Lakhasly

Este estudio tiene como objetivo caracterizar los tensores de tensión que controlaron la dinámica estructural que afectó a las formaciones del Turoniense Medio a Superior, así como al Turoniense Tardío, dentro de la región de Djebel el Chihet. Específicamente, se centra en la zona altamente fracturada de Oued Kodiat Chachiet el Roumi. La investigación buscó distinguir los regímenes tectónicos locales anidados dentro de una arquitectura regional más amplia, destacando una heterogeneidad significativa en los estilos de deformación influenciados por las condiciones tectónicas evolutivas y las respuestas litológicas diferenciadas.

La metodología adoptó un enfoque multidisciplinario, integrando un examen detallado de mapas geológicos y topográficos (N'Gaous 1/50.000), un modelo digital del terreno (MDT) y software especializado como ArcGIS. Las mediciones de campo sistemáticas documentaron diversas estructuras frágiles, registrando parámetros geométricos como direcciones, buzamientos y ángulos de inmersión, junto con indicadores cinemáticos de movimiento relativo. Estos datos se procesaron utilizando herramientas analíticas clásicas, incluyendo diagramas de rosa, proyecciones estereográficas y diagramas de densidad. La reconstrucción de los campos de paleotensión se basó en la hipótesis fundamental de Bott (1959), que postula que el deslizamiento en un plano frágil ocurre en la dirección de la máxima tensión de cizalla resuelta, asumiendo un campo de tensión espacial y temporalmente homogéneo.

Los tensores de tensión derivados se definen por la orientación y el buzamiento de los tres ejes de tensión principales—σ₁ (compresión máxima), σ₂ (tensión intermedia) y σ₃ (tensión mínima)—y la relación de tensión R = (σ₂ − σ₃) / (σ₁ − σ₃). Esta relación caracteriza las magnitudes relativas de las tensiones principales y la geometría del elipsoide de tensión, permitiendo la identificación de regímenes tectónicos (extensional, de cizalla, compresional) y estilos específicos (p. ej., extensión pura, transpresión). Para comparaciones regionales consistentes, se introdujo un índice numérico de régimen de tensión R’, que varía de 0 a 1 para regímenes extensionales, de 1 a 2 para regímenes de cizalla y de 2 a 3 para regímenes compresionales. El procesamiento automático de los datos microtectónicos (fallas estriadas, grietas de tensión, fracturas de compresión) se realizó utilizando el software TENSOR, que integra el módulo PBT. La inversión tectónica inicial empleó el Método del Diedro Recto Mejorado para una estimación de los ejes de tensión y R, capaz de integrar fracturas no estriadas. El tensor de tensión resultante se refinó mediante el método de Optimización Rotacional, un enfoque iterativo que minimiza una función compuesta F5 para evaluar la compatibilidad de cada estructura con el tensor de tensión probado. Las estructuras con valores F5 altos se excluyeron, asegurando la generación de tensores de tensión robustos y geológicamente consistentes, que cumplen con los estándares del Proyecto World Stress Map. Las grietas de tensión, como estructuras de apertura de Modo I perpendiculares a σ₃, a menudo en arreglos "en échelon", sirven como indicadores estructurales clave para reconstruir la cinemática tectónica y analizar los campos de tensión regionales.

Las estaciones de medición se ubicaron estratégicamente en la base de Djebel Chihat, dentro de formaciones altamente representativas de la serie Turoniense Medio a Superior. La reconstrucción de paleotensiones implicó la subdivisión de las mediciones de campo en dos categorías: características con planos de cizalla y trazas de desplazamiento (p. ej., fallas normales y de desgarre), y características sin trazas de desplazamiento (p. ej., diaclasas tectónicas, fracturas extensionales, grietas de tensión). Todos los datos se sometieron a una inversión tectónica generalizada, arrojando tres tensores representativos para probables regímenes de tensión regionales. Estos se optimizaron aún más para su fiabilidad y consistencia utilizando una combinación de los ejes PBT, diedros rectos y métodos de optimización rotacional, incluyendo la función F5.

