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(a) Map view of normal faults. The picture was taken parallel to a bedding surface that is cut by numerous normal faults. The rock tends to part preferentially along bedding surfaces or along fault planes. The fault scarps appear as shadows.
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Recent earthquakes have shown that fault interaction can affect rupture sequences. However, few criteria are currently available to determine which fault segments are strongly interacting. Here we develop a simple, elastic-plastic model of fault interaction that can assess degrees of interaction within a population of faults using only map traces o...
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... basin (Schlische, 1993;Schlische et al., 1996). The Solite Quarry faults all dip toward the basin bounding fault. They lie at high angles to ®nely laminated bedding of siltstones, which tend to part along bedding planes. With such exposures, accurate measurements can be made of D±L pro®les of a large number of faults ( Schlische et al., 1996) (Fig. ...
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... sampled only one oset marker layer for each fault, such as in Fig. 2. Often we did not know whether this layer crossed the fault near the center or edge of an elliptical fault plane. The location of the marker layer can aect the observed D±L pro®le ( Muraoka and Kamata, 1983), depending on the shape of the overall displacement distribution. For an ellipti- cal slip distribution, such as in an elastic ...
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... displacement ®elds in the Solite Quarry faults are obviously permanent now (Fig. 2), we assumed that displacement ®elds were elastic at the time that these faults stopped growing. We previously validated this assumption by comparing observed fault displacement ®elds from the Solite Quarry population with an elastic boundary element solution (Gupta and Scholz, 1998). We found that a dislocation model within an elastic ...
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... regions around larger faults (master faults) are devoid of other faults (Fig. 12). A linear relationship between the displacement on the master fault (d ) and the perpendicular distance to the nearest fault (S ) is expressed by Ackermann and Schlische (1997) as S I 3d. Faults from the Solite Quarry do not grow into stress drop regions that are higher than 200±300 MPa. The observed shadow zone boundaries occur in ...
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... Quarry, as the characteristic Malawi pro®le is unknown. Because we cannot rule out the eect of material properties, boundary con- ditions, and growth mechanism on the displacement pro®les, only relative changes between interacting fault tips in Malawi are interpretable (Fig. 13b). We cannot determine whether the displacement anomalies are sig- Fig. 12. `Shadow zone' around a master normal fault and surround- ing smaller faults in map view (see text for de®nition). Displacement, d, is shown schematically. S is the perpendicular distance from the master fault to the nearest fault (after Ackermann and Schlische, 1997). Fig. 8, we see the overall range of possible separation± overlap ...
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... C 2 is a constant that depends on the slip distri- bution and shape of the fault plane. The depth of Solite Quarry faults, h(x ), typically varies from zero near the mode III tips to L/4 near the center of the fault plane (Fig. A2). We approximate the variable fault plane depth, h(x ), with H = h avg I L/8. We also assume the slip is uniform with depth as is equal to the surface slip, u(x ) (Fig. A1b). Because slip must actually decrease towards zero at the base of the fault (Fig. A1a), our approximation of uniform slip with depth will produce too broad a surface ...
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... of interacting faults are asymmetric with steep D ± L gradients near interacting tips. The point of maximum displacement in a displacement±length pro®le, d max , is shifted toward the interacting tip. Elastic boundary element modeling results con®rmed that d max is closer to interacting tips and that the average displacement gradient is steeper in the interacting region (Willemse et al., 1996; Willemse, 1997). While the observations of displacement pro®les generally agree with boundary element models of fault interaction, presently no quanti- tative criteria exist to evaluate degrees of fault interaction based on variations in displacement pro®les. Separation±overlap ratios (Fig. 1) provide a crude measure of fault interaction. Aydin and Schultz (1990) measured separation±overlap ratios but did not relate these ratios to their model. Their model shows that underlapping fault tips are favored to propagate towards each other, while overlapping tips are retarded. Huggins et al. (1996) also measured separation±overlap ratios. They acknowledged that separation±overlap ratios provide little information about the interaction state of the overlap zone. Cartwright and Mans®eld (1998) measured displacement gradients and suggested that the wide range of gradients in normal faults occur because of fault interaction. Later we show that increasing displacement gradients and anomalous displacement accumulation occur with increasing fault interaction. Thus rather than separation±overlap ratios, displacement anomalies can be used as a proxy for interaction, but, as we shall see, the two are related. To quantify displacement anomalies near interacting fault tips, we compare D ± L pro®les of the `isolated' faults in a population with the remaining interacting population. Using the Dugdale model (Cowie and Scholz, 1992a), and knowledge of stress ®eld variations around isolated elastic cracks (Segall and Pollard, 1980; Willemse et al., 1996), we develop a simple static criterion for fault propagation which takes into account shear stress contributions from nearby faults. Using predictions from this model, we can quantify the degree of interaction between pairs of normal faults using information about their map view con®guration and displacement pro®les. Two main types of fault interaction occur. Hard linkage is the case where fault segments are physically linked to another fracture or fault. This interaction changes the geometry of the fault plane (e.g. ®gure 8 in Gupta and Scholz, 1998). When faults interact only through their stress ®elds they are soft linked. In this case the geometry of the fault plane does not change signi®cantly. For the faults we study no physical linkage is observed and we assume fault segments are soft linked and interacting only through their stress ®elds. However, segments may be physically linked outside the plane of observation. We measured the in ̄uence of stress ®eld interaction on displacement by selecting a representative set of `non-interacting' faults and comparing them to the remaining interacting population. Ideally, to isolate the eects of interaction, well-resolved D ± L pro®les are required for interacting and non-interacting faults within a homogeneous tectonic setting and rock type. Our fault interaction model is based on a population of faults from the Solite Quarry near Eden, North Carolina, because they closely approximate this ideal data set. Hundreds of small ( L < 1 m) normal faults in Meso- zoic siltstones are exposed in the Solite Quarry. The deep-water lacustrine siltstones of the Cow Branch Member were deposited within the long, linear Meso- zoic Dan River rift basin (Schlische, 1993; Schlische et al., 1996). The Solite Quarry faults all dip toward the basin bounding fault. They lie at high angles to ®nely laminated bedding of siltstones, which tend to part along bedding planes. With such exposures, accurate measurements can be made of D ± L pro®les of a large number of faults (Schlische et al., 1996) (Fig. 2). The size of the faults ( L < 1 m) permitted measurements to be made in the laboratory, where we illumi- nated slabs of faulted siltstone so that the fault scarps appeared dark compared to the surrounding rock (Fig. 3a). The image was captured with a digital video camera and then processed to increase contrast using NIH Image software (Fig. 3b). By using a special fea- ture of NIH Image (version 1.43) we could calibrate the horizontal and vertical pixel scales independently. Millimeter scales were placed parallel to and along the dip of faults to provide ®ducials for the pixel cali- bration (Fig. 3a). We also scaled the pixel size with fault size by zooming in or out, so that small and large faults were measured with about the same amount of detail. Using this technique, only the portion of the fault with discernible displacement was recognized, even if the fault trace appeared longer in map view. We sampled only one oset marker layer for each fault, such as in Fig. 2. Often we did not know whether this layer crossed the fault near the center or edge of an elliptical fault plane. The location of the marker layer can aect the observed D ± L pro®le (Muraoka and Kamata, 1983), depending on the shape of the overall displacement distribution. For an elliptical slip distribution, such as in an elastic crack pro®le (Willemse et al., 1996), D ± L ratio does not vary with the observation location (Fig. 4). However, for a cone- shaped distribution (Fig. 4a), D ± L ratio varies linearly with distance from the center of the fault plane (Fig. 4c). Most real faults have slip distributions some- where between the elliptical and conical end members (Rippon, 1985; Barnett et al., 1987; Childs et al., 1995; Gupta and Scholz, 1998). The population of faults from Solite have nearly elliptical D ± L pro®les (Fig. 4b), meaning that only near the edges of fault planes does the D ± L ratio vary signi®cantly from the ratio at the center (Fig. 4c). We minimized this source of variabil- ity in the sample of D ± L pro®les by eliminating any faults that have D ± L ratios much lower than the ma- jority of the population. We selected a subset of the population that is `non- interacting' to compare with the remaining interacting population. The non-interacting faults are separated from other faults by at least 15% of their total length (Fig. 1a). This criterion is consistent with An's (1997) observation that strike-slip faults do not link if separation is more than 10% of the total length. In addition, a 15% separation value is consistent with boundary element models of normal fault interaction (®gure 10 in Willemse, 1997). Willemse ®nds that as separation becomes greater than 12.5% of length for short faults ( L / W = 2), the ability of nearby cracks to in ̄uence propagation tendency becomes small, even for large overlaps. For the non-interacting set, we also chose faults that have relatively symmetrical D ± L pro®les; this is because a highly asymmetrical pro®le is a clear indication of interaction (Peacock and Sanderson, 1991, 1994; Dawers and Anders, 1995; Willemse et al., 1996). Using these selection criteria we obtained 16 characteristic or `isolated' pro®les. Because the non- interacting faults may be aected slightly by fault interaction, the eects of interaction on D ± L pro®les may be underestimated. Our best estimate of an isolated fault pro®le from the Solite Quarry was found by averaging characteristic pro®les (Fig. 5). We cut each displacement±length pro®le in half along its length and averaged 32 halves instead of 16 complete faults. This approach is justi®ed in that each fault tip is isolated and can grow separ- ately. This enabled us to obtain a better estimate of the variance around the mean pro®le. We thus obtained a less noisy characteristic pro®le, without altering the overall shape of the pro®le. The variance in characteristic displacement pro®les partly represents variations in material properties, shape of the fault plane, and location of the observation horizon with respect to the fault plane. Although we could not completely eliminate the in ̄uence of these factors, the average or characteristic pro®le is our best estimate of an isolated fault pro®le. The shape of the isolated fault pro®le may change with material properties, boundary conditions, and growth mechanisms (Cowie and Scholz, 1992a; Bu È rgmann et al., 1994; Cowie, 1998). Consequently, for each new population studied we must de®ne a new characteristic pro®le. Comparing faults within a par- ticular population is reasonable if material properties, growth mechanisms, and boundary conditions do not change signi®cantly within the population. One advan- tage of using characteristic pro®les is that we do not need to know the details of how faults accumulate displacement because we assume isolated faults grow by the same processes as interacting faults. The method should work the same for populations of faults that grow by creep, are seismogenic, or that have ®nite, linear, or zero displacement gradients near the tips. Though displacement ®elds in the Solite Quarry faults are obviously permanent now (Fig. 2), we assumed that displacement ®elds were elastic at the time that these faults stopped growing. We previously validated this assumption by comparing observed fault displacement ®elds from the Solite Quarry population with an elastic boundary element solution (Gupta and Scholz, 1998). We found that a dislocation model within an elastic material can describe the displacement ®eld around a fault accurately despite the large strains and time scales often associated with faulting. Because a model with elastic rheology can reproduce observed fault displacement ®elds, we could assume that the elastic stresses did not relax during fault growth. All accumulated displacement contributed to the stress ®eld around these normal faults. Thus we can de®ne a net static stress drop which is calculated based on the net ...
