correlation between fault parameters and earthquake magnitudes in regions of extension and compression, respectively, or in transpression and transtension stress fields. Shear stress in combination with compression or extension plays a major role in the evolution of faults with vertical offset. 4. Regions of compression are the most complicated environments for faults of any geometry, which is consistent with the ideas of more energy-consuming faulting in collision zones than elsewhere. The functions found with regard to slip geometry and stress field can provide more accurate estimates of paleo-earthquake magnitudes and the parameters of their causative faults. 1397

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