El análisis del tensor de tensión derivado de fracturas con trazas de desplazamiento (fallas) indica un régimen de tensión oblicuo a transpresional. Los ejes de tensión principales se determinaron como σ₁ = 28°/327°, σ₂ = 03°/059° y σ₃ = 62°/155°, lo que significa que la compresión máxima (σ₁) se inclina moderadamente hacia el noroeste, el eje intermedio (σ₂) es casi horizontal y se extiende NE-SW, y el eje menos compresivo (σ₃) se inclina fuertemente hacia el sur-sureste. Esta configuración refleja un acortamiento orientado NW–SE combinado con un componente extensional subordinado hacia el SE. Los parámetros numéricos (AD ≈ 16.1°, CD ≈ 10.6, F5 = 13.5, R = 0.5 / R′ = 2.50) confirman una solución estadísticamente robusta. Esta cinemática oblicuo-compresiva es totalmente compatible con la fase Atlassica regional, caracterizada por una compresión post-Nummulítica NW–SE responsable del marco estructural principal.

Para las fracturas sin trazas de desplazamiento, se identificaron dos tensores de tensión extensional distintos. El primer tensor, derivado del diagrama PBT, reveló un régimen extensional con un componente oblicuo pronunciado (σ₁ = 25/045, σ₂ = 00/135, σ₃ = 65/225). Esto indica una extensión principal NE–SW (045°) y una compresión máxima dirigida hacia el SW (225°). Resultados consistentes de los métodos del Diedro Recto y Optimización Rotacional (F8 = 13.8; R = 2.50, según lo informado) validaron un régimen extensional oblicuo coherente asociado con una fase distensiva regional NE–SW a ENE–WSW. Esto se interpreta como una relajación post-tectónica frágil o una fase tardía/post-Atlassica, marcando una transición de un régimen compresional a uno más abierto y extensional en la corteza superior.

El segundo tensor de tensión para fracturas sin desplazamiento (PBT: σ₁ = 86/338, σ₂ = 00/068, σ₃ = 04/158) representó un campo de deformación dominado por la extensión a lo largo de σ₃, sugiriendo una dirección de extensión principal SSE–NNW a NW–SE. La concordancia entre los métodos del Diedro Recto y Optimización Rotacional (F8 = 13.2; R = 1 / R′ = 1) confirmó un campo de tensión extensional homogéneo, responsable de la apertura de grietas de tensión en échelon sin deslizamiento medible. Esta fase extensional se interpreta como una fase tectónica distensiva regional de edad Atlassica o post-Atlassica, que refleja la relajación y reorganización del campo de tensión cortical tras las principales etapas compresionales de la orogenia Atlassica.

En conclusión, el trabajo de campo detallado y el análisis estructural en el área de Chihat–Aïn Touta permitieron reconstruir con éxito los campos de paleotensión, identificando dos fases tectónicas principales. En primer lugar, un régimen compresional a transpresional anterior, orientado aproximadamente NW–SE y vinculado a la orogenia Atlassica, que formó los principales pliegues y fallas. En segundo lugar, una fase extensional posterior, predominantemente orientada SSE–NNW a NW–SE, interpretada como una relajación post-Atlassica o post-orogénica, que condujo a la generación de fracturas de tensión y deformación frágil dentro de la corteza superior. En general, la investigación demuestra que la evolución tectónica de la región de Bellezma refleja una transición crucial de la orogenia compresional a una reorganización extensional frágil de la corteza, proporcionando un marco sólido para comprender la evolución estructural y geodinámica del centro-este de Argelia.