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... the fault scarps appeared dark compared to the surrounding rock (Fig. 3a). The image was captured with a digital video camera and then processed to increase contrast using NIH Image software (Fig. 3b). By using a special fea- ture of NIH Image (version 1.43) we could calibrate the horizontal and vertical pixel scales independently. Millimeter scales were placed parallel to and along the dip of faults to provide ®ducials for the pixel cali- bration (Fig. 3a). We also scaled the pixel size with fault size by zooming in or out, so that small and large faults were measured with about the same amount of detail. Using this technique, only the portion of the fault with discernible displacement was recognized, even if the fault trace appeared longer in map view. We sampled only one oset marker layer for each fault, such as in Fig. 2. Often we did not know whether this layer crossed the fault near the center or edge of an elliptical fault plane. The location of the marker layer can aect the observed D ± L pro®le (Muraoka and Kamata, 1983), depending on the shape of the overall displacement distribution. For an elliptical slip distribution, such as in an elastic crack pro®le (Willemse et al., 1996), D ± L ratio does not vary with the observation location (Fig. 4). However, for a cone- shaped distribution (Fig. 4a), D ± L ratio varies linearly with distance from the center of the fault plane (Fig. 4c). Most real faults have slip distributions some- where between the elliptical and conical end members (Rippon, 1985; Barnett et al., 1987; Childs et al., 1995; Gupta and Scholz, 1998). The population of faults from Solite have nearly elliptical D ± L pro®les (Fig. 4b), meaning that only near the edges of fault planes does the D ± L ratio vary signi®cantly from the ratio at the center (Fig. 4c). We minimized this source of variabil- ity in the sample of D ± L pro®les by eliminating any faults that have D ± L ratios much lower than the ma- jority of the population. We selected a subset of the population that is `non- interacting' to compare with the remaining interacting population. The non-interacting faults are separated from other faults by at least 15% of their total length (Fig. 1a). This criterion is consistent with An's (1997) observation that strike-slip faults do not link if separation is more than 10% of the total length. In addition, a 15% separation value is consistent with boundary element models of normal fault interaction (®gure 10 in Willemse, 1997). Willemse ®nds that as separation becomes greater than 12.5% of length for short faults ( L / W = 2), the ability of nearby cracks to in ̄uence propagation tendency becomes small, even for large overlaps. For the non-interacting set, we also chose faults that have relatively symmetrical D ± L pro®les; this is because a highly asymmetrical pro®le is a clear indication of interaction (Peacock and Sanderson, 1991, 1994; Dawers and Anders, 1995; Willemse et al., 1996). Using these selection criteria we obtained 16 characteristic or `isolated' pro®les. Because the non- interacting faults may be aected slightly by fault interaction, the eects of interaction on D ± L pro®les may be underestimated. Our best estimate of an isolated fault pro®le from the Solite Quarry was found by averaging characteristic pro®les (Fig. 5). We cut each displacement±length pro®le in half along its length and averaged 32 halves instead of 16 complete faults. This approach is justi®ed in that each fault tip is isolated and can grow separ- ately. This enabled us to obtain a better estimate of the variance around the mean pro®le. We thus obtained a less noisy characteristic pro®le, without altering the overall shape of the pro®le. The variance in characteristic displacement pro®les partly represents variations in material properties, shape of the fault plane, and location of the observation horizon with respect to the fault plane. Although we could not completely eliminate the in ̄uence of these factors, the average or characteristic pro®le is our best estimate of an isolated fault pro®le. The shape of the isolated fault pro®le may change with material properties, boundary conditions, and growth mechanisms (Cowie and Scholz, 1992a; Bu È rgmann et al., 1994; Cowie, 1998). Consequently, for each new population studied we must de®ne a new characteristic pro®le. Comparing faults within a par- ticular population is reasonable if material properties, growth mechanisms, and boundary conditions do not change signi®cantly within the population. One advan- tage of using characteristic pro®les is that we do not need to know the details of how faults accumulate displacement because we assume isolated faults grow by the same processes as interacting faults. The method should work the same for populations of faults that grow by creep, are seismogenic, or that have ®nite, linear, or zero displacement gradients near the tips. Though displacement ®elds in the Solite Quarry faults are obviously permanent now (Fig. 2), we assumed that displacement ®elds were elastic at the time that these faults stopped growing. We previously validated this assumption by comparing observed fault displacement ®elds from the Solite Quarry population with an elastic boundary element solution (Gupta and Scholz, 1998). We found that a dislocation model within an elastic material can describe the displacement ®eld around a fault accurately despite the large strains and time scales often associated with faulting. Because a model with elastic rheology can reproduce observed fault displacement ®elds, we could assume that the elastic stresses did not relax during fault growth. All accumulated displacement contributed to the stress ®eld around these normal faults. Thus we can de®ne a net static stress drop which is calculated based on the net displacement on these faults. This is analogous to the static stress drops produced by earthquakes. For an earthquake, the average static stress drop, D s , is given ...
