Table of contents
Chapter 1 Basic Concepts
Chapter 2 Forward Modeling
Chapter 3 Conventional Inversion
Chapter 4 Forward Based FWI
Chapter 5 CNN and its Application in FWI
Chapter 6 U-Net and its Application in FWI
Chapter 7 Chapter GAN and its application in FWI
Chapter 8 The main challenges of deep learning for FWI
| symbol | meaning | Remark |
|---|---|---|
| t t t | time | |
| x x x | a point in space | Can be one-dimensional or multi-dimensional |
| x \mathbf{x} x | a sample | x = ( x 1 , … , x m ) \mathbf{x} = (x_1, \dots, x_m) x=(x1,…,xm) |
| r\mathbf{r}r | a point in space | Generally three-dimensional |
| Δx\DeltaxΔx _ | x xx change | |
| u ( x , t ) u(x, t) u(x,t) | A type of geophysical field determined by position and time | Such as the sound field, a certain component of the electromagnetic field, etc. When xxWhen x is one-dimensional, it can be considered as amplitude, and sometimes as speed |
| f ( x , t ) f(x, t) f(x,t) | source function | |
| p ( r , t ) p(\mathbf{r}, t)p(r,t) | Stress field | pressure |
| v ( r ) v(\mathbf{r}) v(r) | speed chart | |
| s ( r , t ) s(\mathbf{r}, t) s(r,t) | source term | |
| ∇ \nabla∇ | Hamilton operator | ∇ f ( x ) = ( ∂ f ( x ) ∂ x 1 , … , ∂ f ( x ) ∂ x m ) \nabla f(\mathbf{x}) = \left(\frac{\partial f(\mathbf{x}) }{\partial x_1}, \dots, \frac{\partial f(\mathbf{x}) }{\partial x_m}\right) ∇f(x)=(∂x1∂f(x),…,∂xm∂f(x)) |
| ∇ 2 \nabla^2∇2 | Laplace operator | ∇ 2 f ( x ) = ( ∇ ⋅ ∇ f ) ( x ) = ∑ i = 1 m ∂ 2 f ( x ) ∂ x i 2 \nabla^2 f(\mathbf{x}) = (\nabla \cdot \nabla f)(\mathbf{x}) = \sum_{i=1}^m \frac{\partial ^2 f(\mathbf{x})}{\partial x_i^2} ∇2f(x)=(∇⋅∇f)(x)=∑i=1m∂xi2∂2f(x) |