Jim Lin, [09/10/2025 13:48]

1. Introduction :
   This section aims to characterize the stress tensors that controlled the structural dynamics affecting the Middle to Upper Turonian formations as well as the Late Turonian within the study area. A total of (number) strategically distributed stations was established in the Djebel el Chihet region, where the redite facies outcrops, particularly in the highly fractured area of Oued Kodiat Chachiet el Roumi, which exhibits a markedly higher degree of tectonic strain compared to other parts of the structural framework. A campaign of (number) structural measurements was conducted to document the spatial and spatio-temporal variations in the orientations of the principal stress axes (σ₁, σ₂, σ₃), allowing the distinction of local tectonic regimes nested within a broader regional architecture. The cross-analysis of mechanical parameters and petro-structural markers highlights significant heterogeneity in the deformation styles affecting this Mesozoic sedimentary sequence, reflecting the influence of evolving tectonic conditions and differentiated lithological responses within the fractured system.


2. Methodes and Materials :

The brittle deformation analysis in this study is based on a multidisciplinary approach integrating a detailed examination of the geological and topographic map of N'Gaous at a 1/50,000 scale, complemented by the use of a digital terrain model (DTM) and specialized software such as ArcGIS, RockWorks, and Global Mapper, systematic field collection of structural data, and the application of various tectonic interpretation methods. Field measurements focused on diverse brittle structures and included geometric parameters such as directions, azimuths, dips, plunge angles, and, when possible, pitch, rake, fracture lengths, and kinematic indicators of relative movement. These data were subsequently processed using classical analytical tools in tectonics and microtectonics, including composite rose diagrams for orientation analysis, stereographic projections for 3D representation of fracture planes, density diagrams and histograms for the statistical visualization of principal directions, ternary diagrams for deformation field classification, focal mechanisms for stress interpretation, and Mohr diagrams for rupture condition assessment. This methodological integration allows for a coherent reconstruction of the local tectonic framework and the dynamics of fracturing.

Jim Lin, [09/10/2025 13:48]
In reconstructing paleostress fields, the calculation of stress tensors is based on the fundamental hypothesis of Bott (1959), which states that slip on a brittle plane occurs in the direction of maximum resolved shear stress. This hypothesis assumes a spatially and temporally homogeneous stress field at the scale of the analyzed rock volume. The inversion of fault-slip data thus enables a partial reconstruction of the stress tensor that governed the recorded brittle deformations.
The derived stress tensors are defined by four fundamental parameters: (i) the orientation and plunge of the three principal stress axes—σ₁ (maximum compression), σ₂ (intermediate stress), and σ₃ (minimum stress), with σ₁ ≥ σ₂ ≥ σ₃ ≥ 0; (ii) the stress ratio R = (σ₂ − σ₃) / (σ₁ − σ₃), which characterizes both the relative magnitudes of the principal stresses and the geometry of the stress ellipsoid (Bishop, 1966; Angelier, 1989, 1991, 1994; Gephart & Forsyth, 1984; Vandycke & Bergerat, 1992; Lund & Townend, 2007; Sippel, 2009; Delvaux & Sperner, 2003; Delvaux, 2012; Tranos, 2017). The combined analysis of stress axis orientations and the value of R allows the identification of several tectonic regimes: extensional (σ₁ vertical), strike-slip (σ₂ vertical), and compressional (σ₃ vertical).
Within these broad categories, the value of R further differentiates specific tectonic styles: biaxial extension (σ₁ vertical, 0 < R < 0.25), pure extension (σ₁ vertical, 0.25 < R < 0.75), transtension (σ₁ vertical, 0.75 < R <
1 or σ₂vertical, 1 > R > 0.75), pure strike-slip (σ₂ vertical, 0.75 > R > 0.25), transpression (σ₂ vertical, 0.25 > R > 0 or σ₃ vertical, 0 < R < 0.25), pure compression (σ₃ vertical, 0.25 < R < 0.75), and biaxial compression (σ₃ vertical, 0.75 < R < 1) (Delvaux et al., 1997).
To ensure consistent regional comparisons and facilitate result mapping, a numerical stress regime index R’ was introduced (Delvaux et al., 1997). Derived from the stress ratio R, this index continuously represents the diversity of tectonic regimes: R’ ranges from 0 to 1 for extensional regimes, from 1 to 2 for strike-slip regimes, and from 2 to 3 for compressional regimes.
Automatic processing of microtectonic data—including striated faults, tension gashes, and compression fractures—is performed using the TENSOR software (Delvaux, 1993a), which integrates the methodological developments proposed by Delvaux & Sperner (2003), particularly the PBT (Paleostress by Tensor) module. This module offers an interactive approach that combines stress tensor inversion with iterative assessment of structural compatibility, enabling optimized integration of heterogeneous datasets and rigorous quality control.
Tectonic inversion is initially conducted using the Improved Right Dihedron Method
(Angelier & Mechler, 1977; Delvaux & Sperner, 2003), providing an initial estimate of the stress axes and the stress ratio R. This method also allows for the integration of unstriated fractures (tension or compression fractures) and uses the Counting Deviation parameter to assess data compatibility.
The resulting stress tensor is further refined through the Rotational Optimization method, an iterative approach based on minimizing a composite F5 function. This function evaluates the compatibility of each structure with the tested stress tensor: for striated faults,

