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Basic concepts for seismic source - Finite fault model

news 来源：原创 2025/5/23 7:32:51

下面主要介绍与finite fault model有关的一些参数，有限断层模型更深入的一些认识，可以参考该文：有限断层模型(Finite-fault model)-CSDN博客

In finite fault modeling, the rupture is treated as a 2D surface (as opposed to a point source in simpler models), allowing for a more realistic simulation of earthquake source processes. Several key concepts and parameters are involved in defining and analyzing a finite fault model:

🔹 1. Fault Geometry

Defines the shape and orientation of the rupture plane:

Length (L) and Width (W): Physical dimensions of the rupture area.
Strike: Angle between north and the fault trace (measured clockwise).
Dip: Angle between the fault plane and the horizontal.
Rake: Direction of slip on the fault plane.
Depth to Top of Rupture: Often set near the seismogenic zone surface (e.g., 1–5 km).
Segmented Faults: Faults can be modeled with multiple segments or bending geometries.

🔹 2. Slip Distribution

Describes how much slip occurred on different parts of the fault:

Heterogeneous Slip: Non-uniform, varies spatially across the fault plane.
Often derived from inversion of seismic, GPS, or InSAR data.
Sometimes uses stochastic models or empirical Green’s functions.

🔹 3. Rupture Kinematics

Describes how the rupture propagates:

Rupture Velocity (Vr): Speed at which rupture front travels (~70–90% of shear wave speed).
Rise Time: Duration of slip at each point on the fault.
Nucleation Point: Starting location of rupture.
Slip Time Function: Time history of slip (e.g., isosceles triangle, Kostrov-type).

🔹 4. Stress and Friction Parameters (in dynamic models)

Initial Shear/Normal Stress: Pre-stress on fault.
Friction Law: Describes how friction evolves (e.g., slip-weakening, rate-and-state).
Critical Slip Distance (Dc): Slip required for frictional weakening.

🔹 5. Seismic Source Parameters

These link the fault model to observed ground motions:

Moment Magnitude (Mw): Related to total slip and rupture area via:

$M_0 = \mu A \overline{D}, \quad M_w = \frac{2}{3} \log_{10}(M_0) - 6.06$

where:
- M_0 = seismic moment
- \mu = shear modulus (usually ~30 GPa)
- A = fault area
- \overline{D} = average slip
Corner Frequency (fc): Used in source spectra and stress drop calculation.
Stress Drop (Δσ): Approximate strength of the rupture, related to slip and fault dimensions.

🔹 6. Ground Motion Simulation Inputs

If the model is used to generate synthetic ground motions:

Green’s Functions or Wave Propagation Models: For convolving the fault slip.
Site Effects: Local amplification due to Vs30, Q, topography, etc.
Kinematic vs. Dynamic Modeling: Kinematic uses prescribed slip; dynamic solves for slip based on stress.

🔹 Common Tools for Finite Fault Modeling

Slip Inversion Codes (e.g., Finite Fault Inversion by Ji, Gasperini’s code)
Dynamic Rupture Simulators (e.g., SPECFEM3D, SeisSol, FAULTS, AWP-ODC)
Stochastic Finite Fault Generators (e.g., Graves & Pitarka 2010)