# 2-D multiparameter viscoelastic shallow-seismic full-waveform inversion: reconstruction tests and first field-data application

## Summary (2 min read)

### 1 INTRODUCTION

- The reconstruction of near-surface models by using shallow-seismic wavefields plays an important role in geophysical and geotechnical site investigation.
- With the rapid development of computational power, it has become increasingly popular to use 2D FWI of surface wave to reconstruct near-surface models.
- Besides the velocity model, seismic attenuation also plays a crucial role in subsurface characterization.
- Brossier (2011) showed the potential of multi-parameter viscoelastic FWI by using frequency-domain synthetic examples.

### 2.1 Forward modelling

- In order to consider the attenuation into time-domain modelling, the generalized standard linear solid (Liu et al. 1976) is widely applied.
- The parameter α is used to ensure that the waves travel with the model phase velocity at the reference frequency ω0 (Bohlen 2002).
- (6) Fig. 1 shows the shape of a desired and the simulated Q values by using only one Maxwell body and the corresponding velocities dispersion for both P and S waves.
- Therefore, the authors only use a single relaxation mechanism in this paper.

### 2.2 Full waveform inversion

- The authors use the least-squares l2-error between the true-amplitude (non-normalized) synthetic and observed particle-velocity waveforms as the objective function: Ψ(m) = 1 2 ||dsyn(m)− dobs||2, (7) where dsyn(m) and dobs are the synthetic and observed particle-velocity seismograms, respectively.
- Adjoint state method provides an efficient way to calculate the gradient of misfit function by cross-correlating the forward (state variables) and backward (adjoint state variables) wavefields.

### 3 SYNTHETIC EXAMPLES

- The authors firstly perform two multi-parameter (five-parameters) examples by using a spatially uncorrelated and a spatially correlated model, respectively.
- Results of viscoelastic and elastic FWIs are also compared.
- Then the authors further investigate the crosstalk between coupled parameters VS and τS by comparing multi-parameter (two-parameters) viscoelastic and mono-parameter elastic FWI results.

### 3.1 Multi-parameter examples

- A triangular lowvalue anomaly is superimposed on each parameter model at different positions (Fig. 2).
- The 1-D background models are used as the initial models, and the true source wavelet is used during the inversion.

### 3.2 Crosstalk between coupled velocity and quality factor

- The authors perform another two synthetic tests to investigate the crosstalk between coupled parameters: VS and τS .
- The authors use the same 1D background models for velocities and quality factors, but only superimpose a low-VS anomaly and a low-QS (high-τS) anomaly at different positions (first column, Fig. 6).
- The sources are generated with a delayed Ricker wavelet of 30 Hz.
- Nevertheless, the reconstructed VS model suffers stronger crosstalk from the τS anomaly compared to the results of viscoelastic FWI.
- These artefacts behave as vertical-stripped anomalies, which are parallel to the wavefront of Rayleigh-wave.

### 4 APPLICATION TO FIELD DATA

- The authors apply the multi-parameter viscoelastic FWI strategy to a shallow seismic field dataset.
- The authors only use vertical-component data in their example because the horizontal-component data has a relatively low signal-to-noise ratio.
- The first source position is located between the first and second geophones.
- It consists of two layers with sharp velocity 2D viscoelastic shallow-seismic FWI 15 contrast at a depth around 6 m which corresponds to the groundwater table (Pasquet et al. 2015; Wittkamp et al. 2019).
- The multi-parameter inversion results are shown in the 2nd column in Fig.

### 5 DISCUSSION

- In the field-data application, the elastic FWIs also nicely reconstruct the S-wave velocity models because the authors adopt good passive Q models in the elastic FWI.
- Nevertheless, the numerical tests show that, when encountering heterogeneous Q model, multi-parameter viscoelastic FWI can further improve the accuracy of estimated velocity model and is superior to elastic FWI in which attenuation is considered as a passive modelling parameter only.
- Therefore, it is meaningful to incorporate attenuation into the inversion for reconstructing accurate multi-parameter results to better delineate the subsurface structures and properties, especially when the Q model is highly heterogeneous.
- Since the authors only use single relaxation mechanism, the estimated Q values might be lower than their true values (Fig. 1).
- The authors use a preconditioned conjugate gradient algorithm to invert the data, which cannot reduce the parameter trade-off between coupled parameters appropriately.

### 6 CONCLUSIONS

- The authors applied 2D multi-parameter viscoelastic full-waveform inversion (FWI) to shallow-seismic surface waves.
- The authors tested the capability of this method to reconstruct reliable parameters on synthetic datasets with spatially correlated and uncorrelated models.
- The synthetic results of spatially uncorrelated models showed that shallow-seismic data has the highest sensitivity with respect to VS , then 2D viscoelastic shallow-seismic FWI 19 VP , and relatively low sensitivity to density, QS and QP .
- The authors compared their viscoelastic FWI result to the results estimated by elastic FWI in which Q models were included but not updated during the inversion.
- They were contaminated by vertical-striped artefacts, which was mainly caused by the neglecting of heterogeneity in theQmodels.

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...Many studies are focused on the viscoacoustic FWI, in which P-wave velocity (VP ) and quality factor (Q) can be inverted recursively or simultaneously (Kamei & Pratt 2013; Malinowski et al. 2011; Virieux & Operto 2009)....

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...Since the viscoelastic wave equation is not self-adjoint, it is difficult to calculate the gradient by using the adjoint state method with the same numerical solver (Plessix, 2006)....

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##### Frequently Asked Questions (2)

###### Q2. What are the future works in "2d multi-parameter viscoelastic shallow- seismic full waveform inversion: reconstruction tests and first field-data application" ?

Mitigation of crosstalk between coupled parameters needs to be studied in the future.