Jim Lin, [09/10/2025 13:48]
F5 minimizes the angular deviation between the measured and calculated striae while maximizing shear stress (Angelier, 1991; Delvaux & Sperner, 2003); for tension gashes, F5 simultaneously minimizes normal and shear stress to promote fracture opening without slip (Angelier, 1991, 1992; Delvaux & Sperner, 2003). Structures with F5 values exceeding 20 (for tension gashes) or 22 (for striated faults) are excluded from the final dataset as incompatible with the optimized tensor (Delvaux & Sperner, 2003).
This integrated approach, structured around the PBT method, ensures the generation of robust, geologically consistent stress tensors that meet the standards of the World Stress Map Project and are well-suited for analyzing complex geodynamic contexts and polyphase brittle deformation sequences.
2.1. Tension gashes in en echelon vein arrays :

Tension gashes (or extension fractures) are Mode I opening structures oriented perpendicular to the minimum principal stress (σ₃), and are often filled with quartz or calcite. Their formation may result from pure extension or from mechanical interactions between nearby fractures, particularly in non-coaxial shear settings, leading to characteristic en echelon arrangements typical of brittle-ductile deformation zones (Olson & Pollard, 1991; Coelho et al., 2006; Jacques et al., 2022).
These structures can appear as straight, sigmoidal, or pennant veins, the latter resulting from the interaction between Riedel shear fractures (R and R′), typically forming at 15° and 75° to the shear plane, respectively (Davis et al., 2000; Coelho et al., 2006). The orientation and evolution of these fractures are controlled by factors such as fluid overpressure, temperature, strain rate, and the frictional properties of the rocks (Marchesini et al., 2019).
The coexistence of brittle and ductile deformation observed in the brittle-ductile transition zone reflects cyclic behavior triggered by fluid pressure fluctuations (Marchesini et al., 2019). The study of en echelon tension gashes thus provides key structural indicators for reconstructing tectonic kinematics, identifying fluid-bearing reservoirs, and analyzing regional tectonic stress fields, as demonstrated in the Purros Mylonite Zone (Kaoko Belt, Namibia) (Coelho et al., 2006; Du et al., 2024).
3. Results and Discussion:
3.1. Geolocation of measuring stations:
The measurement stations are located at the base of Djebel Chihat, within a relief mainly composed of Middle to Upper Turonian formations. Analysis of the topographic and structural maps shows that the stations are situated at the base of the relief. The outcropping formations belong successively to the Upper Turonian (C²c) in the summit areas, and to the Middle–Upper Turonian (C²b) in the lower parts. These observations suggest that the measurements were conducted within stratigraphic units that are highly representative of the Turonian series of Djebel Chihat, reflecting the lithostratigraphic continuity and the typical structural framework of this sector.