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... between pairs of faults. The growth of isolated faults provides a basis for quanti®cation of fault interaction. Theoretical models and observations of natural faults have led to an understanding of the mechanisms and characteristics of isolated fault growth. Isolated faults have constant D ± L ratios (Fig. 1) within a particular setting (Dawers et al., 1993; Schlische et al., 1996). The physical basis for the constant D±L ratio is derived in the Dugdale fault growth model (Cowie and Scholz, 1992a). There are two central features of the Dugdale model. First, the stress concentration at the fault tip is ®nite; when the stress concentration equals the yield strength the fault will propagate (Fig. 1). Second, the maximum displacement±length ratio ( D max / L max ) depends on the ratio of yield strength to shear modulus of the rock. Peacock and Sanderson (1991, 1994) were the ®rst to observe that displacement pro®les are aected by fault interaction. They found that D ± L pro®les of interacting faults are asymmetric with steep D ± L gradients near interacting tips. The point of maximum displacement in a displacement±length pro®le, d max , is shifted toward the interacting tip. Elastic boundary element modeling results con®rmed that d max is closer to interacting tips and that the average displacement gradient is steeper in the interacting region (Willemse et al., 1996; Willemse, 1997). While the observations of displacement pro®les generally agree with boundary element models of fault interaction, presently no quanti- tative criteria exist to evaluate degrees of fault interaction based on variations in displacement pro®les. Separation±overlap ratios (Fig. 1) provide a crude measure of fault interaction. Aydin and Schultz (1990) measured separation±overlap ratios but did not relate these ratios to their model. Their model shows that underlapping fault tips are favored to propagate towards each other, while overlapping tips are retarded. Huggins et al. (1996) also measured separation±overlap ratios. They acknowledged that separation±overlap ratios provide little information about the interaction state of the overlap zone. Cartwright and Mans®eld (1998) measured displacement gradients and suggested that the wide range of gradients in normal faults occur because of fault interaction. Later we show that increasing displacement gradients and anomalous displacement accumulation occur with increasing fault interaction. Thus rather than separation±overlap ratios, displacement anomalies can be used as a proxy for interaction, but, as we shall see, the two are related. To quantify displacement anomalies near interacting fault tips, we compare D ± L pro®les of the `isolated' faults in a population with the remaining interacting population. Using the Dugdale model (Cowie and Scholz, 1992a), and knowledge of stress ®eld variations around isolated elastic cracks (Segall and Pollard, 1980; Willemse et al., 1996), we develop a simple static criterion for fault propagation which takes into account shear stress contributions from nearby faults. Using predictions from this model, we can quantify the degree of interaction between pairs of normal faults using information about their map view con®guration and displacement pro®les. Two main types of fault interaction occur. Hard linkage is the case where fault segments are physically linked to another fracture or fault. This interaction changes the geometry of the fault plane (e.g. ®gure 8 in Gupta and Scholz, 1998). When faults interact only through their stress ®elds they are soft linked. In this case the geometry of the fault plane does not change signi®cantly. For the faults we study no physical linkage is observed and we assume fault segments are soft linked and interacting only through their stress ®elds. However, segments may be physically linked outside the plane of observation. We measured the in ̄uence of stress ®eld interaction on displacement by selecting a representative set of `non-interacting' faults and comparing them to the remaining interacting population. Ideally, to isolate the eects of interaction, well-resolved D ± L pro®les are required for interacting and non-interacting faults within a homogeneous tectonic setting and rock type. Our fault interaction model is based on a population of faults from the Solite Quarry near Eden, North Carolina, because they closely approximate this ideal data set. Hundreds of small ( L < 1 m) normal faults in Meso- zoic siltstones are exposed in the Solite Quarry. The deep-water lacustrine siltstones of the Cow Branch Member were deposited within the long, linear Meso- zoic Dan River rift basin (Schlische, 1993; Schlische et al., 1996). The Solite Quarry faults all dip toward the basin bounding fault. They lie at high angles to ®nely laminated bedding of siltstones, which tend to part along bedding planes. With such exposures, accurate measurements can be made of D ± L pro®les of a large number of faults (Schlische et al., 1996) (Fig. 2). The size of the faults ( L < 1 m) permitted measurements to be made in the laboratory, where we illumi- nated slabs of faulted siltstone so that the fault scarps appeared dark compared to the surrounding rock (Fig. 3a). The image was captured with a digital video camera and then processed to increase contrast using NIH Image software (Fig. 3b). By using a special fea- ture of NIH Image (version 1.43) we could calibrate the horizontal