18162502. IMPLICIT FINITE-DIFFERENCE METHOD FOR WAVE EQUATION BASED ON RECURSIVE DECONVOLUTION simplified abstract (Saudi Arabian Oil Company)
Contents
IMPLICIT FINITE-DIFFERENCE METHOD FOR WAVE EQUATION BASED ON RECURSIVE DECONVOLUTION
Organization Name
Inventor(s)
Hussain J. Salim of Dhahran (SA)
IMPLICIT FINITE-DIFFERENCE METHOD FOR WAVE EQUATION BASED ON RECURSIVE DECONVOLUTION - A simplified explanation of the abstract
This abstract first appeared for US patent application 18162502 titled 'IMPLICIT FINITE-DIFFERENCE METHOD FOR WAVE EQUATION BASED ON RECURSIVE DECONVOLUTION
The abstract describes a method for solving spatial partial differential equations within a wave equation by determining a linear system of equations using an approximate solution at grid nodes, evaluating an inverse matrix, vectors, and deconvolution filters, and determining the wavefield using the evaluated vectors, a velocity model, and the wave equation.
- Simplified Explanation:
The method outlined in the patent application solves spatial partial differential equations within a wave equation using an approximate solution at grid nodes and evaluating an inverse matrix, vectors, and deconvolution filters.
- Key Features and Innovation:
- Solving spatial partial differential equations within a wave equation efficiently. - Determining a linear system of equations using an approximate solution at grid nodes. - Evaluating an inverse matrix, vectors, and deconvolution filters for each equation. - Determining the wavefield using the evaluated vectors, a velocity model, and the wave equation.
- Potential Applications:
- Seismic imaging and exploration. - Medical imaging for ultrasound or MRI technology. - Structural health monitoring for buildings and bridges. - Environmental monitoring for detecting underground water or oil deposits.
- Problems Solved:
- Efficiently solving complex spatial partial differential equations within a wave equation. - Improving accuracy and speed of wavefield determination. - Enhancing imaging and exploration techniques in various fields.
- Benefits:
- Increased accuracy in solving spatial partial differential equations. - Faster computation of wavefield solutions. - Improved imaging and exploration results in various applications.
- Commercial Applications:
Title: Advanced Seismic Imaging Technology for Oil Exploration Description: This technology can revolutionize the oil exploration industry by providing more accurate and faster seismic imaging results, leading to better decision-making in drilling operations and resource discovery.
- Prior Art:
Readers can explore prior research in the field of seismic imaging, wave equation solutions, and deconvolution filters to understand the evolution of this technology.
- Frequently Updated Research:
Researchers are continually improving algorithms and computational methods for solving spatial partial differential equations within wave equations, leading to more efficient and accurate results.
Questions about the technology: 1. How does this method compare to traditional approaches in solving spatial partial differential equations within a wave equation? 2. What are the potential limitations of using deconvolution filters in evaluating the inverse matrix for each equation?
Original Abstract Submitted
Systems and methods are disclosed. The method includes, for each of a plurality of spatial partial differential equations (sPDEs) within a wave equation, determining a linear system of equations using an approximate solution at a plurality of grid nodes. The linear system of equations includes an inverse matrix, a first vector, and a second vector. The method further includes, for each of the plurality of sPDEs, evaluating the inverse matrix by evaluating a first portion of the inverse matrix using a first deconvolution filter and evaluating a second portion of the inverse matrix using a second deconvolution filter. The method further still includes, for each of the plurality of sPDEs, evaluating the first vector using the evaluated inverse matrix and the second vector as well as determining the wavefield using the evaluated first vector for each of the plurality of sPDEs, a velocity model, and the wave equation.