3.2. Reconstruction and Characterization of Paleostresses:
3.2.1. Operating Procedure:
In this study, the reconstruction of paleostresses was conducted by subdividing the field measurements into two main categories based on their mechanical behavior and rheological response: on the one hand, features with shear planes and displacement traces (tectoglyphs), represented mainly by normal faults and strike-slip faults, and on the other hand, features without displacement traces or shear planes, including a large population of various fractures

Jim Lin, [09/10/2025 13:48]
such as tectonic joints, extensional fractures, and conjugate or isolated en echelon tension gashes.
All the data were then prepared for numerical processing and subjected to a generalized tectonic inversion, resulting in three tensors representative of probable regional stress regimes (Table 1). These results were subjected to successive optimization iterations aimed at improving their reliability and consistency with field observations, thanks to the combined use of several methods (PBT axes, right dihedra, rotational optimization), including the F5 function that allows the simultaneous integration of different types of data (faults with slip, extensional fractures, shear, and compressional fractures) in order to construct a robust and representative tensor.
3.2.2. Results of Tectonic Inversion and Characterization of Stress Tensors:
The graphic results are presented in the diagrams below, while the characteristic values of the tensors have been summarized in a summary table (Table 1), in accordance with the operating procedure described previously.
3.3.2.1. Fractures with Displacement Traces and Shear Planes:

The analysis of the stress tensor derived from the fault mirror indicates a coherent system of principal stresses characterized by σ₁ = 28°/327°, σ₂ = 03°/059°, and σ₃ = 62°/155° (in plunge/azimuth notation), which is very close to the previously obtained set of axes (σ₁ ≈ 37°/324°, σ₂ ≈ 7°/059°, σ₃ ≈ 53°/158°). The maximum compressive stress axis (σ₁) plunges moderately toward the northwest, the intermediate axis (σ₂) is nearly horizontal and trends NE–SW, whereas the least compressive axis (σ₃) plunges steeply toward the south-southeast. This stress configuration reveals an oblique to transpressional stress regime, combining NW–SE-oriented shortening with a subordinate extensional component toward the SE. Such an arrangement reflects a non-purely Andersonian stress field, as none of the principal stress axes is perfectly vertical.
The associated numerical parameters (AD ≈ 16.1°, CD ≈ 10.6, F5 = 13.5, R = 0.5 / R′ = 2.50) indicate a statistically robust solution, characterized by moderate dispersion and good agreement between the calculated tensor and the observed fault-plane geometry. In the context of a single fault mirror, this regime corresponds to a predominantly reverse movement with an oblique strike-slip component, indicative of an oblique-compressive (transpressional) kinematics involving NW–SE-oriented shortening coupled with a subordinate extension toward the SSE. Consequently, the fault mirror is expected to display oblique slickensides and striations, recording a combination of both vertical and horizontal displacement components.
Overall, the results obtained from both the right-dihedron and the rotational optimization (F5) methods converge toward a consistent tectonic interpretation: an oblique transpressional regime oriented NW–SE. This stress regime is fully compatible with the regional Atlassic phase, characterized by a NW–SE post-Nummulitic compression responsible for the major structural framework of the Atlassic tectonic domains.

Jim Lin, [09/10/2025 13:48]
3.3.2.2. Fractures without Displacement Traces and without Shear Planes:
The PBT diagram for the first tensor reveals a stress tensor defined by σ₁ = 25/045, σ₂ = 00/135, and σ₃ = 65/225, indicating an extensional regime with a pronounced oblique component. This configuration is characterized by a principal extension oriented NE–SW (045°) and a maximum compression directed toward the SW (225°). The low angular misfit (AD = 10.7°) denotes an excellent consistency between the field measurements and the computed tensor solution, providing strong confidence in the reliability of the interpretation.
Similarly, the Right Dihedra method yields principal stress axes that are closely comparable (σ₁ = 10/347, σ₂ = 25/081, σ₃ = 63/236; CD = 10.1°), confirming an extensive regime of predominantly normal type, with a main extension oriented ENE–WSW (≈236°) and compression directed NNW–SSE (≈347°). These structural features correspond to pure opening joints (tensile fractures) with no measurable displacement, typical of a brittle post-tectonic relaxation regime within the upper crust.
Furthermore, the rotational optimization method (F8) refines this stress model, yielding σ₁ = 16/351, σ₂ = 20/087, and σ₃ = 64/225 (F8 = 13.8; R = 2.50). This result further validates the stability of the stress tensor and confirms the recurrence of a principal compression oriented toward the SW (σ₃ ≈ 225°) and a subhorizontal extension trending N–S to NNW–SSE (σ₁ ≈ 351°). The consistency among these three independent methods demonstrates a coherent oblique extensional regime associated with a NE–SW to ENE–WSW regional distensive phase, reflecting a post-orogenic relaxation process.
Consequently, this first tensor — representative of the joint systems without measurable displacement — records an initial phase of brittle extension, most likely related to the late or post-Atlasic phase at the regional scale. This phase marks the transition from a compressional to a more open extensional regime within the shallow crust, signaling the tectonic relaxation and adjustment that followed the major compressional events responsible for the Atlasic orogeny

