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We present a new technique to image deformation, 3D seismo-tectonic imaging, which juxtaposes instantaneous and accumulated deformation by combining earthquake and structural geology data. We test the technique using three independent data sets. We find concordance between the predicted finite deformation field and related instantaneous deformation surfaces inferred from aftershock and background seismicity data as well as structure imaged by seismic reflection data. These results indicate that: [1] The 1994 Northridge event ruptured a transverse, high-angle reverse fault linking two EW striking listric thrust systems, the Pico and Oak Ridge. The rupture terminated on the thrusts and was capped by a north dipping, forward-breaking imbricate of the Santa Susana Fault. [2] The Los Angeles Seismic Zone is a region of thrusting associated with the development of a new mountain front forming south of the present one represented by the Santa Monica Anticline. The thrust is rooted on a mid-crustal ramp forming beneath the Los Angeles basin. We conclude that seismo-tectonic imaging by linking earthquake data to an empirically based quantitative description of the finite deformation field provides a new and fruitful method for integrating geological and seismological data.

Given the direction cosines a i ′ = (a 1 i , a 2 i , a 3 i )corresponding to a set of pspherically projected fabric poles, an initial estimate x′ = (x1, x2, x3, x4)for the angular radius x4,and direction cosines of the center of the least-squares small circle which minimizes the sum of the squares of the angular residuals $$r = \sum\limits_p {\left[ {x_4 - \cos ^{ - 1} \left( {a_1^i x_1 + a_2^i x_2 + a_3^i x_3 } \right)} \right]} ^2 $$ can be iteratively improved by taking xj+1 = xj + Δxwhere xj is the value of xat the jth iteration and $$\Delta x = - H_j^{ - 1} \left[ {q_j + x_j \left( {x'_j H_j^{ - 1} x_j } \right)\left( {q_j - x'_j H_j^{ - 1} q_j } \right)} \right],$$ where As an initial approximation for xwe have found it convenient to ignore the fact that the data are constrained to lie on the surface of the reference sphere and to use the parameters of a least-squares plane through the given poles. Generalization of this approach to fitting variously constrained great and small circles is easily made. The relative merits of differently constrained fits to the same data can be tested approximately if it is assumed that the errors in the location of the poles are isotropic and normally distributed. It is thus possible to statistically assess the relative significance of conflicting structural models which predict different geometrical patterns of fabric elements.

To compare the orientation and development of jointing with the orientation and magnitude of finite strain recorded in the Upper Devonian rocks of the Appalachian plateau, New York, we mapped systematic joint sets on an area of 20,000 km2. In this area, Wedel [1932] mapped folds with limb dips of less than a degree and axes that change strike by 30° from 090° in the east to 060° in the west. We observed two different cross-strike joint sets that maintain their approximate cross-strike position from east to west. Yet, in detail the angle between the sets is 18°±2° in the east and 30°±4° in the west. In many outcrops one joint set parallels the direction of maximum compressive strain (eƒ) as recorded by deformed fossils, whereas the other joint set never parallels eƒ. Rare calcite-filled joints are oriented parallel to the direction of eƒ. In addition, the calcite-filled joints both cut and are cut by solution cleavage. These observations suggest that the joint set paralleling eƒ formed during the deformation event represented by the deformed fossils. The joint set that does not parallel eƒ somehow reflects a deformational event other than that producing fossil distortion, as suggested by strain relaxation experiments. In an outcrop of the Machias formation, where the direction of eƒ is 15° from the trace of a cross-strike joint set, the tensor average from 14 subsurface strain relaxation tests shows in situ maximum comprehensive strain (eoc = 10−4) parallel to cross-strike joints but not the direction of eƒ. Strain relaxation is coaxial with a fabric anisotropy indicated by sonic velocity tests. Our idea is that the orientations of cross-strike joints parallel to eoc were controlled by the same rock property that causes strain relaxation on overcoring, whereas the orientations of the cross-strike joints parallel to eƒ were controlled by the stress field causing the fossil distortion. Placing these structural data in a regional context allowed us to construct a dynamic and kinematic model for the structural evolution of the New York plateau. The model indicates variation in both boundry conditions and material behavior through a series of four distinct deformational events, which begin prior to lithification and end in the Recent. Thus our analysis suggests that the structural features we have used represent a set of highly sensitive tools for investigating the deformational history of the Appalachian foreland.