# US 9,536,143 B2 · Systems and methods for imaging seismic data

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- Number: US 9,536,143 B2
- Document ID: US9536143B2
- Status: Granted
- Kind: B2
- Application number: 14/422,096
- Filed: 2012-08-17
- Published: 2015-08-20
- Granted: 2017-01-03
- Earliest claimed: 2012-08-17
- Assignees: Landmark Graphics Corporation
- Applicants: Fan Jiang; Shengwen Jin
- Inventors: Fan Jiang; Shengwen Jin
- Web page: https://patentgrep.com/patent/US9536143B2

## CPC

- G01V 1/282: {Application of seismic models, synthetic seismograms}
- G06T 7/50: Depth or shape recovery
- G06V 30/422: Technical drawings; Geographical maps
- G01V 2210/512: Pre-stack
- G01V 2210/586: Anisotropic media
- G01V: GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS (means for indicating the location of accidentally buried, e.g. snow-buried, persons A63B29/02)
- G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06V: IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING

## Abstract

Systems and methods for imaging seismic data using hybrid one-way wave-equation-migration in tilted transverse isotropic media and/or hybrid two-way reverse-time-migration in tilted transverse isotropic media.

## Claims

### Claim 1

A method for imaging seismic data, which comprises:
approximating TTI coefficients using a Pade approximation and a dispersion relation equation;
applying hybrid TTI-WEM to a velocity model and anisotropic parameters for a pre-stack shot gather using the approximated TTI coefficients and a computer system to determine a source side wavefield propagation value and a receiver side wavefield propagation value in a frequency-space domain;
converting the source side wavefield propagation value and the receiver side wavefield propagation value from the frequency-space domain to a time-space domain; and
applying a zero-lag cross-correlation image condition equation to form a partial output image using the converted source side wavefield propagation value and the converted reservoir side wavefield propagation value.

### Claim 2 (depends on 1)

The method of claim 1, further comprising:
applying hybrid TTI-RTM to the velocity model and the anisotropic parameters for the pre-stack shot gather using the converted source side wavefield propagation value and the converted receiver side wavefield propagation value to determine another source side wavefield propagation value and another receiver side wavefield propagation value in the time-space domain; and
applying the zero-lag cross-correlation image condition equation to form another partial output image using the another source side wavefield propagation value and the another receiver side wavefield propagation value.

### Claim 3 (depends on 2)

The method of claim 2, further comprising:
stacking each partial output image; and
displaying the stacked partial output images.

### Claim 4 (depends on 1)

The method of claim 1, wherein the dispersion relation equation is created from a phase velocity function and a rotation matrix.

### Claim 5 (depends on 2)

The method of claim 2, further comprising applying a phase shift algorithm to the velocity model and the anisotropic parameters for the pre-stack shot gather before applying the hybrid TTI-WEM to determine the source side wavefield propagation value and the receiver side wavefield propagation value.

### Claim 6 (depends on 5)

The method of claim 5, further comprising setting a migration depth between the hybrid TTI-WEM and the hybrid TTI-RTM.

### Claim 7 (depends on 6)

The method of claim 6, wherein the phase shift algorithm is applied to the velocity model and the anisotropic parameters from a water surface to a subsurface where the water meets earth.

### Claim 8 (depends on 6)

The method of claim 6, wherein the hybrid TTI-WEM is applied to the velocity model and the anisotropic parameters from an earth surface or a subsurface where water meets the earth to the migration depth.

### Claim 9 (depends on 6)

The method of claim 6, wherein the hybrid TTI-RTM is applied to the velocity model and the anisotropic parameters from the migration depth to an extent of the velocity model.

### Claim 10 (depends on 2)

The method of claim 2, further comprising:
filtering and smoothing each partial output image to generate a respective amplitude-consistent partial output image;
stacking each amplitude-consistent partial output image; and
displaying the stacked amplitude-consistent partial output images.

### Claim 11

A non-transitory program carrier device tangibly carrying computer executable instructions for imaging seismic data, the instructions being executable to implement:
approximating TTI coefficients using a Pade approximation and a dispersion relation equation;
applying hybrid TTI-WEM to a velocity model and anisotropic parameters for a pre-stack shot gather using the approximated TTI coefficients and a computer system to determine a source side wavefield propagation value and a receiver side wavefield propagation value in a frequency-space domain;
converting the source side wavefield propagation value and the receiver side wavefield propagation value from the frequency-space domain to a time-space domain; and
applying a zero-lag cross-correlation image condition equation to form a partial output image using the converted source side wavefield propagation value and the converted reservoir side wavefield propagation value.

### Claim 12 (depends on 11)

The program carrier device of claim 11, further comprising:
applying hybrid TTI-RTM to the velocity model and the anisotropic parameters for the pre-stack shot gather using the converted source side wavefield propagation value and the converted receiver side wavefield propagation value to determine another source side wavefield propagation value and another receiver side wavefield propagation value in the time-space domain; and
applying the zero-lag cross-correlation image condition equation to form another partial output image using the another source side wavefield propagation value and the another receiver side wavefield propagation value.

### Claim 13 (depends on 12)

The program carrier device of claim 12, further comprising:
stacking each partial output image; and
displaying the stacked partial output images.

### Claim 14 (depends on 11)

The program carrier device of claim 11, wherein the dispersion relation equation is created from a phase velocity function and a rotation matrix.

### Claim 15 (depends on 12)

The program carrier device of claim 12, further comprising applying a phase shift algorithm to the velocity model and the anisotropic parameters for the pre-stack shot gather before applying the hybrid TTI-WEM to determine the source side wavefield propagation value and the receiver side wavefield propagation value.

### Claim 16 (depends on 15)

The program carrier device of claim 15, further comprising setting a migration depth between the hybrid TTI-WEM and the hybrid TTI-RTM.

### Claim 17 (depends on 16)

The program carrier device of claim 16, wherein the phase shift algorithm is applied to the velocity model and the anisotropic parameters from a water surface to a subsurface where the water meets earth.

### Claim 18 (depends on 16)

The program carrier device of claim 16, wherein the hybrid TTI-WEM is applied to the velocity model and the anisotropic parameters, from an earth surface or a subsurface where water meets the earth to the migration depth.

### Claim 19 (depends on 16)

The program carrier device of claim 16, wherein the hybrid TTI-RTM is applied to the velocity model and the anisotropic parameters from the migration depth to an extent of the velocity model.

### Claim 20 (depends on 12)

The program carrier device of claim 12, further comprising:
filtering and smoothing each partial output image to generate a respective amplitude-consistent partial output image;
stacking each amplitude-consistent partial output image; and
displaying the stacked amplitude-consistent partial output images.