In this study, a new method of permanent displacement estimation and simplification of seismic ground motion is developed. In the method, the displacement is extracted from the acceleration record or the velocity record using wavelets. The basic wavelet used in this study is expressed as a product of the Gaussian function and the complex exponential function. To extract the characteristic element of original wave including the pulse-like ground motion causing the permanent displacement, a wavelet set defined as the linear combination of basic wavelets is used. Each wavelet in the linear combination reflects a permanent or transient displacement component.
 Acceleration records by servo accelerometers usually have baseline fluctuation. Caused by this feature, the displacement by integration of the acceleration usually diverse like a quadratic function. Although the effect of the baseline change of the acceleration can be removed by fitting the velocity as a multilinear function in many cases, the displacement becomes unrealistic if the baseline change is small.
 Applying the method to the ground motion records at KiK-net Mashiki and K-NET Ozu during the 2016 Kumamoto Earthquake, the validity of the method is demonstrated. The former record includes relatively large baseline change of the acceleration. As a result, the displacement is extracted adequately using low order wavelet sets with the high-cut filter or high order wavelet sets without the filter if the baseline change of the acceleration is not corrected. If the baseline change of the acceleration is corrected, the displacement is extracted adequately using any wavelet set with the high-cut filter. On the other hand, the latter record includes small baseline change of the acceleration. As a result, the displacement is extracted adequately using low order wavelet sets and high-cut filter without the baseline change correction. Therefore, the method is particularly useful in the case of the ground motion record which has slight change of the acceleration baseline.
 In addition, it is shown that the method is available to simplification of the seismic ground motion by applying to the strong motion record at Takatori station during the 1995 Southern Hyogo Prefecture Earthquake. The acceleration record is rapidly decomposed to element waves by the method compared to the result using Ricker wavelet. Furthermore, the velocity response and the pseudo-velocity response spectrum are well simulated by the extracted wavelet sets. The efficiency of decomposition increases with the order of the wavelet set. Especially, a complicated wave element can be extracted by the method. This is caused by the feature that the wavelet set used in this study seems to be a Fourier series in the limited time interval. Using the wavelet sets proposed in this study, the length of the extracted element wave can be determined by the order of the wavelet set. The higher the order of the wavelet set is, the longer the extracted element wave becomes, vice versa.