and vertical pixel scales independently. Millimeter scales were placed parallel to and along the dip of faults to provide ®ducials for the pixel cali- bration (Fig. 3a). We also scaled the pixel size with fault size by zooming in or out, so that small and large faults were measured with about the same amount of detail. Using this technique, only the portion of the fault with discernible displacement was recognized, even if the fault trace appeared longer in map view. We sampled only one oset marker layer for each fault, such as in Fig. 2. Often we did not know whether this layer crossed the fault near the center or edge of an elliptical fault plane. The location of the marker layer can aect the observed D ± L pro®le (Muraoka and Kamata, 1983), depending on the shape of the overall displacement distribution. For an elliptical slip distribution, such as in an elastic crack pro®le (Willemse et al., 1996), D ± L ratio does not vary with the observation location (Fig. 4). However, for a cone- shaped distribution (Fig. 4a), D ± L ratio varies linearly with distance from the center of the fault plane (Fig. 4c). Most real faults have slip distributions some- where between the elliptical and conical end members (Rippon, 1985; Barnett et al., 1987; Childs et al., 1995; Gupta and Scholz, 1998). The population of faults from Solite have nearly elliptical D ± L pro®les (Fig. 4b), meaning that only near the edges of fault planes does the D ± L ratio vary signi®cantly from the ratio at the center (Fig. 4c). We minimized this source of variabil- ity in the sample of D ± L pro®les by eliminating any faults that have D ± L ratios much lower than the ma- jority of the population. We selected a subset of the population that is `non- interacting' to compare with the remaining interacting population. The non-interacting faults are separated from other faults by at least 15% of their total length (Fig. 1a). This criterion is consistent with An's (1997) observation that strike-slip faults do not link if separation is more than 10% of the total length. In addition, a 15% separation value is consistent with boundary element models of normal fault interaction (®gure 10 in Willemse, 1997). Willemse ®nds that as separation becomes greater than 12.5% of length for short faults ( L / W = 2), the ability of nearby cracks to in ̄uence propagation tendency becomes small, even for large overlaps. For the non-interacting set, we also chose faults that have relatively symmetrical D ± L pro®les; this is because a highly asymmetrical pro®le is a clear indication of interaction (Peacock and Sanderson, 1991, 1994; Dawers and Anders, 1995; Willemse et al., 1996). Using these selection criteria we obtained 16 characteristic or `isolated' pro®les. Because the non- interacting faults may be aected slightly by fault interaction, the eects of interaction on D ± L pro®les may be underestimated. Our best estimate of an isolated fault pro®le from the Solite Quarry was found by averaging characteristic pro®les (Fig. 5). We cut each displacement±length pro®le in half along its length and averaged 32 halves instead of 16 complete faults. This approach is justi®ed in that each fault tip is isolated and can grow separ- ately. This enabled us to obtain a better estimate of the variance around the mean pro®le. We thus obtained a less noisy characteristic pro®le, without altering the overall shape of the pro®le. The variance in characteristic displacement pro®les partly represents variations in material properties, shape of the fault plane, and location of the observation horizon with respect to the fault plane. Although we could not completely eliminate the in ̄uence of these factors, the average or characteristic pro®le is our best estimate of an isolated fault pro®le. The shape of the isolated fault pro®le may change with material properties, boundary conditions, and growth mechanisms (Cowie and Scholz, 1992a; Bu È rgmann et al., 1994; Cowie, 1998). Consequently, for each new population studied we must de®ne a new characteristic pro®le. Comparing faults within a par- ticular population is reasonable if material properties, growth mechanisms, and boundary conditions do not change signi®cantly within the population. One advan- tage of using characteristic pro®les is that we do not need to know the details of how faults accumulate displacement because we assume isolated faults grow by the same processes as interacting faults. The method should work the same for populations of faults that grow by creep, are seismogenic, ...
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Citations
... However, our understanding of across-strike fault behaviour during individual earthquake sequences in terms of slip vectors and displacement profiles is limited. While long-term interactions between acrossstrike normal faults are known, e.g. the fault arrays of the rifted region of the Timor Sea, offshore north-west Australia (Meyer et al., 2002) and the faults close to Athens (Iezzi et al., 2021), with geological throws developed over thousands or millions of years, and the throw-rates averaged over shorter time periods showing patterns that reveal cooperation between faults across strike to produce the regional strain (Gupta et al., 1998;Gupta and Scholz, 2000;McLeod et al., 2000;Meyer et al., 2002;Cowie et al., 2005;Faure Walker et al., 2010;Iezzi et al., 2019), it remains unclear how or whether such interactions occur during individual earthquake sequences. ...
