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# T-TECTO Studio X5

*Integrated software for the stress-strain inversion of the fault-slip data and the earthquake focal mechanisms *

T-TECTO Studio X5 is a result of 23 years of research, development, numerical testing, and analyses of earthquake focal mechanisms and fault-slip data. The program is based on several innovative mathematical algorithms:

1. Gauss stress inversion (Žalohar and Vrabec, 2007);

2. Multiple-Slip Method (MSM) (Žalohar and Vrabec, 2008);

3. Cosserat stress-strain inversion (Žalohar and Vrabec, 2010);

4. Tectonic wedge-faulting and fault-interaction theory (Žalohar, 2012 and 2014).

Compared to T-TECTO 3.0 Professional (2012 version), the new T-TECTO Studio X5 (2015 - 2022 versions) includes more than 60 new functions and several large modules added to improve the performance of earthquake focal mechanism and fault-slip data analyses. Quantectum AG uses the most advanced versions of T-TECTO Omega Architect to generate earthquake forecasts.

## New modules of the T-TECTO Studio X5:

1. Active analysis of faults;

2. Active analysis of fractures;

3. Tectonic-wedges analysis;

4. Distribution density analyses for several orientation parameters;

5. Shear stress and shear strain analysis;

6. Rose diagrams.

## Full Corel Draw compatibility

T-TECTO Studio X5 has considerably improved graphics and allows users to adjust their working space, for example, by defining the background color of the stereographs and tectonic wedges, etc. All figures and graphs can be saved as vector WMF or EMF graphics, fully compatible with Corel Draw or other vector-based graphic programs.

## Analysis of tectonic wedges

After the discovery of mathematical equations that describe the wedge faulting in the Earth’s crust (Žalohar, 2012, 2014), it has become clear that tectonic wedge faulting represents an important deformation mechanism that defines several aspects of faulting, such as:

1. Geometry of fault systems;

2. Type of interaction between faults;

3. Local tectonic strain and stress fields;

4. Stability of large fault planes;

5. Underground water flow.

Studying the tectonic wedges from fault-slip data and earthquake focal-mechanism data is, therefore, an important task for future structural geologists and geophysicists. T-TECTO Studio X5 incorporates extensive mathematical and computer algorithms that enable semi-automatic analysis and separation of differently oriented wedges.

T-TECTO Studio X5 is optimized for earthquakes

While previous versions of T-TECTO were best for structural geologists working with fault-slip data, T-TECTO Studio X5 is fully equipped for stress-strain analysis of earthquake focal mechanism data. It enables the calculation of a wide variety of parameters and an almost indefinite number of graphic options.

Optimization of the stress-strain phases separation

T-TECTO Studio X5 allows full control over the analysis of different stress-strain phases that affected the observed faults. The module for stress-strain inversion is improved and now works in combination with the module for active analysis of faults. In this second module, the stress and strain tensors are calculated based on the geometry of conjugate fault systems or the geometry of tectonic wedges. These tensors are then optimized by the module for stress-strain inversion.

This combination of algorithms considerably improves the resolution of the stress-strain phase separation. In many cases, the fault systems that were found to be homogeneous by older versions of T-TECTO 3.0, are now determined to be heterogeneous, indicating multiple deformational mechanisms.

## Right Dihedra Method

The widely used Right Dihedra Method (RDM) of Angelier and Mechler (1977) was significantly improved in T-TECTO Studio X5, allowing for the analysis of the stress-strain fields in the defined planes. There are also numerous combinations of the RDM method, such as Gauss-weighted RDM (VGF), or Multiple-Slip Mechanism (MSM) visualization for various types of data: faults, fractures, joints, extension fractures, compression fractures, etc.

This graphical method is based on the idea that the orientation of the maximum principal stress axis is constrained to the pressure (P) quadrant, while the orientation of the minimum principal stress axis is constrained to the tension/extension (T) quadrant associated with a chosen fault. Spatial orientation and position of the P and T quadrants are defined by the orientation of the fault plane and slip direction along with it. It is assumed that faults active in the same stress field have a common intersection of the P and T quadrants. This enables the construction of the approximate direction of the principal stresses as the geometrical center of the common intersection of the P and T quadrants.

## Visualization of the Gauss object function (VGF)

In the T-TECTO Studio X5, the Gauss object function (GF) described in the article (Žalohar and Vrabec, 2007) is visualized through a complicated procedure. There are several options available to visualize the GF; colored (red-blue), colored (red, for sigma1 only), colored (for sigma3 only, blue), black and white (for sigma1 or sigma3 only), etc.

The VGF method can be extended to allow an analysis of various fractures (joints) without visible slip. Three main types are used in T-TECTO Studio X5:

- E (or T) type - Extension/tension fractures and veins: In this case, the maximum principal stress axis lies in the fracture plane, while the minimum principal stress is perpendicular to the fracture plane.
- C type - Compression fractures and stylolites: The maximum principal stress axis is perpendicular to the fracture plane, while the minimum principal stress axis lies in the fracture plane.
- F type - Shear fractures: In this case, the maximum principal stress axis is inclined at the angle PhiRDM concerning the fracture plane. The minimum principal stress is perpendicular to the maximum principal stress.

Normally, we can perform a combined analysis of faults and fractures. By plotting the value of the objective function in each point on the stereogram by using various colors, we can visualize the areas of a high probability of maximum and minimum principal stress orientation.

## Stress-strain inversion

The T-TECTO Studio X5 enables classical and micropolar (Cosserat) analysis of heterogeneous and homogeneous fault-slip data using several different numerical methods including the Gauss method. The program is based on the classical philosophy of fault-slip data inversion which involves the concept of the best-fitting stress and strain tensors. The defined compatibility measure and compatibility function verify the compatibility of a given strain or/and stress tensor with observed fault-slip data. To constrain inversion results to mechanically acceptable solutions, the program additionally considers the ratio between the normal and the shear stress on the fault plane, since it is assumed that the results of (paleo)stress and strain inversion should agree with Amonton's Law. The optimal solution for stress and strain tensors related to the observed faults is found by searching for the global and highest local maxima of the object function F defined as a sum of compatibility functions for all fault-slip data.

## Multiple-Slip Mechanism (MSM)

T-TECTO Studio X5 also uses the Multiple-slip method (MSM) and the Cosserat MSM method to reconstruct the deformation gradient tensor which describes the faulting-related deformation of the region. Three elements are needed in the analysis: 1) the orientation of fault planes; 2) the direction of slip along with them; and 3) the number of faults with specified sizes belonging to different fault set present in the studied area or outcrop. The data on the orientation of faults and direction of slip along them define the geometric moment tensor for each fault, while the data on the number of the faults belonging to the fault-set constrain the weighting factors for each fault. In the MSM method, the weighting factors also depend on the driving stress that produced the displacement along the faults. The driving stress is defined as the difference between the resolved shear stress in the direction of movement along the fault planes and the frictional resistance for sliding. The stress state on the observed faults at the time of faulting can be calculated based on the (paleo)stress analysis. Therefore, the MSM method represents a combination of kinematic and (paleo)stress techniques, and the (paleo)stress analysis should be performed before the kinematic analysis. The MSM method allows for calculating the direction of kinematic axes (directions of maximum shortening and extension), the direction and relative magnitude of faulting-related rotation, and the shape of the strain ellipsoid (relative ratio between the principal strains).

## Fault-plane stability

T-Tecto Studio X5 can be used to calculate average stress-strain fields, using multiple earthquake focal mechanisms data of fault slip history. The state of stress on individual faults, and their stability can be analyzed.