Seismic imaging apparatus and method for performing iterative application of direct waveform inversion

1. A seismic imaging apparatus to perform iterative application of direct waveform inversion to image a subsurface structure of an area to be measured, the seismic imaging apparatus comprising:

a waveform inverter implemented by a signal processor and configured to

update a reference velocity model while changing a frequency band in a set order, by using parameter perturbation that is obtained from a virtual scattering source and an updated reference wavefield, wherein the reference velocity model updated in a previous frequency band is set as the reference velocity model of a next frequency band, which is then updated, and

set again the reference velocity model, updated in a last frequency band, as the reference velocity model of a first frequency band so as to set a velocity model, updated in the set order in a previous frequency band, as the reference velocity model of a next frequency band, which is then updated; and

a subsurface structure imager implemented by the signal processor and configured to image a subsurface structure by using the updated reference velocity model.

2. The seismic imaging apparatus of claim 1 , wherein the waveform inverter is further configured to:

in response to a frequency being a complex number, change the frequency band while changing, in the set order, each one of a damping coefficient which adjusts an imaginary part, and a size of a real part.

3. The seismic imaging apparatus of claim 1 , wherein the waveform inverter comprises:

a reference wavefield calculator implemented by the signal processor and configured to calculate a reference wavefield that is a solution of a wavefield equation by using data collected from at least one of a source and receivers;

a virtual scattering source obtainer implemented by the signal processor and configured to obtain the virtual scattering source from a data residual, which is the difference between actual and reference wavefields;

a scattered wavefield calculator implemented by the signal processor and configured to calculate a scattered wavefield from the virtual scattering source;

a reference wavefield reconstructor implemented by the signal processor and configured to reconstruct the reference wavefield by summing the reference wavefield and the scattered wavefield;

a parameter perturbation obtainer implemented by the signal processor and configured to obtain the parameter perturbation from the virtual scattering source and the reconstructed reference wavefield; and

a reference velocity model updator implemented by the signal processor and configured to update the reference velocity model by using data collected from at least one of the source and receivers, and through the obtained parameter perturbation.

4. The seismic imaging apparatus of claim 3 , wherein the reference wavefield calculator is further configured to calculate the reference wavefield from a wave equation of a frequency domain, which is transformed from the wave equation of a time domain through Fourier transform, by using a finite element method or a finite difference method.

5. The seismic imaging apparatus of claim 3 , wherein the virtual scattering source obtainer is further configured to obtain the virtual scattering source from an equation that is yielded from a Lippmann-Schwinger equation by using the data residual and Green's function.

6. The seismic imaging apparatus of claim 3 , wherein the parameter perturbation obtainer is further configured to obtain the parameter perturbation by applying a Newton's method or a least-squares method to an objective function.

7. A seismic imaging method of performing iterative application of direct waveform inversion to image a subsurface structure of an area to be measured, the seismic imaging method comprising:

performing waveform inversion, comprising

updating a reference velocity model while changing a frequency band in a set order, by using parameter perturbation that is obtained from a virtual scattering source and an updated reference wavefield, wherein the reference velocity model updated in a previous frequency band is set as the reference velocity model of a next frequency band, which is then updated, and

setting again the reference velocity model, updated in a last frequency band, as the reference velocity model of a first frequency band so as to set a velocity model, updated in the set order in a previous frequency band, as the reference velocity model of a next frequency band, which is then updated; and

imaging a subsurface structure by using the updated reference velocity model.

8. The seismic imaging method of claim 7 , wherein the performing of the waveform inversion further comprises:

in response to a frequency being a complex number, changing the frequency band while changing, in the set order, each of a damping coefficient which adjusts an imaginary part, and a size of a real part.

9. The seismic imaging method of claim 7 , wherein the performing of the waveform inversion further comprises:

calculating a reference wavefield that is a solution of a wavefield equation by using data collected from at least one of a source and receivers;

obtaining a virtual scattering source from a data residual, which is the difference between actual and reference wavefields;

calculating a scattered wavefield from the virtual scattering source;

reconstructing the reference wavefield by summing the reference wavefield and the scattered wavefield;

obtaining the parameter perturbation from the virtual scattering source and the reconstructed reference wavefield; and

updating the reference velocity model by using data collected from at least one of the source and receivers, and through the obtained parameter perturbation.

10. The seismic imaging method of claim 9 , wherein the calculating of the reference wavefield further comprises calculating the reference wavefield from a wave equation of a frequency domain, which is transformed from the wave equation of a time domain through Fourier transform, by using a finite element method or a finite difference method.

11. The seismic imaging method of claim 9 , wherein the obtaining of the virtual scattering source comprises obtaining the virtual scattering source from an equation that is yielded from a Lippmann-Schwinger equation by using the data residual and Green's function.

12. The seismic imaging method of claim 9 , wherein the parameter perturbation is obtained by applying a Newton's method or a least-squares method to an objective function.