The relationships between kinematics and fault geometry for the coseismic ruptures from the 24th and 25th February 1981 earthquake sequence in the eastern Gulf of Corinth (Ms 6.7 and 6.4) are analysed. The two earthquakes ruptured faults located across strike rather than along strike as typifies other earthquake sequences. In detail, surface ruptures formed on the sub-parallel Pisia and Skinos Faults, with an 8 km along-strike overlap zone, separated across strike by < 2 km. The largest coseismic offsets occurred in the overlap zone. The 41-year-old ruptures are still well preserved as bedrock fault plane lichen-free stripes and colluvial ruptures, allowing detailed structural mapping at 213 rupture localities. A comparison between our measurements and Jackson et al. (1982) showed no overall consistent signal of post-seismic slip as some of our measurements were greater and some smaller than those recorded in 1981. The ruptures produced a single maximum asymmetric profile (Pisia: maximum throw of 223 cm) and a double maxima profile (Skinos: maximum throw of 109 cm and 130 cm). The shapes of the profiles differed in previous earthquakes on these faults, as evidenced by an older lichen-free stripe, implying non-characteristic earthquakes. Summing the two overlapping throw profiles across-strike reveals a single maximum symmetric bell-like profile. Using the above observations on coseismic offsets, kinematic information, and the geometry of faults, a rupture scenario has been proposed in terms of fault bends and corrugation orientations which suggests that parts of each fault may have ruptured in each earthquake.
... Moreover, strain localization during fault formation and interaction has been confirmed by means of statistical analysis (Manighetti et al., 2001;Walsh et al., 2002;Torabi and Berg, 2011), sandbox modeling, field observations, and numerical simulations (Dooley and Schreurs, 2012;Nabavi et al., 2018). It is also widely accepted that a fault system becomes increasingly linked with the accumulation of finite strain (Gupta and Scholz, 2000;Meyer et al., 2002). There is no doubt that the fault-growth process is accompanied by strain localization and strain partitioning, as such behaviors have been observed in fault evolution at various scales (e.g., Soliva and Schultz, 2008;Nixon et al., 2012). ...
... The proposed tectonostratigraphic model suggests that tilting associated with normal faults, based on the results of extensional margins induced drainage patterns strongly influenced by fault length. The catchment area in each footwall block was located far from the active margin (e.g., Gupta and Scholz, 2000;Ezquerro et al., 2019) assuming a scenario in which inherited structures play an essential role in tectonostratigraphic evolution (Trudgill, 2002). The replacement of marine carbonates of the Mozduran Formation by the siliciclastic rocks of the Shurijeh Formation was probably caused by the uplift of the southern basin shoulders (Binaloud Block). ...
... The proposed tectonostratigraphic model suggests that tilting associated with normal faults, based on the results of extensional margins induced drainage patterns strongly influenced by fault length. The catchment area in each footwall block was located far from the active margin (e.g., Gupta and Scholz, 2000;Ezquerro et al., 2019) assuming a scenario in which inherited structures play an essential role in tectonostratigraphic evolution (Trudgill, 2002). The replacement of marine carbonates of the Mozduran Formation by the siliciclastic rocks of the Shurijeh Formation was probably caused by the uplift of the southern basin shoulders (Binaloud Block). ...
... Several models describe fault curving in response to an inferred stress field of an approaching fault zone (Sieh et al., 1993;Jones et al., 1994;Amato et al., 1998;Scholz and Gupta, 2000;Perrin et al., 2016;Preuss et al., 2020). For example, Gupta and Scholz (2000) described an area of stress drop along the fault length. As a fault approaches another fault's stress drop area, the shear stress of the propagating fault decreases in response while accumulating relatively anomalous displacement . ...
The interactions among dip-slip and strike-slip faults are critical features in rift segmentation, including strain and slip transfer between faults of different rift segments. Here, we focused on the influence of factors such as fault and fracture geometries, kinematics, and local stress fields on the interaction and linkage of synchronous strike-slip and normal faults. Well-exposed faults along the tectonically active boundary between the central and northern Basin and Range provided for both reliable geometric data and consideration of rift segment development. We documented relative ages and distributions of Quaternary deposits, scarps, and geometries of three ~20–65-km-long Quaternary faults: the N-striking, normal Coyote Spring fault; the ENE-striking, left-lateral Kane Springs Wash fault; and the N-striking, normal Wildcat Wash fault.
The normal faults bend to accommodate slip-type differences across linkage zones, with the strike-slip fault and local processes influencing interactions. Influenced by the local stress field of the Kane Springs Wash fault, the Coyote Spring fault bends SE as it approaches and links to the Kane Springs Wash fault. Influenced by the off-fault or process-zone fractures of the Kane Springs Wash fault, the Wildcat Wash fault bends NE and links with the Kane Springs Wash fault. The Kane Springs Wash fault continues beyond the normal fault terminations, suggesting slip transfer between them via the Kane Springs Wash fault. These relations and the ages of offset units suggest that activity on the faults was approximately synchronous despite slip-type differences. Consequently, in slip transfer, the local strike-slip stress environment and off-fault fractures influenced the geometry of the normal fault terminations; the strike-slip fault formed a boundary to dip-slip fault propagation; and this boundary facilitated kinematic and geodetic segmentation, forming a Basin and Range rift segment boundary.