Jim Lin, [09/10/2025 13:48]
The results obtained of The second stress tensor from the PBT diagram indicate a maximum compressive stress (σ₁) oriented at 86/338, an intermediate stress (σ₂) at 00/068, and a maximum extensional stress (σ₃) at 04/158. This configuration represents a deformation field dominated by extension along σ₃, reflecting a stress regime in which tensile opening is the principal mechanism of deformation. The orientation of σ₃ suggests a dominant SSE–NNW to NW–SE direction of extension, consistent with an extensional phase of regional significance.
Similarly, the Right Dihedra method produces comparable results, with σ₁ = 79/322, σ₂ = 03/067, and σ₃ = 10/157, confirming preferential opening along a SSE–NNW axis (approximately 157°/337°). The low angular dispersion (CD = 9°) indicates excellent consistency between the calculated tensor and the measured structural data, underscoring the high precision of the solution.
The Rotational Optimization method refines the analysis and yields a comparable stress tensor characterized by σ₁ = 64/256, σ₂ = 26/067, and σ₃ = 04/158. This result further supports an extensional regime dominated by tensile fractures (mode I opening) without significant shear or displacement components. The quality indicators (F8 = 13.2; R = 1 / R′ = 1) denote a well-constrained solution with a balanced stress ratio among the principal axes, confirming the internal coherence of the dataset and the robustness of the model.
The concordance of the three independent analytical methods highlights a homogeneous stress field characterized by a dominant SSE–NNW (or equivalently NW–SE) extensional direction, responsible for the opening of en échelon tension fractures without measurable slip. This direction of extension is interpreted as reflecting a regional distensive tectonic phase of Atlassic or post-Atlasic age, marking the late-stage evolution of the tectonic regime in the studied area. It likely represents the relaxation and reorganization of the crustal stress field following the main compressional stages of the Atlassic orogeny, indicative of a transition toward post-orogenic brittle extension within the upper crust.
Conclusion
Finally, the intensive fieldwork carried out in the Chihat,Aïn-Touta area allowed us to obtain a rich set of measurements, which ultimately paved the way for completing this study and achieving these results, as it facilitated the analysis of the sequence of tectonic events that occurred in this region.
Through detailed fieldwork and structural analysis in the Chihat–Aïn Touta area (southern flank of the Batna–Bellezma Mountains), the study successfully reconstructed the paleostress fields that shaped this region. The combination of several analytical methods — notably the PBT, Right Dihedron, and Rotational Optimization techniques — allowed the authors to identify a coherent and consistent stress regime.
The results reveal two major tectonic phases:

1. An earlier compressional to transpressional regime linked to the Atlasic orogeny, oriented roughly NW–SE, which structured the main folds and faults of the massif.


2. A subsequent extensional phase, oriented mainly SSE–NNW to NW–SE, interpreted as a post-Atlasic or post-orogenic relaxation. This later regime generated tension fractures and brittle deformation within the upper crust.
   Overall, the research demonstrates that the Bellezma region’s tectonic evolution reflects a transition from compressional mountain-building to brittle extensional reorganization of the crust. The fieldwork, supported by quantitative modeling, provides a solid framework for understanding the structural and geodynamic evolution of central-eastern Algeria.