... Using the derived pixel-offset data, a fault slip distribution model has been developed based on triangular dislocation elements in an elastic half-space and discussed its implication for the rupture processes of the 2016 Kumamoto earthquakes (Himematsu and Furuya 2016). An elastic-plastic model of fault interaction that can assess degrees of interaction within a population of faults using only map traces or displacement profiles (Gupta and Scholz 2000). The geology and fault kinematics are used to analyse conditions that favour isolated seismicity, clustered earthquakes or propagating sequences along the North Anatolian Fault (NAF) and the Sea of Marmara pull-apart (Pondard et al. 2007). ...
In seismology, the nature of ground deformation in seismically active regions between two major seismic events has an immense connection with fault movement and other ground damages in those regions. So, understanding of geophysical stress accumulation scenario in this aseismic period and its effects on the faults is a very important aspect of figuring out which faults are most likely to generate further fault movement in the future. The way that faults interact with each other controls fault geometries, displacements and strains. Faults rarely occur individually but as sets or networks, with the arrangement of these faults producing a variety of different fault interactions. In this study, the effect of movement of a sequence of interacting faults on ground deformation where the interaction occurs between a sequence of infinite faults with a finite fault has been analyzed. The nature of the faults is taken as buried, inclined, creeping, strike-slip and the medium of the fault is considered as an isotropic homogeneous viscoelastic half-space of Maxwell medium. The ground displacement due to fault interaction and stress–strain accumulation/release across one fault effected by the neighbouring faults has been established by using integral transform and modified Green’s function technique. The significant effect of various affecting parameters viz. inclinations of the faults, velocity of the fault movement and depth of the faults from the free surface on ground deformation have been represented graphically. This study allows us to better understand the rapture process history of an earthquake and this could be a contribution to the earthquake prediction program.
... Once the formerly segmented faults are large enough compared to other unlinked segments, they have better ability to release shear stresses within larger volumes in their vicinity, suppressing activity on adjacent segments of smaller sizes (anticlustering process, e.g. Segall and Pollard 1980;Ackermann and Schische, 1997;Gupta and Scholz 2000). This process, leading to the abandonment of the smaller segments (Fig. 6, e.g., Peacock and Sanderson, 1991), is probably enhanced by the efficiency of fault segments to be larger, and probably contributes to localisation of activity into zones within the corridors. ...
... Jackson & Sanderson, 1992;Kakimi, 1980;Marrett & Allmendinger, 1992;Scholz & Cowie, 1990;Villemin et al., 1995;Walsh & Watterson, 1991), similar to the Gutenberg-Richter relationship observed for earthquakes (Gutenberg & Richter, 1956;Kanamori & Anderson, 1975). However, numerical (Ackermann et al., 2001), physical (Spyropoulos et al., 1999) and observational Gupta & Scholz, 2000;Soliva & Schultz, 2008) studies of fault length distributions suggest that faults may scale exponentially in higher strain settings ( Figure 2). This has implications for the forecasting of the size, and density of sub-resolution faults, which typically uses a power-law distribution for extrapolation (e.g., Marrett & Allmendinger, 1992;Torabi and Berg, 2011). ...
... The finite size of data sets leads to underestimation of small faults due to limited resolution (truncation) and undersampling of the largest faults (censoring), which overall alter the appearance of the distribution ( Figure 2) and may lead to erroneous conclusions of the style and factors controlling fault patterns. Previous statistical strain analyses are often presented in 1D (through borehole images and well logs) or 2D (fault lengths in outcrop or summing heaves across cross sectional transects; Cowie et al., 1995;Gupta & Scholz, 2000;Marrett & Allmendinger, 1992;Torabi & Berg, 2011;Walsh & Watterson, 1991). It remains a challenge to extrapolate results obtained from 1D and 2D data sets to 3D systems (Bonnet et al., 2001). ...
... For example, analog modeling from Ackermann et al. (2001) found that size distributions changed from powerlaw to exponential. Similarly, observational data from Gupta and Scholz (2000) found that size distributions are power law for low strain, and exponential for high strain settings. In contrast, for fault distributions that appear similarly curved, Cowie et al. (1995), Bonnet et al. (2001), and Soliva and Schultz (2008) describe a transition from widespread distributed faulting to localized faulting as an initially exponential distribution that evolves into a power law scaling distribution. ...
Continental extension is primarily accommodated by the evolution of normal fault networks. Rifts are shaped by complex tectonic processes and it has historically been difficult to determine the key rift controls using only observations from natural rifts. Here, we use 3D thermo‐mechanical, high‐resolution (<650 m) forward models of continental extension to investigate how fault network patterns vary as a function of key rift parameters, including extension rate, the magnitude of strain weakening, and the distribution and magnitude of initial crustal damage. We quantitatively compare modeled fault networks with observations of fault patterns in natural rifts, finding key similarities in their along‐strike variability and scaling distributions. We show that fault‐accommodated strain summed across the entire 180 × 180 km study area increases linearly with time. We find that large faults do not abide by power‐law scaling as they are limited by an upper finite characteristic, ω0. Fault weakening, and the spatial distribution of initial plastic strain blocks, exert a key control on fault characteristics. We show that off‐fault (i.e., non‐fault extracted) deformation accounts for 25%–45% of the total extensional strain, depending on the rift parameters. As fault population statistics produce distinct characteristics for our investigated rift parameters, further numerical and observational data may enable the future reconstruction of key rifting parameters through observational data alone.
... 1.8 (Figure 11e). The study fault zone was hence characterized by scale-dependent geometries throughout the whole Cenozoic era, although underestimation of fault length data due to poor resolutions at fault tips might have affected our interpretation of the seismic data [97,98]. Moreover, we highlight that the data scattering in the Dmax-L diagrams was likely associated with the fault segment linkage processes discussed above. ...
... Focusing, therefore, on the time-dependent throw intervals computed for the study fault zone, our result differs from those documented by La Bruna et al. [36] for the Pre-Early Messinian high-angle faults of the Monte Alpi area and hence shows that the scale-dependent geometries characterized the study fault zone since the beginning of its activity. Moreover, following Walsh et al. [33], we suggest that the slightly steeper slopes of the Miocene-Pliocene and Pleistocene fault growth lines (Figure 11d,e) reflect the higher degree of maturity reached by the entire fault zone subsequent to Paleocene-Eocene deformation [28,86,98]. Finally, we invoke that the linkage processes took place in correspondence with the stepover/relay zones (Trudgill and Cartwright, 1994), as documented for the A2 + B fault segment during the Paleocene-Eocene time interval and for the A1 + A2 + B + C + D1 fault segment during the Miocene-Pliocene interval. ...
This work focuses on a ca. 55 km-long extensional fault zone buried underneath the fore-deep deposits of the southern Apennines, Italy, with the goal of deciphering the Cenozoic fault growth mechanisms in the Outer Apulian Platform. By considering public 2D seismic reflection profiles , well logs, and isochron maps data, the study normal fault zone is interpreted as made up of four individual fault segments crosscutting Top Cretaceous, Top Eocene, Top Miocene, and Top Pliocene chrono-stratigraphic surfaces. The computed cumulative throw profiles form either bell-shaped or flat-shaped geometries along portions of the single fault segments. The computed incre-mental throw profiles also show an initial fault segmentation not corresponding with the present-day structural configuration. Data are consistent with the initial, post-Cretaceous fault segments coalescing together during Miocene-Pliocene deformation and with fault linkage processes localizing at the stepover/relay zones. Pleistocene faulting determined the evolution of a coherent fault system. The computed n-values obtained for the single time intervals by considering the maximum fault throw-fault length relations indicate that the fault segments formed scale-dependent geome-tries. Variations of these computed values are interpreted as due to the higher degree of maturity reached by the entire fault system during Miocene to Pleistocene deformation.
... (2009) delineated the formation and evolution stages of transfer zone of Liaodong Bay depression in Bohai Bay Basin. Gupta and Scholz (2000) further subdivided the fault interaction process into five stages, such as weak interaction, medium interaction, strong interaction, connection, and merging, on the basis of theoretical and actually observed normal fault interaction models. Based on the fault segmentation growth mechanism, Wang et al. (2013) divided the fault segmentation growth process into isolated fault stage, fault soft-linked stage and fault hard-linked stage. ...
Transfer zones are structural areas of faults interactions where fault motion or displacement can be transferred from one fault to another, regional strain maintains laterally constant. Transfer zones are widely developed in rift basins and have significance on hydrocarbon accumulation. In this review article, we attempt to summarize recent advances on the types, distance-displacement curves, evolutionary stages and controlling factors of transfer zones in rift basins and their effects on sedimentary systems, reservoir properties, trap formation and hydrocarbon migration. The formation of transfer zones is genetically related to the segmented growth of normal faults. Depending on the degree of interaction between these normal faults, transfer zones in rift basins could be divided into two types: soft-linked and hard-linked, which are further subdivided into transfer slope, oblique anticline, horst and transfer fault based on the combination patterns of normal faults. In general, the development of transfer zones experiences several stages including isolated normal faulting, transfer slope forming, complicating and breaking. During the interaction and growth of segmented normal faults, stress-strain and spatial array of faults, pre-existing basement structures, and mechanical conditions of rocks have a great influence on the location and development processes of transfer zones. A transfer zone is commonly considered as a pathway for conveying sediments from provenance to basin, and it hence exerts an essential control on the distribution of sandbodies. In addition, transfer zone is the area where stresses are concentrated, which facilitates the formation of various types of structural traps, and it is also a favorable conduit for hydrocarbon migration. Consequently, there exists great hydrocarbon potentials in transfer zones to which more attention should be given.
